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MATHEMATICAL MODELLING THROUGH TOP-LEVEL
STRUCTURE
Katherine Mary Doyle Dip Teach (Primary)
Grad Dip.Reading
Thesis submitted in fulfilment of the requirements for the degree
Masters of Education, undertaken in the Centre for Learning Innovation,
Faculty of Education,
Queensland University of Technology,
2006
ii
Paragraph of Keywords
Mathematical modelling, problem solving, mathematising, mathematical knowledge,
literacy, top-level structure, comprehension, discourse, oral communication, written
communication, science, design research, metacognition, meta-language.
Abstract
Mathematical modelling problems are embedded in written, representational, and graphic
text. For students to actively engage in the mathematical-modelling process, they require
literacy. Of critical importance is the comprehension of the problems’ text information,
data, and goals. This design-research study investigated the application of top-level
structuring; a literary, organisational, structuring strategy, to mathematical-modelling
problems. The research documents how students’ mathematical modelling was changed
when two classes of Year 4 students were shown, through a series of lessons, how to
apply top-level structure to two scientifically-based, mathematical-modelling problems.
The methodology used a design-based research approach, which included five phases.
During Phase One, consultations took place with the principal and participant teachers.
As well, information on student numeracy and literacy skills was gathered from the
Queensland Year 3 ‘Aspects of Numeracy’ and ‘Aspects of Literacy’ tests. Phase Two
was the initial implementation of top-level structure with one class of students. In Phase
Three, the first mathematical-modelling problem was implemented with the two Year 4
classes. Data was collected through video and audio taping, student work samples,
teacher and researcher observations, and student presentations. During Phase Four, the
top-level structure strategy was implemented with the second Year 4 class. In Phase
Five, the second mathematical-modelling problem was investigated by both classes, and
data was again collected through video and audio taping, student work samples, teacher
and researcher observations, and student presentations.
The key finding was that top-level structure had a positive impact on students’
iii
mathematical modelling. Students were more focussed on mathematising, acquired key
mathematical knowledge, and used high-level, mathematically-based peer questioning
and responses after top-level structure instruction.
This research is timely and pertinent to the needs of mathematics education today
because of its recognition of the need for mathematical literacy. It reflects international
concerns on the need for more research in problem solving. It is applicable to real-world
problem solving because mathematical-modelling problems are focussed in real-world
situations. Finally, it investigates the role literacy plays in the problem-solving process.
iv
Table of Contents
Paragraph of Keywords……………………………………………………………..ii
Abstract………………………………………………………………………………ii
Table of Contents……………………………………………………………………iv
List of Tables………………………………………………………………………...vi
List of Figures……………………………………………………………………….vi
List of Abbreviations………………………………………………………………..vi
Statement of Authorship……………………………………………………………vii
Acknowledgements………………………………………………………………….viii
Chapter 1. INTRODUCTION TO THE STUDY
Preamble ……………………………………………………………………………..1
1.1 Introduction ……………………………………………….............................2
1.2 Background to Study …………………………………..……………………7
1.3 The Research Problem and the Aims of the Study………………………...7
1.4 Overview of the Study Design……………………………....…………….....8
1.5 Significance, Justification and Outcomes of Study…………………….......9
1.5.1 International foci……………………………………………………...10
1.5.2…Connections to real world problems………………………………..12
1.5.3…Literacy underpinnings……………………………………………...12
1.6 General Overview of This Thesis………………………………………...…14
Chapter 2. LITERATURE REVIEW
2.1 Chapter Overview ……………………………………………………..........16
2.2 Problem Solving …………………………………………………………….17
2.2.1…Mathematical modelling…………………………………………….22
Processes of mathematical modelling………………………………23
The structure of mathematical modelling……………………….…26
2.3 Literacy……………………………………………………………………….29
2.3.1 Comprehension ………………………………………………...…….30
2.3.2 Top-level structure …………………………………………………..33
2.4 Mathematics and Literacy………………….…………………………….…38
2.5 Mathematic Modelling and Top-level structure ……………………….….41
2.6 Conclusion ………………………..………………………………………….44
Chapter 3. RESEARCH DESIGN AND METHOD
3.1 Introduction …………………………………………………………………48
3.2 Research Design ……………………………………………………………..48
v
3.3 Methods ………………………………………………………………………51
3.3.1 Participants ……………………………………...................................51
3.3.2 Data collection………………………………………………………...53
3.3.2.1 Phase 1…………………………………………………………………54
3.3.2.2 Phase 2…………………………………………………………………55
3.3.2.3 Phase 3…………………………………………………………………55
3.3.2.4 Phase 4…………………………………………………………………56
3.3.2.5 Phase 5…………………………………………………………………57
3.3.3 Data Analysis …………………………………………………………..58
3.4 Research Issues and Limitations……………………………………………...60
3.4.1 Ethical issues……………………………………………………………60
3.4.2 Research limitations……………………………………………………62
3.4.3 Research issues………………………………………………………....63
3.5 Conclusion……………………………………………………………………...65
Chapter 4. RESULTS
Preamble………………………………………………………………………………67
4.1 The Historical Setting………………………………………………………...67
4.2 TLS and Mathematical Modelling…………………………………………...69
4.2.1 Student use of TLS key words during discussion……………………71
4.2.2 TLS and written and oral communication of mathematical ideas….78
4.2.3 TLS, mathematising, and constructing mathematical
knowledge………….………………………………………………..….81
4.2.4 TLS, peer questioning and responses………………………..………..90
Chapter 5. DISCUSSION, IMPLICATIONS AND CONCLUSION
5.1 Discussion………………………………………………………………………94
5.1.1 The effects of key word usage during mathematical modelling……..97
5.1.2 The effects of TLS on mathematising and constructing
mathematical knowledge……………………………………..............100
5.1.3 TLS and questioning……………………………...…………………...103
5.2 Implications for further research……………………………………………105
5.2.1 Implications for mathematical modelling……………………………105
5.2.2 Implications for mathematics…....………………………………...….106
5.3 Conclusion …………………………………………………………………….107
REFERENCES:…………………………………………….........................................111
vi
APPENDICES
Appendix 1 – Lesson Plans Term 3...………………………………………………..120
Appendix 2 – Beans, Beans Glorious Beans Problem………………………………132
Appendix 3 – Beans Problem with TLS notetaking guidelines…………………….138
Appendix 4 – TLS Practice Book…………………………………………………….148
Appendix 5 -- TLS Lesson Outlines Term 4…………………………………………171
Appendix 6 – Paper Planes Contest Problem…………………………..……............177
Appendix 7 – Information for parents……………………………………………….182
Appendix 8 – Parental and student consent forms……………………..…………...185
Appendix 9 – Ethical clearance………………………………….…………………...189
LIST OF TABLES
Table 1 Organisational structures in text ………………………………..…………35
Table 2 Data collection and data analysis strategies …………………..………….47
Table 3 An overview of the data collection period of the research ……………….54
LIST OF FIGURES
Figure 1 Top-level structure and comprehension……………………………………5
Figure 2 What does ‘top-level’ mean?..........................................................................6
Figure 3 Top-level structure and mathematical modelling…………………………45
Figure 4 Summary of results………………………………………………………….70
Figure 5 Student Chart………………………………………………………………..80
Figure 6 Student Chart………………………………………………………………..81
LIST OF ABBREVIATIONS
NCTM National Council of Teachers of Mathematics
TLS Top-Level Structure
UK United Kingdom
vii
Statement of Authorship
The work of this thesis is original and has not been previously submitted for a degree or
diploma at any other higher education institution. To the best of my knowledge and
belief, the thesis contains no material previously published or written by another person
except where due reference is made.
Signed:
Katherine Doyle
Date: 08 September 2006
viii
Acknowledgements
I sincerely thank my principal supervisor, Professor Lyn English and associate
supervisor, Associate Professor Jim Watters for their assistance and support throughout
the process leading to the completion of this thesis. I am most appreciative of their time,
their guidance and the wisdom they shared with me. They have considerably contributed
to ensuring this learning experience was a most beneficial and enjoyable one for me.
My sincere thanks go also to the principal, teachers and students with whom I worked
throughout the data collection period. Their contributions through sharing of knowledge,
programming, and time were much appreciated. Thank you also to the whole staff and
community of the particular school for their friendly welcome to me. Without the
support of all these people, this thesis would not have been possible.
Thank you to my family and friends for all their love, encouragement, interest and
prayers throughout the process. Especially, thank you to my mother, who forever has
supported, listened, discussed, and tirelessly continued being a ‘Mum’ through all ‘ups
and downs’. It is impossible to put into words all she has done for me.
My gratitude goes also to my friends and colleagues in the Centre for Learning
Innovation and School of Mathematics, Science and Technology at the Queensland
University of Technology. So often, they offered ‘pearls of wisdom’, encouragement, a
‘listening’ ear or a laugh when it was most needed. Thank you also to Associate
Professor Brendan Bartlett who imparted to me the initial knowledge that led to the
formation of the thesis, and who continued to offer support as I undertook this project.
1
CHAPTER 1
MATHEMATICAL MODELLING THROUGH TOP-LEVEL STRUCTURE
PREAMBLE
We live in a technologically advancing society. Students need to be prepared
thoroughly through the provision of learning opportunities that equip them with the
necessary skills to operate effectively in this world. Mathematics and complex
mathematical reasoning are essential components of these learning opportunities. The
view taken here is that mathematical modelling is one way to provide students with
such opportunities (English & Watters, 2005). Through mathematical modelling
processes, students are able to understand complex situations or phenomena in a
quantitative and conceptual way. As mathematical information is often embedded in
complex textual material, high levels of literacy are critical to enable people to access
numerical information and mathematical understandings. Top-level structuring (TLS)
has proven to provide an opportunity to increase literacy levels in various genre areas
(Meyer, 2003; Bartlett, 2003). Therefore, the purpose of this research is to gauge the
extent to which TLS may change students’ mathematical modelling outcomes. Skills
promoted through mathematical modelling, such as constructing, describing,
explaining, manipulating and predicting complex situations for example, budgeting
plans or business plans are foundational to future-oriented curricular (Lesh & Doerr,
2003b; English, in press). To gain such skills through mathematical modelling
investigations requires literacy, that is, students must be able to interpret information
contained in the problems’ texts and use that information to communicate by oral and
written means. Meaning must be gained and meaning must be given.
2
The purpose of this chapter is to introduce the concepts of mathematical modelling and
of top-level structure. The chapter provides the background, reasons, significance and
aims of the study. It also provides an overview of the research design and finally
outlines the contents of the thesis chapters.
1.1 INTRODUCTION
In light of the aims of current curriculum documents in Australia and the United States,
(National Council of Teachers of Mathematics, 2000; Queensland Studies Authority,
2004), educators are seeking to empower students with skills that equip them to
function effectively in a technological world. The Queensland Mathematics Syllabus
(2004) and the NCTM (2000) concur that problem solving should be contextually
varied and occur throughout the content areas while the U.K. National Curriculum
(2000) seeks to develop in students flexible approaches to problem solving and ways to
explain their methods and reasoning in structured and organised ways. Therefore,
most current curriculum documents assume that participation in a variety of problem-
solving experiences should prepare students for life outside the classroom. Due to the
life events encountered in today’s world, students require the ability to describe,
analyse and predict the behaviour of mathematical domains practically, such as
numerical data, measurement, probability, geometry and algebraic issues in the real
world in order to make informed decisions. Mathematics can provide students with
practical skills to solve real-world problems. Recent research (English, 2003; English
& Doerr, 2004; English & Watters, 2005) indicates that participating actively in
mathematical problem-solving activities, which involve cooperative planning,
3
investigating and decision making, is central to the development of crucial life skills.
Mathematical modelling provides such a tool. Mathematical modelling requires
students to produce products/models that Lesh and Doerr (2003a) describe as going
beyond short answers to narrowly specified questions- which involve
sharable, manipulatable, modifiable, and reusable conceptual tools (e.g.
models) for construction, describing, explaining, manipulating,
predicting, or controlling mathematically significant systems. Thus,
these descriptions, explanations, and constructions are not simply
processes that students use on the way to producing “the answer”, and,
they are not simply postscripts that students give after “the answer” has
been produced. They are the most important components of the
responses that are needed. So, the process is the product (p. 3).
The term ‘model’ has various connotations. In this thesis, it refers to the conceptual
systems that problem solvers develop “to construct, describe or explain mathematically
significant systems they encounter” (Lesh & Doerr, 2003a, p. 9).
It is argued here that mathematical modelling is very much a language-based process.
Literacy and language are central to our being. Freebody and Luke (1990) argued that
literacy basically encompasses four roles: code-breaking (how do I crack this?), text-
participant (what does this mean?), text-user (what do I do with this here and now?),
and text-analyst (what does this do to me?). Every section of our lives has its own
language, its own literacy. Bartlett, Liyange, Jones, Penridge and McKay (2001)
discussed ‘science education through literacy and language’ and in this project, I am
investigating mathematics education through literacy and language. Mathematics is
not an entity divorced from literacy and language, but in fact is consumed by its own
literacy and language. It is through this literacy and language that mathematical
thinking occurs. Bartlett et al (2001, p. 6) stated that “teaching students how to be
4
smart in their thinking about science needs a set of thinking outcomes comprehensive
enough to enhance both mastery of essential content and exploration of what such
mastery means.” It is the same for mathematics. Students need to learn how to be
smart in their thinking, how to master the essential content of a task, and how to
explore that mastery.
Top-level structuring of text can provide students with a tool to structure textual
information, that is, to organise information as they participate in a literacy process. In
particular, TLS complements the text-participant, text-user, and text-analyst roles of
the process proposed by Freebody and Luke (1990). Therefore, top-level structuring is
a heuristic tool to guide effective reading for understanding. Figure 1 demonstrates
Meyer and Poon’s (2001) claim that as readers read they build a mind picture of what
they understand as the message of the text. Top-level structure is one strategy which
can facilitate the organisation of that information within the mind of the reader and
allow the reader to select and use the most relevant information.
5
Figure 1. Top-level structure and comprehension.
Top-level structuring (TLS) is described by Bartlett, Liyange, Jones, Penridge, and
McKay (2001) as:
a procedure through which a strategist applies what is known about
the hierarchal organisation of content in order to achieve memory,
comprehension and expression outcomes. This procedure applies
to both encoding and retrieval features of learning. It allows the
strategic reader, listener or reviewer to form an opinion on what a
writer, speaker or performer considers as essential content and if
necessary, then to move on to critical or inferential analysis.
Conversely, it allows a strategist as writer, speaker or performer to
produce coherent text and to signal what he/she wants to be seen as
essential content (P. 67).
Essentially, a reader, listener, or reviewer determines how an author has organised the
text. Basically, having the knowledge that text has a particular structure helps the
reader to seek and apply a structure to the text, then subsequently extract a main idea
(Bartlett, 2003) as portrayed in Figure 2.
TTOOPP--LLEEVVEELL SSTTRRUUCCTTUURREE MMeeyyeerr aanndd PPoooonn,, 22000011..
READING The reader builds a MENTAL REPRESENTATION
of the textual information
TOP-LEVEL STRUCTURE
ONE WAY to build a coherent
mental representation of textual information
Helps readers build an organised bank
of selective information.
Helps readers to select the most
Important information
6
Figure 2. What does ‘top-level’ mean?
Bartlett et al (2001) described the main structures for text as: comparison, cause/effect,
problem/solution and listing/description. Table 1 in Section 2.3.2 lists these structures
and the signalling or ‘key’ words that appear throughout texts and help the reader to
identify the structure of the text. This study adopts Bartlett’s view of TLS and refers to
key words as listed in table 2.1.
.
READ AND CHOOSE
An author’s structure.
The key words help
Organise textual information
Choose the MAIN IDEA
The text is now in manageable parts.
.Use these parts to:
gain information.
take notes.
use the most appropriate information.
The Text
Top Level
WWhhaatt ddooeess ‘‘ttoopp--lleevveell’’ mmeeaann??
7
1.2 BACKGROUND TO STUDY
Recently the study “Mathematical modelling in early education” was undertaken by
English and Watters through an Australian Research Council Discovery Grant (2003-
2005); (English & Watters, 2005). Emerging from this work is the recognition of
students’ need to comprehend the substantial text of modelling problems. The
research, “Mathematical Modeling through Top-Level Structure” was designed to
build upon this work by introducing the notion that literacy is strongly related to the
ability to solve textually-based problems.
To date, comprehension questions to be completed by students have been included in
the modelling problems that English and Watters (2005) have presented to students
(Appendices 2 & 6). These questions have served to aid students’ understanding of the
problem context and background prior to their engagement in the problem itself. This
study seeks to go beyond the comprehension questioning to promote students’
understanding of text through employing strategies that aid textual organisational
structuring for comprehension, recall, and communication.
1.3 THE RESEARCH PROBLEM AND THE AIMS OF THE STUDY
This study addressed the need to help students develop mathematical knowledge
through mathematical modelling problem solving. Mathematical modelling goes
beyond computational mathematics to engage students in eliciting mathematical
concepts or ideas, describing mathematical concepts or ideas, and explaining
mathematical concepts or ideas (Lesh & English, 2005). Mathematical modelling is
8
immersed in textual information. Students’ literacy abilities are paramount for their
learning. As a result the research explored the question: ‘to what extent will students’
mathematical modelling be changed by engaging them in top-level structuring of text?’
Through the design and implementation of innovative learning experiences, this study
aimed to determine how a literacy-based strategy, namely top-level structure, could
change children’s mathematical modeling abilities. Specifically, the study’s goals were
to:
1. Develop TLS skills in two cohorts of year 4 students.
2. Implement two related mathematical-modelling problems with the
Year 4 students.
3. Critically analyse these students’ mathematical modelling
subsequent to TLS instruction.
4. Explain the role of TLS in assisting these students to engage in the
mathematical-modelling process.
5. Determine these students’ use of the language derived from TLS
in their social interactions about the problems and how this
language facilitated the construction, explanation, and
communication of their mathematical knowledge.
1.4 OVERVIEW OF THE STUDY DESIGN
The study took on a multidisciplinary approach as it investigated students’
performances in mathematical modelling tasks by applying the literary strategy TLS to
the tasks. The problems’ textual information was based in scientific settings. The
research was a design experiment (Bannan-Ritland, 2003), as discussed in Section 3.2.
It used a variety of data collection methods (Section 3.3) ranging from historical data
on students’ mathematical and literacy abilities to audio and video taping of the
research process. It took place in two year four classrooms over a period of three
school terms. One of these classes formed the TLS group, which was taught the TLS
9
strategy prior to undertaking any mathematical modelling tasks. The second class
formed the non-TLS group, which was only taught the TLS strategy subsequent to
completing the first mathematical-modelling task and before participating in the
second modelling task. There were five phases of this research process:
• Prior to the actual research process, the historical information
on the students’ literacy and numeracy abilities was examined.
• TLS was taught to the TLS group
• After the initial teaching of top-level structure to the TLS
group, the first mathematical modelling problem was
implemented with the TLS and non- TLS groups.
• Prior to the implementation of a second mathematical-
modelling problem, the non-TLS group was taught top-level
structure. The TLS group practised applying TLS through
using the top-level structure booklet (Appendix 4) and in their
class program.
• The second mathematical-modelling problem was
implemented with the TLS and non TLS groups.
This process is discussed in full in Sections 3.3.2.1 to 3.3.2.5. In the final analysis, the
data collected after the implementation of the two problems were compared according
to the attributes and questions set out in Section 3.3.3. Due to time constraints and the
overwhelming amount of data collected, it was decided that two representative groups
per cohort would be analysed in detail for the purpose of this research.
1.5 SIGNIFICANCE, JUSTIFICATION AND OUTCOMES OF THE STUDY
This study is significant for three reasons: (1) its reflection of international concerns,
(2) its applicability to real-world problem solving, and (3) its provision of insights into
the role literacy plays in problem solving.
10
1.5.1 International Foci
Internationally, the pendulum of research has swung between an emphasis on basic
skills and an emphasis on problem solving (Schoenfeld, 1992). Lesh and Zawojewski
(in press) have reported on the apparent turn of the tide with the pendulum seemingly
swinging back to problem solving, which will help to meet the need for more current
research on problem solving. However, Lesh and Zawojewski discuss further that the
amount of research on problem solving seems to be declining particularly in recent
years. The general term ‘problem solving’ as used in this thesis encompasses all
aspects of mathematical problem solving and working mathematically, including the
way problems were traditionally conceived (where students were given information
and taught a direct method of solving the problem to attain the correct answer), and
problem solving through mathematical modelling. Therefore, this general term
‘problem solving’ when used in this thesis differs from the specific terminology of
mathematical modelling problem solving, which refers to mathematical modelling as
described by Lesh and Doerr (2003a) in Section 1.1.
In Australasia, however, Anderson and White (2004, p. 127) reported that mathematics
research had been focusing strongly on problem solving that is, “the process of
students exploring non-routine questions, using a range of strategies to solve
unfamiliar tasks, as well as developing the processes of analysing, reasoning,
generalising and abstracting.” They reviewed research that focused on improving
students’ problem-solving abilities through technology and visualisation strategies,
problem-solving assessment, and the relationship between cognitive processes and
11
problem solving. They also looked at teachers’ beliefs and practices with problem
solving as well as teaching approaches to problem solving.
Graham Jones (2004) has given some attention to the impact of Australian research in
language and mathematics throughout the 1980’s and 1990’s. He noted that while in
the 1980’s research in language and problem solving focussed on comprehension,
during the 1990’s it moved to psycholinguistics which included semantic and syntactic
structures in problem solving and writing. He claimed that Australasian research in
mathematics generally has made a significant impact on the global stage and that future
research in mathematics will adopt multifaceted and integrated approaches. A
literature search on mathematics, problem solving, and research in Australia for the
years 2003 to 2006 revealed that recent Australian research has focussed on topics
ranging from teacher belief systems on problem solving, to students’ attitudes and
performance, to implementing problem solving in classrooms, to the problem-solving
process to mathematical modelling as described in this thesis. Only two of the thirty
studies and papers reviewed were language based, both focussing on communication
during problem solving. One was early childhood centred and examined teaching and
learning practices through teacher/child discourse during problem solving (Wood &
Frid, 2005). Muir and Beswick (2004) reported on strategies used by year 6 students in
solving six non-routine problems, and the effectiveness of their written and verbal
communication in illustrating their thinking during the problem-solving process.
12
1.5.2 Connections to real world problems
The current Queensland Mathematics Syllabus (Queensland Studies Authority, 2004)
identifies particular experiences in mathematics which are integral in preparing
students to solve problems and work mathematically in real life situations.
Significantly, many of these types of experiences are presented through mathematical
modelling and to a great extent through TLS, including: planning, investigating,
conjecturing, justifying, thinking critically, generalising, communicating, reflecting on
mathematical understandings and procedures, as well as selecting and using relevant
mathematical knowledge, procedures, strategies and technologies to analyse and
interpret information. Mathematical knowledge encompasses “knowing about
mathematics, knowing how to do mathematics, and knowing when and where to use
mathematics” (Queensland Studies Authority, 2004, p. 2). Learning relevant
mathematical skills is best achieved when they are learnt through a supportive, social
context. This enables meaningful learning through which students can show different
representations of their own mathematical thinking and “are encouraged to investigate,
evaluate and reflect on their personal ways of thinking, reasoning and working
mathematically” (Qld Studies Authority, 2004, p. 9).
1.5.3 Literacy underpinnings
Mathematical modelling can provide such a learning environment because of its social
and supportive disposition and through the types of problem-solving investigations it
employs. Specific learning experiences required to develop mathematical knowledge
for the twenty-first century include those that elicit interpretations of such situations or
13
systems as designing a sports program or creating water management programs. These
are the types of experiences/systems investigated through mathematical modelling.
They also require meaningful communication of understandings of mathematical
knowledge required to negotiate such situations. To interpret and communicate
requires literacy and to learn mathematics through engaging in mathematics,
mathematical literacy is essential. The Queensland Mathematics Syllabus (Qld.
Studies Authority, 2004, p. 5) outlines the fact that students must engage as
code breakers, text participants, text users and text analysts when they:
• read, view, analyse and interpret the mathematics represented by text, pictures,
symbols, tables, graphs, and technological displays,
• comprehend and analyse conversations and media presentation that
convey different mathematical points of view,.
• organise information, ideas and arguments, using a variety of media.
• communicate in various ways --- for example, orally, visually, electronically,
symbolically and graphically.
• compose and respond to questions and problems that challenge their own and
others’ mathematical thinking and reasoning
The present study addresses these issues and is thus significant in its potential input to
this area of problem solving through the incorporation of the literacy-based, text-
structuring strategy, top-level structure, with mathematical modelling. This research is
both timely and pertinent to the needs of mathematics education today because of its
recognition of the need for mathematical literacy. More specifically, we stand on the
edge of a world where there is an explosion in knowledge growth, an increase in mass
media and a rapid increase in the use of complex systems such as budgeting, leasing
plans, finance plans, finance portfolios and so on. Problem solving is the foundation of
the ability to control these situations, therefore the associated skills needed to manage
the problem solving must be cultivated.
14
Summary
To advance our ways of dealing with the problems of today’s world, new research and
new approaches to problem solving are warranted (Lesh & Zawojewski, in press). This
research introduced a new aspect to problem solving, specifically to mathematical
modelling, as it investigated how organising problem-solving information through TLS
might aid the mathematical-modelling, problem-solving process. This approach is
potentially advantageous to the mathematical modelling process because it could
benefit the quality of active participation and outcomes of the whole process.
The study drew on research that has shown TLS to be effective in the areas of literacy,
science, mathematics and studies of society and environment both in classrooms and
beyond school experience (Bartlett, 1979; Lorch & Lorch, 1995; Meyer, 2003; Meyer
et al., 2002; Meyer & Poon, 2001). This past research led me to question why it could
not also be effective when employed with mathematical modelling, thus adding a new
dimension to mathematical problem-solving research. A text organisation strategy like
TLS has not previously been applied to mathematical modelling.
1.6 GENERAL OVERVIEW OF THIS THESIS
Chapter One has established the need to investigate how the application of TLS will
change mathematical-modelling, problem-solving abilities in young children.
Chapter Two reviews literature pertinent to problem solving, mathematical modelling,
mathematical literacy, general literacy, comprehension, and top-level structure.
15
Firstly, mathematical problem solving is discussed and then specifically mathematical
modelling as real-world problem solving is investigated. Following this, literacy,
comprehension strategies, and top-level structure are presented. An examination of
top-level structure from the perspectives of comprehension of the main idea, oral and
written text organization, and text recall (Meyer, 2003) is given. Mathematics and
literacy, including how comprehension impacts upon problem-solving abilities, is
investigated leading to the potential impact of the incorporation of TLS into
mathematical modelling. Finally, the literature is merged to form a genre that
constitutes the foundation of this study.
Chapter Three outlines the research design, research method, data collection and
analysis processes. Ethical issues and the limitations of the study are then discussed.
Chapter Four presents and discusses background information on students’
mathematical abilities before reporting on the results and main findings of the research.
Data have been analysed in relation to each of the major aims of the study.
Chapter Five concludes the thesis with a discussion of the results and the findings of
this research and the implications of these for mathematical modelling. Finally
insights are given on the overall implications of this research for mathematics and also
other areas such as science, the possibilities for further research of top-level structure
with the various textual components of mathematics science and so on, and the
.importance of the multi-literacy focus for a modern, dynamic, apt curriculum.
16
CHAPTER 2
LITERATURE REVIEW
TOP-LEVEL STRUCTURE AND MATHEMATICAL MODELLING
2.1 CHAPTER OVERVIEW
This literature review explores the relationship between top-level structure (TLS) and
mathematical modelling. It develops the argument that due to the literary nature of
modelling tasks, top-level structuring of text may serve to maximize student abilities to
participate in the modelling process and to present, explain and justify their models to
their audience. This is because TLS provides a means to apply organisational strategies
to the production and presentation of their models.
In addressing the above, the following aspects are explored: (a) traditional problem
solving, that is, where formulae and procedures previously learnt lead to a solution
(Verschaffel, Greer, & De Corte, 2000) versus mathematical modelling where
problems are embedded in complex story lines and there are multiple approaches to
solution, (b) the nature of problems in the context of real-world experience, (c) the
nature of literacy and comprehension, (d) the role of top-level structuring in literacy
and comprehension, and (e) the role of strategic approaches in students’ ability to
actively participate in modelling tasks. Finally, a summary of the review and
concluding points are given to indicate the theoretical framework that has been
developed, and how it informs the research.
17
2.2 PROBLEM SOLVING
A key focus of this study is students’ engagement in complex problem solving. Here,
an argument is built up that solving problems for a contemporary world involves far
more than what has been considered adequate in the past. Traditionally, problem
solving has been regarded as a question-answer type of phenomenon: a puzzle-like
scenario where students are faced with finding one correct answer (Lesh, Lester, &
Hjalmarson, 2003; Verschaffel & DeCorte, 1997). So, problem solving was a closed
process where once the method was determined, one had a good chance of finding the
correct answer.
Descriptions and definitions of problem solving have in the past related to the work of
Polya during the 1940s. Problem solving was once described as "finding the unknown
means to a distinctly conceived end...Problem solving is a process of accepting a
challenge and striving to resolve it" (Polya, 1965, p. 117). Although Polya referred to
the process of problem solving, there nevertheless remains the perspective of the
traditionalists with their reference to a 'distinctly conceived end'. Traditional
definitions alluded to problem solving as being a somewhat 'closed' event, that is, its
process and solution were prescribed and predestined even when problems were
worked in a group situation. In some mathematical literature words like 'attack' and
'struggle' have been used to describe problem solving, (e.g. Reys, Suydam & Lindquist,
1989; Mayer 1998). Such words can give negative connotations of problem solving.
Schoenfeld (1989) suggested that Polya’s view needed enhancing as problem solving is
about: (a) motivation, (b) students not having the instant mathematical means to solve
18
a problem, (c) more specific strategies linking to specific types of problems that need
to be taught and, (d) metacognitive strategies that need to be taught for the more
effective deployment of strategies.
Siemon and Booker (in Booker, Bond, Sparrow & Swan, 2004) define problem solving
“as a process of achieving the solution to a problem and a problem as something you
are to solve, that you believe you have a reasonable chance of solving individually or
as a group and that you have no immediate solution.” The definition presented by the
National Council of Teachers of Mathematics (NCTM, 2000, p. 52) states that
"problem solving means engaging in a task for which the solution method is not known
in advance. In order to find a solution, students must draw on their knowledge, and
through this process, they will often develop new mathematical understandings.
Solving problems is not only a goal of learning mathematics but also a major means of
doing so." Zawojewski and Lesh (2003) discussed the range of definitions that have
surfaced over the years like those mentioned but ultimately agree with the definition
offered by Lester and Kehle (2003):
problem solving is an extremely complex form of human endeavour
that involves much more than the simple recall of facts or the
application of well-learned procedures...the ability to solve
mathematics problems develops slowly over a very long period of
time because success depends on much more than mathematical
content knowledge. Problem-solving performance seems to be a
function of several interdependent categories of factors including:
knowledge acquisition and utilization, control, beliefs, affects, socio
cultural contexts, implicit and explicit patterns of inference making,
and facility with various representational modes (e.g., symbolic,
visual, oral, and kinaesthetic). These categories overlap (e.g., it is
not possible to completely separate affects, beliefs, and socio-cultural
contexts) and they interact in a variety of ways...(p. 509)
19
In the past, problem solving was an isolated part of the mathematics curriculum rather
than an integral part of the whole curriculum as it is recognised today (National
Council of Teachers of Mathematics, 2000; Queensland Studies Authority, 2004). In
more recent years, a cross-curricula view of problem solving has been adopted with a
focus on social influences and problem solving in context (Lester & Kehle, 2003).
However in many ways, the underlying belief of teaching specific skills and then
having students solve a problem, that is, a "given to goals" perspective has remained
the same (Zawojewski & Lesh, 2003, pp. 318, 319). Today, classroom teachers
incorporate a variety of routine problems - those the students have learnt to solve and
non-routine problems -those that are completely new to the students (Mayer, 1998).
In conjunction with these, students are taught to identify the characteristics of various
problems. They are also taught strategies such as making a diagram, looking for
patterns, constructing tables, guessing and checking, working backwards etc. to help
them the solve the problems (Reys et al., 1989).
Problem solving for the twenty-first century envisages students not only learning how
to solve problems, but gaining mathematical knowledge through the process of
problem solving. Lesh, Doerr, Carmona and Hjalmarson (2003) argued that
knowledge is not only constructed, but that there are a number of processes engaged in
the development of knowledge such as, filtering information, organising ideas, or
representing information. Lamon (2003) argued also that constructivism perhaps
requires the connection of complementary perspectives such as, eliciting and directing
students’ thinking and understandings, in order to significantly develop mathematical
20
knowledge. Mathematical modelling aims to provide conditions which facilitate
growth in mathematical knowledge because it focuses students on such characteristics
as interpreting, reasoning, seeking relationships and patterns between elements, and
explaining, justifying and predicting situations (Lesh & Doerr, 2003a).
Recently there has been an emphasis on incorporating 'real-life' problems into
classroom programs but as Verschaffel and DeCorte (1997) discovered, in the past
students have tended to disregard their real-world knowledge and considerations when
solving traditional classroom word problems. In fact, the real-world problems of the
classroom have not required real-world mathematics to solve them (English & Lesh,
2003). So it would appear that good intentions have been somewhat lost in the overall
scheme of real-world classroom problem solving. Incorporating real-life problems,
teaching students problem-solving skills, and presenting students with a wide variety
of problem types are essential to successful problem-solving classroom programs.
There is no attempt in any way to detract from their importance in the present
discussion. But, there is the suggestion that these practices need to be expanded upon,
which is reflected in literature that explores mathematical modelling (Lesh & Doerr,
2003; NCTM, 2000; Verschaffel & De Corte, 1997; Zawojewski & Lesh, 2003).
Conventionally, students have been taught problem-solving strategies like drawing a
picture or acting a problem out, to help lead to a solution for a problem (Zawojewski &
Lesh, 2003). Lesh and Zawojewski (in press) and Mayer (1998) note that a major
difficulty with the teaching of strategies is that students not only have to remember the
21
strategies, but also when to effectively use the strategies. The evidence lies in many
classrooms today where students are presented with a problem and respond "we haven't
done this yet!" or the other favourite "I'm stuck!" (Lesh & Zawojewski, in press;
Zawojewski & Lesh, 2003). Such comments appear to be the result of students not
remembering strategies they have been taught or even if they do remember, they are
not recognising when to apply them. This suggests that metacognitive abilities need to
be enhanced so that they can manage their cognitive abilities (Kehle & Lester, 2003;
Mayer, 1998).
In reviewing substantial literature on metacognition, Lesh and Zawojewski (in press)
have highlighted different views of the role of metacognition by adding some
captivating twists to the argument. They suggest that metacognition needs to be
intergrated with cognition, in other words, teaching metacognition concurrently while
students learn content. Lesh and Zawojewski also ascertained that problem solvers
report that they actually design specific strategies to deal with the problem at hand as
they partake in the problem-solving process rather than relying on previously learned
strategies. Ultimately, the authors concluded that more research is needed on the role
of metacognition in the problem-solving process.
The definition of problem solving by Lester and Kehle (2003) cited above in this
section goes beyond the promotion of problem solving as a procedure that moves from
"givens to goals" to a perspective that views problem solving as a 'multi-way' process
moving back and forth between the givens and the goals that is, "a cyclical process" of
22
interpretation and then selecting and applying procedures (English & Lesh, 2003;
Zawojewski & Lesh, 2003). Zawojewski and Lesh (2003) have compared the
information-processing perspective of problem solving and the modelling perspective
of problem solving. Mathematical modelling expands on the previous dimensions of
problem solving (e.g. Lesh & Doerr, 2003a; Lesh, Lester & Hjalmarson, 2003; Mayer,
1998; Verschaffel & De Corte, 1997; Wood, 2001; Zawojewski & Lesh, 2003).
Contrary to past practices, mathematical-modelling problems are solved over a period
of time and involve a cyclical process where mathematical ideas and knowledge
undergo continuing development. In the light of these arguments, Lesh and
Zawojewski (in press) have developed a new definition of problem solving which calls
for the problem solver to develop "a more productive way of thinking” about a
particular problematic situation. Further investigation comparing mathematical
modelling with traditional problem solving is discussed in Section 2.2.1.
The selection of literature reviewed here has described problem solving evolving from
the traditional notion of “givens-to-goals” to “givens” and “goals” as part of a cross-
curricula, cyclical process (Zawojewski & Lesh, 2003). It is this latter view of
problem solving that is the focus of this study.
2.2.1 MATHEMATICAL MODELING
Mathematical modelling provides a rich basis for empowering students and teachers
with skills to function effectively in today’s world. It features authentic problem
situations in which students can explore and create models as possible solutions while
23
investigating in a social context. The term ‘model’ has been defined in Section 1.1.
The sophistication of the model will depend on the mathematical finesse and expertise
of the modeller/student. In the situation of the proposed research, very rudimentary
models will be explored as students are young and inexperienced. These models form
a basis for conceptualising the nature of modelling.
Model-eliciting problems allow for multi-interpretations and approaches to problem
solving. The multifaceted end-products that are generated are to be shared in a social
context and can be revised accordingly. English (2003) claimed that this process
provides learning opportunities that encourage optimal development of mathematical
skills. Furthermore, English and Lesh (2003) have emphasised that it is not just
reaching the goal that is important, but also the interpretation of the goal, the
information provided and the possible steps to solution. Students must realize that
some models are more appropriate than others and be able to provide the reasons why.
There is constant consultation within the social forum, that is, the group in which the
student is working throughout the process, and throughout the product presentation,
allowing for this product to be further revised and optimised.
Processes of Mathematical Modelling
Mathematical modelling moves beyond traditional views to present situations where
students are given opportunities to acquire skills such as interpreting, thinking,
communicating of ideas, justifying, revising, refining, and extending ideas while
participating in a team of investigators to produce a model (Lesh & Doerr, 2003a;
24
Zawojewski & Lesh, 2003). The contrast is evident as problem-solvers are required
“to process information using procedures associated with a fixed construct that simply
needs to be identified, retrieved and executed correctly” (Lesh & Doerr, 2003a, p. 23).
English (2004, p. 208) argued the fact that although traditional problems hold some
importance within a curriculum, they “do not address adequately the knowledge,
processes and social developments” that are required to operate with our increasingly
sophisticated systems in today’s society.
English (2004), Lesh and Doerr (2003), and Lesh and Yoon (2004) have all maintained
that when students participate in the process of mathematical modelling, they are
participating in a process of interpretation of information from various text sources
such as, narrative texts, graphic texts like tables, diagrams or graphs and expository
texts of facts and explanation. They must extract the main ideas, make assumptions,
decide on their goal, explain their ideas, predict outcomes, and construct their case in
an interactive social context. In doing so, students may employ other mathematical
skills such as, number sense, measuring and comparing amounts. Additionally, they
need to coordinate and organise all information gathered in their group.
Other authors such as English (2003), English and Lesh (2003), Johnson and Lesh
(2003), Lehrer and Schauble (in press), Lesh & Doerr (2003a), and Lesh, Zawojewski,
and Carmona (2003) concurred that these skills are the focus of mathematical
modelling and the attainment of such skills prepares students to operate in our societal
context The skills manifest themselves as tools to be engaged not only in mathematics,
25
but also as multi-disciplinary devices enabling problem solvers to function effectively
within their own domain, that is, the area in which the problem solver is working e.g.
science. Lehrer and Schauble (2003) discussed the connections of mathematics and
science through modelling. This relationship is evident in the recent research of
English and Watters (2005). Lesh and Carmona (2003) viewed mathematical
modelling through the art of quilt-making and Lesh, Zawojewski and Carmona (2003,
p. 211) investigated “the nature of the most important mathematical understanding and
abilities that are likely to be needed beyond school in the twenty-first century” citing
various occupations that use mathematical modelling.
These points have been ratified by the current Queensland mathematics syllabus (2004)
in which it is emphasised that students need to develop and use the type of skills
promoted through mathematical modelling in today’s world. The NCTM (2000) has
also endorsed this perspective by emphasizing that those who become proficient at
understanding and doing mathematics will in fact enhance their opportunities and
future options. Additionally, the NCTM argued that mathematics is not just for the
select few but is for everyone. All children are entitled to learning opportunities and
support in developing mathematical understandings and skills.
It has been argued further that the processes of mathematical modelling have to date
been underutilized in the everyday classroom. Perhaps this is because traditionally it
was seen as easier to teach specific skills by which, once learnt, students could solve
text book and test problems. Lesh and Doerr (2003a) refuted this once accepted logic
26
and argued that understanding is a developing process that occurs through stages.
Essentially, learning occurs in a context of meaning, that is, a context that is personally
relevant, and with which students have had prior experience or want to be involved
with. In other words, meaningful situations enhance understanding of new concepts.
Conceptual understanding is crucial to being mathematically proficient (NCTM, 2000).
Schoenfeld (1992, 1989) and the NCTM (2000) argued: if new knowledge in
mathematics is built upon existing knowledge in meaningful ways, it will make more
sense and be easier to remember and apply.
The notion that learning occurs more readily when it can be related to the known is
significant for mathematical modelling where students are sharing their knowledge and
applying it to new situations. Sharing and discussing understandings of ideas promotes
correct understanding. In this way, opportunities for learning occur as students
interpret and interact in a relevant social setting, where conceptual understandings can
be clarified. Modelling activities are evolving tasks, that is, models can be revised as
students communicate in social contexts and realize better ways of presenting their
model. In this way, the activities mirror real-life situations.
The structure of mathematical-modelling problems
Sfard (2003) argued against using the real-life mathematics method of teaching
mathematics. She cited the arguments that, (a) educators can become preoccupied with
finding real-life settings to teach every mathematical concept for reasons such as the
learning of abstract concepts, (b) if a concept does not have a practical use it is not
27
worth learning, (c) if the real-life problem in the real-life context is actually contrived
in the school situation then it depletes the problem's power as a real-life episode, and
(d) to teach only through real-life experiences would lead to segmented and
impoverished subject matter. These points may be valid in some incidents such as the
apparent trend in some classrooms to present traditional word problems or 'puzzles'
with a real-life flavour (Lesh, Lester & Hjalmarson, 2003, p. 388).
The point of mathematical-modelling experiences is not to narrow the scope of
teaching but to widen it. Although there is no indication that real-life problem solving
is the only way to teach every mathematical concept, mathematical modelling provides
learning experiences to enrich the total mathematics program. The fact remains that in
real-life, managers, human resource personnel, teachers, board and committee
members etc. get together in teams to address particular problem situations.
Mathematical modelling provides opportunities for students to learn the skills to
successfully operate in these situations.
As part of her total argument for accumulative learning, Sfard (2003) discussed the
role of social interaction as being essential to obtaining meaning. As she stated, it is
basically an accepted fact nowadays. But central to this fact and most importantly are
the skills such as, communication skills as well as the mathematical skills of number
sense, statistics, measuring etc. that are acquired through the social process. Forman
(2003) supported the issues of mathematical learning through the process of social
communication. Learning takes place as individuals are goaded to learn as part of the
28
group and with the assistance of others with a common goal. The social process
creates opportunities for cognitive learning as well as motivational and attitudinal
enhancing. However, we need to realize that teams are not always cooperative, and the
cooperation/collaboration aspect is a concern.
Lesh and Doerr (2003b) drew similarities between mathematical modelling and
pragmatism as mathematical modelling “draws on many of the most basic ideals that
were emphasised by pragmatists” (p. 529). Pragmatists believed “good mathematics is
useful mathematics” (p. 529) and that it is “inherently a social enterprise” (p. 525)
where ideas are expressed freely using “resources of the whole group to produce ways
of thinking that will be optimally useful, sharable, powerful and transportable (p. 528).
“Pragmatism is about how things are learned …rather than what things should be
learned” (p. 529). The fact that we are individuals with our own interpretations
operating within the social climate of a changing world accentuates the need for
communication and sharing.
Ultimately, mathematical modelling is about how a wider range of mathematics skills
are learned and used. It offers “a rich platform for students’ independent development
of powerful math ideas” (Doerr & English, 2003, p. 122). Compared to the
right/wrong mentality of traditional problems, mathematical modelling involves
“multiple cycles of interpretation and re-interpretation of evolving products,” therefore,
there is no one approach to a solution. There are communication and sharing,
describing, explaining, justifying and decision making. (Doerr & English, 2003).
29
Mathematical-modelling problems are structured to promote open methodology for
solving problems. The efficient employment of communicative skills suggests the
need for strategic interpretation of the language of mathematics, strategic planning,
sharing and justification of mathematical information. In other words, a strategic
approach to mathematizing “real life” problem situations could serve to enhance
students’ engagement in the mathematical process and their communication of the
mathematical product resulting from active participation in model-eliciting tasks.
2.3 LITERACY
The employment of effective communicative skills requires students to harness the
core meaning of the textual information with which they are working. Only when the
meaning of the subject matter is grasped can students actively participate in oral and
written communication about that subject. Therefore literacy is fundamental to
interactive learning. Students must develop an intimate relationship with the textual
information. Section 1.1, I referred to the four roles that encompass the core of literacy
put forth by Freebody and Luke (1990). In 1999, Luke and Freebody described these
roles as practices focusing on literacy as a dynamic social practice rather than a
psychological role. Effective literacy draws on a repertoire of practices that allow
learners, as they engage in reading and writing activities, to
• break the code of written texts by recognizing and using
fundamental features and architecture, including alphabet, sounds in
words, spelling, and structural conventions and patterns;
• participate in understanding and composing meaningful written,
visual, and spoken texts, taking into account each text's interior
meaning systems in relation to their available knowledge and their
experiences of other cultural discourses, texts, and meaning systems;
30
• use texts functionally by traversing and negotiating the labor and
social relations around them -- that is, by knowing about and acting
on the different cultural and social functions that various texts
perform inside and outside school, and understanding that these
functions shape the way texts are structured, their tone, their degree
of formality, and their sequence of components;
• critically analyse and transform texts by acting on knowledge that
texts are not ideologically natural or neutral -- that they represent
particular points of views while silencing others and influence
people's ideas -- and that their designs and discourses can be
critiqued and redesigned in novel and hybrid ways (Luke &
Freebody, 1999, pp 4 & 5).
These practices, which correlate to the roles originally described, demonstrate how
students must engage with text within a social context. Comber (2002) and Luke and
Freebody (2000) concurred that being literate is to master these practices with both
traditional texts and new communication technologies.
2.3.1 Comprehension
When text of any genre is encountered, the goal is to derive meaning, in other words to
comprehend the text. Reading comprehension has been described by Mayer (2004, p.
723) as "the process of making sense out of a text passage, that is, building a
meaningful mental representation of the text." Mayer confirmed that a reader must
select relevant information from text, organise the information coherently as a mental
representation and integrate new information with existing information for active
learning to occur. The important cognitive processes involved include: using prior
knowledge (integrating), using prose knowledge (selecting and organising), making
inferences (integrating and organising) and using metacognitive knowledge.
Comprehension takes place on two levels: that of higher-order processing and that of
31
lower-order processing. The lower-order processes occur at word level, that is,
decoding and vocabulary. Higher-order processes occur above the word level: relating
what is being read to previous experience as well as flexible use of purpose and
relevance of reading, reading selectively, making associations, evaluating and revising
pre-existing hypothesis when needs be, revising existing knowledge when needs be,
working out meanings to new words, note-taking and, interpreting the text (Pressley,
2000). The correlation between these skills and those of mathematical modelling are
evident even at this point of the discussion. Comprehension skills are developed over a
long-term process that Pressley (2000) says:
depends on rich world, language, and text experiences from early in life;
learning how to decode; becoming fluent in decoding, in part, through the
development of an extensive repertoire of sight words; learning the meanings
of vocabulary words commonly encountered in texts; and learning how to
abstract meaning from text using the comprehension processes used by
skilled readers (p. 556).
The acquisition of comprehension skills depends on classroom instruction. Barton and
Sawyer (2003) supported Pressley's views that the instruction is multi-faceted, and
described comprehension development occurring through students' exposure to a
variety of text types, readers making personal connections with text, student responses
to text through writing, talking or drawing, comprehension strategy instruction, visual
structures and metacognitive awareness of the comprehension process. Central to
arguments supporting this claim on comprehension instruction is discussion on strategy
instruction in particular (Kiewra, 2002; Pressley, 2000). Skilled readers self-regulate
their employment of specific strategies. Our aim as educators is to produce skilled
readers so it appears that strategy instruction is paramount to any worthwhile reading
curriculum. Strategies facilitate the skills required for the reader to gain meaning from
32
text and as such form the basic tools for readers to purposely choose and engage the
derivation of meaning from text. It is the educators’ responsibility to equip students
with suitable strategies so that the students may attain the skills for operating
effectively in our ever-changing, technological world. It is an understatement that to
operate efficiently and effectively, one needs to be a skilled reader, writer, interpreter
and communicator.
Summary
Comprehension is an interactive, complex process involving the reader and the text. In
the light of this overall definition of comprehension and how the skills are best
acquired, this thesis addresses only one aspect of instruction for comprehension, that is,
strategy training, specifically top-level structure. TLS potentially strengthens a
reader's text organisational skills and recall to empower readers with a tool to organise
their thinking during and after reading.
33
2.3.2 TOP-LEVEL STRUCTURE
Bartlett (1979) and Meyer (2003) have stated that in order to read a text, the reader
engages in a process of “complex interaction” between self and the text. The extent to
which a reader extracts meaningful content from text and is able to recall and retrieve
information from memory depends largely on their ability to organise that content
information strategically. Bartlett (2003) contends that top-level structure equates to
the key structuring of the written symbolic language in a logical and systematic
manner. A full definition of TLS is quoted in Section 1.1.
The purpose of TLS is to help the reader or writer make sense of a situation by seeing
the relationships present within the situation: that is, how an oral or written text is put
together or structured to give meaning. In other words, TLS is a strategy which fosters
thinking skills as students recognise, identify and classify structure (Bartlett, Barton, &
Turner, 1987; Bartlett et al., 1989). This structure can be used to elaborate thoughts,
order and compare ideas, and to reflect, discern and infer from text. Giving structure
to ideas enables strategic delivery or communication of ideas. TLS can be applied to
any text, be it narrative, expository or graphic. Kiewra (2002) argued structural
strategies are means of teaching students how to learn.
Meyer and Poon (2001, p. 143) described the five basic organisations of TLS structures
or patterns as “descriptive, sequence, causation, problem/solution and comparison”.
They argued that ‘listing’ can occur “with any of the five writing plans, for example,
listing can occur when groups of descriptions, causes, problems, solutions, views and
34
so on are presented”. Take the following sentence: ‘Air pollution can be caused by
fires, cars and factory emissions.’ The structure of this sentence is cause/effect but
within the sentence there is a list of possible causes of air pollution. Bartlett et al.
(2001) somewhat disagreed with their idea because they claimed that it can be a
“messy or disjointed organisation” especially where readers may be required to impose
their own structure as does happen sometimes when readers do not recognise an overall
structure of a particular text. In such cases, readers can apply their own organisational
pattern to enable them to still approach reading strategically as long as the readers are
able to justify why they chose the particular structure. For example, if a text compared
sedimentary and metamorphic rocks but a reader did not recognise the comparison
structure in the text, that reader could make a list of the identifiable features of the
rocks. The reader is then applying a listing structure to the text. Later, in discussion
and sharing, the comparison structure could be pointed out. Bartlett (2001) argued that
the important point is for the reader to recognise a structure in the text.
Bartlett et al. (2001) provided a simpler and less confusing TLS description involving
just four basic structures: comparison, cause/effect, problem/solution and
listing/description, (see Section 1.1). When one reads a description, the describing
features form a list of features about the topic. Therefore, Bartlett et al. have viewed a
description/list as one type of structure in its own right. Applying a structure to text is
simplified by the fact that texts contain signalling words, listed in Table 1 (adapted
from Meyer and Poon 2001, p. 143).
35
TABLE 1.
Organisational structures in text
______________________________________________________________________
TEXT STRUCTURE SIGNALLING WORDS
______________________________________________________________________
comparison: but, in contrast, all but, instead, act like, however, in
comparison, on the other hand, whereas, unlike, alike,
have in common, share, resemble, the same as, different,
difference, compared to, while, although, despite.
cause/effect as a result, because, since, for the purpose of, caused, led
to, consequence, thus, in order to, this is why, if/then, the
reason, so, in explanation, therefore
problem/solution Problem:- problem question, puzzle, perplexity, riddle,
issue, query, need to prevent, the trouble,
Solution:- solution, answer, response, reply, return,
comeback, to satisfy the problem, to solve this.
list/description and, in addition, also, include, moreover, besides, first,
second, third, etc., subsequent, furthermore, at the same
time, for example, for instance, specifically, such as, that
is, namely, characteristics are, qualities are
_____________________________________________________________________
These give clues to the reader as to which structure is the best choice for a particular
text. For example, in the following text taken from my booklet (Appendix 4), the key
words are highlighted in bold type.
There are many types of plants in the world. They have special
needs so that they can grow well. Firstly, they need nutrients.
Plants also need soil. As well they need water and sunlight.
On identifying these words, a reader could see that the majority of key words are from
the listing/descriptive structure and so could organise the information in the form of a
list of ‘plant needs’.
36
Previous studies by Bartlett (1979), Meyer and Poon (2001), and Meyer, Middlemiss,
Theodorou, Brezinske, McDougall and Bartlett (2002) have found that the
implementation of top level structuring with both younger and older students had
positive effects on student ability to recall text enabling the reader to relate new
information to previous information and retrieve content more efficiently. Therefore,
their ability to make connections, analyse, explain, argue, justify and revise is
enhanced by the strategic influence of TLS. Bartlett (2003) reported that when
students plan, they are more likely to interact and discuss how they extracted a main
idea, to communicate effectively about content of text, and act strategically upon the
content by way of explanation, justification or argument.
TLS is both a process as well as the product: the process of engaging in text and
extracting meaning and the product as the communication about the content of the text
or a product devised as a result of reading the text. Bartlett et al. (2001, p. 69) noted
that as students are taught TLS, they become more “alert and engaged with text” and
so are more likely to interact with others on how they choose the main idea, remember
information and compose from text.
Pressley and McCormick (1995) agreed that strategy instruction enhances students’
ability to analyse and use a text’s structure to abstract the main idea. It would appear
then that this ability would improve students’ writing about a text once they have
determined the main topic to write about. Significant improvements in students'
writing after being taught TLS has also been reported in Bartlett and Fletcher (1997)
37
and Bartlett (2003). Top-level structure provides a strategy by which writing can be
organised according to the same set structure as a reader uses to organise thinking
about reading and thoughts for oral communication. Sentences can then be structured
incorporating key words thus improving the semantics and syntax of the overall written
text. Reading and writing are integrally related due to their common components:
“vocabulary, syntax and understanding of text organization alternatives” (Pressley &
McCormick, 1995, p. 393).
Because mathematical modelling necessitates engaging in different types of texts to
firstly gain sufficient information before continuing with the problem, it seems an
organisational strategy like TLS could relate significantly to mathematical-modelling
outcomes. An exhaustive search of literature has not revealed any adverse writings
regarding top-level structuring. However, skilled readers have been found to already
structure text according to the author's textual organisation (Meyer, Brandt & Bluth,
1980) so it seems particularly relevant to teach the strategy to poorer readers (Section
4.1). Meyer (2003) argued that having strategic knowledge about how to use text
effectively can only serve to give students confidence and as a result encourage
persistence with texts. Because TLS is simple to apply, students can experience
success when interacting with text. This is especially significant for students who have
difficulties in comprehending text. The ability to use a strategy that can give an
organisational structure to text and comprehension of the text's main idea, points to
major benefits for learning enhancement.
38
2.4 MATHEMATICS AND LITERACY
When presented with text, the problem for the reader is to decipher it, that is, to make
sense of the “coded message”. Lesh and Heger (2001) described mathematics codes as
written text, tables, graphs, symbols, specialized languages, concrete models, or other
representational media for purposes that range from construction, to description, to
explanation. Without comprehension of the code there is no meaning, therefore
rendering the printed code worthless. Ultimately, the goal is for readers (in this case
the students) to decipher all of the different representations and find expression in a
common language that is accessible to everyone.
Literacy refers to the way we use language skills to think, make meaning and
communicate. It involves speaking, listening, reading, viewing and writing often in
combination and within a range of contexts (Qld. Studies Authority, 2005). The
NCTM (2000) and the Queensland Mathematics Syllabus (Qld. Studies Authority,
2004) both are in agreement that these skills are paramount in learning mathematics.
They stress mathematical literacy. The Syllabus described mathematics students as:
code breakers, text participants, text users and text analysts
when they:
• Read, view, analyse and interpret the mathematics
represented by text, pictures, symbols, tables, graphs and
technological displays
• Comprehend and analyse conversations and media
presentations that convey different mathematical points of
view
• Organise information, ideas and arguments, using a variety
of media
• Communicate in various ways --- for example, orally,
visually, electronically, symbolically and graphically
• Compose and respond to questions and problems that
challenge their own and others' mathematical thinking and
reasoning (2004, p. 5).
39
This section now specifically addresses mathematical problem solving that involves a
variety of written texts such as those listed above, and focuses on their comprehension
because this relates directly to the issue of mathematical-modelling problems. In the
light of the above statement, successful problem-solving experiences necessitate the
participant to possess successful literacy skills. There is an abundance of literature
which highlights the crucial contribution of comprehension to successful problem
solving such as Helwig, Rozek-Tedesco, Tindal, Heath and Almond (1999), LeBlanc
and Weber-Russell (1996), Littlefield and Rieser (2005), Lucangeli, Tressoldi, &
Cendron, (1998), Mayer (2004) and Passolunghi, Cornoldi, and De Liberto, (1999).
Admittedly, these authors refer in the main to written word problems in the more
traditional sense.
Difficulty in problem solving can relate directly to inaccurate reading comprehension.
Helwig et al. (1999) found that students who could not decode efficiently were at a
distinct disadvantage. In fact, their performance is comparable with that of students
who take problem-solving tests in a foreign language. Those students who have poor
literacy skills inevitably have poor problem-solving skills when it comes to problems
that require reading texts because they cannot gain meaning efficiently from the text.
However, this may not necessarily mean that they are disadvantaged with all
mathematical problem solving. It is possible that these students may achieve with
problems that do not require narrative text interpretation. Therefore, these students are
not necessarily poor at mathematics, but their mathematical performance and
subsequent gaining of mathematical knowledge through problem solving may be
40
negatively affected by their low literacy levels.
Littlefield and Rieser (2005) and Passolunghi, Cornoldi and De Liberto (1999) have
argued that to learn efficiently through written mathematical problems students must
discriminate between relevant information and irrelevant information, which is
problematic for low literacy achievers. Mayer (2004) described four cognitive
processes that students engage as they attempt to solve a written problem. Firstly, they
need to translate each sentence into a mental representation. Secondly, they need to
integrate the information to form a mental representation of the whole problem not just
parts of it. Next, they must plan a solution and monitor or track its progress during the
problem-solving process before finally, carrying out the solution procedure. These
cognitive processes are all linguistically correlated in that they are about interpreting
information into an operable language. They relate to Freebody and Luke’s (1990) and
Luke and Freebody’s (1999) four roles/practices involved in literacy. Linked with the
linguistic cognitive processes is working memory which is required to maintain and
process information efficiently (Le Blanc & Weber-Russell, 1996; Passolunghi et al,
1999). Passolunghi et al. found that poor problem solvers used what they remembered
less efficiently than good problem solvers because they could not filter irrelevant
information.
41
2.5 MATHEMATICAL MODELLING AND TOP-LEVEL STRUCTURE
The nature of modelling tasks requires students to employ high-level literacy skills so
that they can engage fully in working the problem. To think mathematically requires
interpretation and communication of problems at least as much as computation.
Thinking mathematically is particularly about constructing and making sense of
complex systems for example, systems for forecasting economic conditions (Lesh,
Zawojewski, & Carmona, 2003). English (2003, p. 7) stated that solving
mathematical-modelling tasks “involves multiple simultaneous interpretations”.
“Several approaches for goal attainment must be contemplated as well as the goal
itself.”
Interpreting textual information provides the basis through which students begin to
gain mathematical knowledge (Lesh et al, 2003). Students must determine what is
relevant to the solution process and what is relevant to the powerful mathematical
idea/s that underlies the situation. Bartlett (2003) has found that using TLS enables
readers to draw out the main idea/s and incorporating the key words to structure
language (Section 2.3.2) can help students organise their thinking so they can discuss,
argue and to communicate their position in a planful, strategic way.
Lesh and Doerr (2003b) argued the need to find ways to convert all relevant
information and data to a homogenous form, that is, a conversion of relevant
information into a consistent structure for understanding. My hypothesis is that
structuring the text and data using a uniform strategy – in this case top-level structuring
42
of text would be a means to convert this text/data to a homogenous form. That is, the
structuring of text by use of a TLS structure will serve to convert the information
presented to a common language making the text easier to comprehend and use for
example, a very simple scenario of a bar graph. Initially there is a text - words and
symbols to interpret: The heading describes what the information is about. The x and
y axis, the labels, the number symbols, the bars all provide further information on the
subject matter. So the reader can view then organise the information as a list, a
comparison, a cause/effect, a problem/solution. With a graph on ‘Rainfall’, the reader
could initially be comparing the measurement data for rainfall at specific times and
therefore, interpreting and organising the information as a comparison and later using
this information to decide on reasons, causes, effects and so on.
According to the current Queensland mathematics syllabus (Queensland Studies
Authority, 2004), there has been an underutilisation of investigative opportunities
where students can practise pertinent problem-solving skills for our technological
world. Skills such as “constructing, explaining, justifying, predicting and
conjecturing” (English, 2003. p. 4) promoted through mathematical modelling where
they are used in conjunction with “quantifying, coordinating, organizing and
representing data” would seem to fill this gap. It would appear that TLS could
complement mathematical modelling by enhancing. thinking skills and promoting
good information processing skills in students. Bartlett (2003) has reiterated that TLS
employs strategic communication and management techniques to produce effective
outcomes. Pressley, Borkowski, and Schneider (1989, p. 858) agreed that “Good
43
strategy users have cognitive styles that support efficient thinking.” They know how to
implement strategies and “when and where each strategy may be useful”. It appears it
could be beneficial to teach students strategies such as TLS, and to give students
opportunities to apply strategies through innovative, worthwhile, meaningful tasks.
Pressley et al (1989, pp. 858-862) described good information processors. They:
1 are planning their thinking and behaviour,
2 are monitoring their performances- analysing and
changing their strategies and plans to enhance their
performance,
3 have superior short-term memory capacity so they can
process information more efficiently,
4 using strategies becomes automatic
5 can hold large amounts of information in long term
memory—organize it efficiently and appropriately
6 have confidence
7 improve themselves and their performance
8 continue developing information processing
capabilities.
These information-processing skills reflect the cognitive processes described by Mayer
(2004) in Section 2.4 above and the memory requirements discussed by LeBlanc and
Weber-Russell (1996) and Passolunghi et al. (1999) all of which equate to the aims of
mathematical modelling and TLS. Mathematical modelling requires “progressive
assessment of products encouraging revising and refining of models” (English, 2003,
p. 8). Problems “can be solved at many different levels of sophistication” (English,
2002; p. 102). “Many former ‘B’ or below students excel in situations that emphasize
a range of math understandings and abilities that are not restricted to those emphasized
in traditional problem solving” (Lesh & Yoon, 2004; p. 151).
44
It is argued that TLS enhances recall, provides easy to learn strategies and gives
students the means to organise information according to simple plans (Bartlett, 1979,
2003; Bartlett, Lapa, Wilson, & Fell, 1998; Bartlett et al., 2001; Bartlett, O'Rourke, &
Roberts, 1996). Therefore it seems that TLS used in conjunction with mathematical
modelling could have the potential of enhancing the skills of good information
processors and therefore promote greater active participation in the mathematical-
modelling process and so increase the mathematical knowledge gained.
2.6 CONCLUSION
This literature review has provided a theoretical perspective which outlines how
mathematical modelling problems are immersed in text and require both linguistic and
mathematical literacy. It has highlighted the related aspects of mathematical modelling
and top-level structure within the setting of problem solving as a whole and its links to
literacy. Top-level structure is a metacognitive strategy that can provide a pivotal
focus for the whole mathematical-modelling process, in other words when related to
mathematical modelling, it can provide a springboard for the process as depicted in
Figure 3.
45
As outlined in section 2.1, mathematical modelling, as opposed to traditional word
problem solving has been discussed. Critical to understanding mathematical-
modelling problems and developing mathematical knowledge through mathematical-
modelling is the necessity to abstract meaning from texts and to communicate
effectively in social situations. So TLS could play a vital role in aiding students with
mathematical modelling problems. Students engaging in mathematical modelling and
TLS are being involved in “authentic situations where there are multifaceted end-
products” (English, 2003, p. 5) which equips them with tools usable in an ever
changing world. It would seem that mathematical modelling engaged with TLS could
have the potential to contribute to students’ ability to “develop the mathematical
knowledge, procedures, strategies and dispositions that enable students to be
TOP LEVEL STRUCTURE and
MATHEMATICAL MODELLING
A METACOGNITIVE STRATEGY
A SPRINGBOARD TO MATHEMATICAL MODELLING
Enabling structured selection of
information for participation in MM
Enabling structured reception of
information on proposed MODELS
for refinement.
Enabling structured communication of
MODELS
Figure 3. Top-level structure and mathematical modelling
46
competent and confident participants” in an ever-changing technological society
(Queensland Studies Authority, 2004, p. 8).
In light of the literature review there is consolidated evidence that mathematics is not a
field unto itself, but rather an integrated part of a nexus of curriculum strands.
Mathematical-modelling activities attest to the fact that learning opportunities for
acquiring mathematical skills can transpire through the integrated curriculum. The hub
of this integrated activity is literacy. Both the Queensland Mathematics Syllabus
(2004) and NCTM (2000) acknowledge that mathematics has its own literacy and that
mathematical skills are acquired through language and literacy. Mindful of this
testament, this study focused on both mathematical and literacy aspects of
mathematical problem solving. It has brought a comprehension text structuring
strategy to a mathematical setting and tested the effects of doing so. Hence, a
framework has been developed which will inform an intervention to explore the
effectiveness of TLS on changing the outcomes for mathematical-modelling problem
solving. In particular, the following issues relating to the aims listed in section 1.3 and
the questions in Section 3.3.3 will be explored:
• The use of structure in conversation in interpreting and
analysing text (gauged by student use of key words). (Aim 3)
• The use of structure and benefits to students’ mathematising
and gaining mathematical knowledge. (Aims 3 & 4)
• The use of structure in organising and expressing
mathematical knowledge in written and oral presentations
(gauged by student expression of authors’ structure and use of
key words. (Aims 3, 4 & 5)
• The use of structure and students’ ability to ask high level
mathematical questions of presenters. (Aim 3&4)
These issues will be addressed in the context of the following framework (Table 2)
which outlines data collection and data analysis methods described in section 3.3.3
47
TABLE 2
Data collection and data analysis strategies
To what extent will
mathematical
modelling be changed
by the engagement of
top-level structuring of
text
Video
transcripts
Audio
transcripts
Individual
work
samples
Group
work
samples
Teacher &
researcher
observations
Are students using key
words (section 2.3.2)
to identify the
structure of text?
√
√
√
√
√
Do students use the
key words in oral and
written
communication about
the text?
√
√
√
√
√
Do students use key
words and structure to
organise and express
their ideas?
√
√
√
√
√
Is this structure
evident in their written
and oral presentations?
√
√
√
Are students’
questions to presenters
influenced by TLS?
√
√
√
48
CHAPTER 3
RESEARCH DESIGN AND METHOD
3.1 INTRODUCTION
This chapter addresses the use of design experiment research as an approach to
classroom research and provides details of the methods employed in the study. It
details the data analysis techniques and finally discusses research issues and limitations
related to the research.
The purpose of this qualitative study was to investigate complex problem solving via
the focus question: to what extent will mathematical modeling be changed by the
engagement of top-level structuring of text? As argued in the literature review
(Sections 2.3 & 2.5), there appears to be a strong relationship between mathematical
modeling and TLS as the former requires learners to engage with text to acquire
complex skills and the latter provides a strategic method by which to do so. Two year
4 classes at an outer North Brisbane Catholic school participated in the study. One
class participated in mathematical modeling with no prior instruction in Top Level
Structuring. As such, this class formed the non-TLS group. The other class formed
the TLS group and underwent instruction on top-level structuring prior to participating
in mathematical modeling.
3.2 RESEARCH DESIGN
To address this issue, the study used a design research approach, sometimes referred to
as design experiments (Bannan-Ritland, 2003), which employs the use of “empirical
49
educational research” and the “theory-driven design of learning environments” (Anon,
2001, p. 1). It is an appropriate methodology for determining how, when, and why
educational innovations work in a classroom setting. In this case: how would TLS
change mathematical modeling, when could TLS be most beneficial with regard to
mathematical modeling and why did TLS outcomes occur? These points are discussed
in Section 4.4. This study undertook to determine the effects of a literacy-based
strategy on a mathematical setting. In the technological world of today, mathematics
education has moved beyond mere cause/effect relationships in research to more
complex, interactive, adaptable and changing systems involving teachers, students,
classrooms, curricula and resources (Lesh, 2002). As a result, this research delved
deeply into the complexities of learning as discussed particularly in Sections 2.2 and
2.4 of the literature review. The research took place in interactive classroom settings
with the researcher interacting with students and TLS classroom teacher actively
participating in the research process. In the non-TLS classroom, the teacher chose not
to participate in the TLS instruction component of the research process (see Section
1.4). However, this teacher did assist during the group discussions of the
mathematical-modelling process. The researcher understood the composite network
comprising classroom life on levels of practicality and the deeper level of working with
individuals and groups of human beings. These circumstances can mean a changing
system and need for adaptability.
Design-based research was chosen for this project because it allows for the study of
instructional strategies and tools in the context of the learning taking place. It
50
incorporated the development of learning environments and the testing of theories
within that practical environment. Before and during the research process, the
researcher worked collaboratively with the teachers sharing theories and implications
for the research and throughout the process. The teachers learnt from the innovations
taking place in their classroom (Cobb, Confrey, diSessa, Lehrer, & Schauble, 2003).
Therefore, the research catered for the changing learning environment and the
interactive nature of this project as well as the documentation and analysis of learning
and the reflection upon these results.
Multiple methods of data collection were employed in this study. Typical of design
research is the allowance for a variety of data collection sources for example:
classroom discourse, student work samples, tasks, tests, and teacher input (Cobb et al.,
2003) therefore ensuring well-grounded claims and assertions in the analysis. This
variety provided a powerful array of descriptive information pertinent to qualitative
narrative accounts (Shavelson, Phillips, Towne, & Feuer, 2003).
There has been a call for collaboration between fields in research as a multi-
disciplinary approach may lead to a “more integrated knowledge base” that is more
suited “for informing the increasingly complex world in which we live” (Alvermann &
Reinking, 2004, p. 332). This design research used a multi-disciplinary approach as it
investigated mathematical problem solving from a language and literacy perspective
while operating in a scientific setting. The students’ ability to use an organisational,
comprehension strategy to participate in the learning process of mathematical-
51
modelling problem solving was examined within science-based contexts: firstly, that of
growing beans in different environments and secondly, judging the flight patterns of
paper planes. This approach reflects the view discussed in Section 2.6, namely: that
mathematics is not a “unitary discipline” but rather “a multiple discipline” (Cobb,
2004, p. 333). Cobb has called for collaborative relationships between educators in the
literacy/language and mathematics fields. Moreover, he supports the creation of design
experiments which significantly develop mathematical literacy.
3.3 METHODS
This research employed several methods of collecting data (see also Section 1.4).
Information was obtained from: (a) historical records on students’ year 3 Queensland
2004 numeracy test results, (b) teacher information on students’ mathematical abilities,
(c) video and audio evidence of student participation in mathematical-modelling
activities, (d) student work samples, and to a smaller extent (d) teacher observations
and reflections. These presented a range of data for analysis and offered a better
opportunity for a broader picture of results.
3.3.1 Participants
The participants attended an outer Brisbane Catholic primary school. This school was
chosen for three main reasons: the researcher had already established a good collegiate
relationship with the principal and staff of the school through previous work at the
location, the principal and staff were very supportive of the project, and the principal
and staff were willing collaborative workers with the researcher. They could best help
52
the researcher “to understand the central phenomenon” in other words, “purposeful
sampling” was used (Cresswell, 2002, p. 194).
Two year four drafts formed the cohort. One class formed the TLS group which was
taught the TLS strategy prior to any participation in any mathematical-modeling
activities. The second class formed the non-TLS group, which was only taught the
strategy after the first mathematical-modelling problem. This approach was adopted to
enable a clear comparison of the two groups after the initial mathematical-modelling
problem. For equity reasons, the non-TLS group was taught the strategy. This also
allowed for further comparison to reinforce the initial findings.
The TLS whole class group had twenty-eight students: ten girls and eighteen boys. Six
students had learning difficulties including one of these with low muscle tone, two
were hearing impaired, one student was ESL (English as second language), one student
had Autistic Spectrum Disorder and had been ascertained at Level Five that is, having
severe learning difficulties and one student had Oppositional Defiance Disorder, was
ADHD and had been ascertained as Level Six.
The non-TLS class group had twenty-nine students: twelve girls and seventeen boys.
Three of these students had been ascertained as Level Five: one with Speech Language
Impairment, one who had Social Emotional disorder and ADHD and the other student
with Autistic Spectrum Disorder and anxiety. Three students had learning difficulties:
one of these also had low muscle tone and another also received speech therapy. One
53
student had been diagnosed as ADD and another had an auditory processing disability.
To establish a sense of each groups’ experience in problem solving, both teachers were
questioned on how they taught mathematical problem solving. It was established that
the two teachers approached problem solving in a similar fashion through presenting
the students with traditional and non-routine word problems and teaching them
strategies such as, working backwards or guess and check, as discussed in Booker et al.
(2004) and in Section 2.2 of this thesis. The Non-TLS teacher often taught the various
strands of mathematics in blocks so that for example, there could be a solid period of
three weeks focusing on problem solving
For the purpose of this research, two groups per class were focused on in the final
analysis. These particular groups were chosen because they were observed to be
representative of all groups from the two classes. It was decided to focus on just two
groups per class due to the time constraints of this project. However, some overall data
which emerged from other groups has been included in the analysis and discussion
(Section 4.3).
3.3.2 Data Collection
The research process took place over five implementation phases throughout three
terms of the 2005 school year. Table 3 gives an overview of this procedure and then
the phases are described in detail below (Sections 3.3.2.1 --3.3.2.5)
54
TABLE 3
An overview of the data collection period of the research
SEMESTER 1 SEMESTER 2 2005
PHASE 1 PHASE 2 PHASE 3 PHASE 4 PHASE 5
May/June July/August September October November
Principal/Teacher
consultations
TLS instruction
TLS group only
First Modelling
Problem “Beans”
TLS & non-TLS
groups
TLS
instruction
Non-TLS
group
Second Modelling
Problem “Planes”
TLS & non-TLS
groups
Information
Gathering
Year 3 Tests
(2004)
Information
Gathering
Video/audio
Student work
Teacher/researcher
observations
Student
Presentations
Information
Gathering
Video/audio
Student work
Teacher/researcher
observations
Student
presentations
3.3.2.1 Phase One
Prior to beginning the process of the actual research, the results of the student’s 2004
Queensland Year 3 ‘Aspects of Numeracy” and “Aspects of Literacy” tests and
Semester 1 mathematics and English results were viewed. As well, the teachers
provided information orally on the students’ mathematics, general problem-solving,
and language abilities as well as their behaviours. Together, the information from
these sources was used to provide background information on the students’ general
mathematical ability and reading/comprehension ability. These data provided an
assessment of the mathematical attributes (Cresswell, 2002) of number sense, patterns
and algebra, measurement, chance and data and space (Qld Maths Syllabus, 2004) and
also the students’ general reading and comprehension levels.
55
The researcher met with the principal and teachers during semester 1, 2005 to explain
the nature of both top-level structure and mathematical modeling activities and how the
research was to be implemented in collaboration with them. Weekly half hour
planning meetings occurred during the latter part of Semester 1 with the teacher of the
TLS group to discuss the implementation of the TLS lessons during Term 3 and
integration with class programming.
3.3.2.2 Phase Two
The TLS group was taught top-level structuring strategies in collaboration with the
classroom teacher during weekly visits over the Term 3 period of the 2005 school year
(Lesson Plans: Appendix 1). The class teacher considered that this would be more
beneficial rather than an intensified daily program over a period of two weeks. She
preferred this approach because of various behavioural and learning difficulties she
perceived within the class. The TLS program was integrated predominantly with the
teacher’s Term 3 science program: “Soil and Plants in our Environment”. The teacher
also used other opportunities in her class program to draw attention to top-level
structuring of texts throughout cross-curricula activities so that the students
familiarised themselves with the strategy in reading and writing in all curriculum areas.
3.3.2.3 Phase Three
The top-level structure group and the non-top-level structure group participated in the
mathematical-modeling problem-solving task, “Beans, Beans, Glorious Beans”
(Appendix 2). Prior to beginning the actual problem, both classes completed
56
comprehension activities shown at the beginning of the Beans booklet (Appendix 2).
Vocabulary, such as the term ‘scratches’, was also discussed to clarify any ambiguous
meanings. The TLS group also completed note taking activities according to their TLS
instruction (Appendix 3). Both classes worked in small groups of four students each.
All groups were audio taped and one group from each class was video taped during the
process stage of the activity. The students were allocated to pre-established class
groups as both teachers considered this arrangement would be the most beneficial
system for the project.
Following the group discussion and development of mathematical models each student
group shared their solutions/models with their peers in their presentations to the class.
They explained their approaches to the problem/solution, conveyed and then justified
their conclusions. The class audience was encouraged to question the groups on their
findings and offer constructive feedback. All presentations were videoed and student
individual folders, group folders, charts and product presentations were collected.
3.3.2.4 Phase Four
Students from the non-TLS group received the same instruction on TLS as the TLS
group had received during Term 3. However, due to time constraints the lessons were
delivered daily over a period of two weeks. Although the instruction was the same, the
context was slightly different as the teacher preferred not to team-teach and so was not
involved at this stage of the process. Further points of interest relating to this are
examined in the discussion (Section 4.3). The lesson plans differ slightly in context
57
only, but, the content of top-level structuring components is the same. These lesson
outlines are included in Appendix 5.
During this time the TLS group continued with some practice applying TLS to texts.
The class teacher endeavoured to refer to TLS whenever applicable throughout her
classroom program. They were also provided with a practice book on TLS provided
by the researcher (Appendix 4). They were only able to complete some parts of this
due to time constraints.
3.3.2.5 Phase Five
Students from both the TLS and non-TLS groups participated in another model-
eliciting task The Annual Paper Plane Contest (see Appendix 6). Both classes initially
completed the comprehension activities and TLS note taking before actually
undertaking the problem itself. The mathematical-modeling process was video and
audio taped, student work samples were collected and teacher observations and
reflections noted. This phase enabled a further comparison of the groups and
consequently their use of TLS and its effects on mathematical-modeling abilities.
58
3.3.3. DATA ANALYSIS
Predominantly, this study was an evaluative case study. The Year 3, 2004 test results
for the participating students was an historical record of students’ mathematical and
language achievement (see also Section 4.1). This provided part of the explanation for
effectual issues of the learning processes of the study. (Cobb, Confrey, diSessa, Lehrer,
& Schauble, 2003). The available data from the tests in conjunction with information
from teachers regarding student abilities was examined for patterns of reading
behaviour and mathematical abilities.
An interpretational analysis (Tobin, 2000) which endeavours to categorise the data was
engaged to analyse the audio/video taping of student discussions and oral
presentations, their written work as well as teacher/researcher observations. This
allowed all activity to be observed from both social and psychological perspectives
(Cobb, 2000). Video and audiotapes offered a wider view of students’ engagement,
language-in-use and teamwork by presenting “a moving picture” and revealing patterns
that may otherwise have not been apparent e.g. patterns of social interaction. They
made it possible “to observe changes across time” (Lesh & Lehrer, 2000, p. 671). To
avoid focus on one “theoretical window” only (Lesh & Lehrer, 2000, p. 669), which
would have narrowed the researcher’s view, audiotaping was used in conjunction with
video taping of group discourse, student work samples, the year 3 test results and
teacher reflections/observations. “Multiple sources of data ensure that a retrospective
analyses conducted when the experiment has been completed will result in rigorous,
empirically grounded claims and assertions” (Cobb et al, 2003, ¶ 23). This gives rise
59
to a theory building analysis so that relationships among the categories can be
established.
The comparative aspect of the design was assessed using retrospective analysis (Cobb
et al, 2003), whereby the account of learning, in this case for the four main focus
groups, was connected to the means by which it was generated that is, mathematical
modelling and top-level structure. The researcher compared the following attributes
between the groups after phase 3 and then after phase 5 using the data described above.
1. The students’ thinking processes (analyzing the problem situations,
planning solutions, explaining and justifying suggested actions,
predicting their consequences, drawing together results and
communicating these in forms that are meaningful and useful to
others, critically evaluating one another’s products, and responding
productively to peer critiques.)
2. The students’ application of mathematics and literacy concepts
(interpreting, and representing data, relating mathematical ideas,
comprehending narrative, expository and graphic texts) to gain
mathematical knowledge.
These attributes draw upon the insights discussed in Section 2.6, which focus on
mathematical literacy and its links with comprehension of texts. As these attributes
were compared, the evidence of the language that students applied during the process
of mathematical modelling and during the presentations of their models was
specifically identified. This correlates with issues highlighted in Section 2.5 above,
‘Mathematical Modelling and Top-level structure’: that mathematical modelling draws
heavily on literacy skills. The following questions were addressed in the analysis:
1. Did the students use the key words in their conversation about
the text as they interpreted and analysed the text, planned
solutions, explained and justified their ideas, made predictions
about their ideas and responded to others’ ideas?
60
2. Was there evidence that students used an author’s structure
and/or key words to organize and subsequently express their
ideas in written and oral presentations? e.g. “We recommend
that Farmer Bean grows beans in the sunlight/shade because
….” “We found … as a result of ….” “Farmer Bean will
make the most money if he … for the following reasons….”
3. Was there evidence that structuring the text beneficially
changed the way students could mathematise and gain
mathematical knowledge through mathematical modelling?
4. Were the students’ questions to the presenters influenced by
TLS? e.g. did they ask open-ended questions that lead the
presenters into explaining their models thoroughly, justifying
their models, and predicting future outcomes?
3.4 RESEARCH ISSUES AND LIMITATIONS
Although research can play a vital role in decision-making, there are issues that can
limit its ability to give clear prescriptions. Research can positively contribute to
educational programming and curriculum but it cannot answer all the questions
(Hiebert, 2003). Inevitably there are issues of limitations and problems to be taken
into account. Therefore to present a clear view of what is true, this research was
critically analysed prior to its undertaking. Robert Burns (1990) listed the issues of
ethics in research relating to subjects, methods and procedures. The most pertinent to
this study were: informed consent, confidentiality, debriefing, researcher obligations,
publication of findings and intervention studies. These are discussed in Section 3.4.1.
3.4.1 Ethical Issues
Informed Consent.
The researcher fully informed the principal, participating teachers and parents and
guardians of the students of the exact purpose, methods, process risks and benefits
involved (Appendices 7, & 8). The principal and teachers were given written and oral
61
advice on these matters and parents/guardians sent a letter outlining the related
information so that they were fully informed before giving consent for their child to
participate. All participants and parents/guardians were given contacts for the
University Human Research Ethics Committee and contact details for me.
Confidentiality
All direct participants retained their anonymity by being referred to by Christian names
only or simply as ‘student’ in data recording. The principal, teachers and
parents/guardians were informed of the commitment to confidentiality. The name of
the school has been withheld.
Debriefing
All aspects of the study were shared with the principal and teachers. The teachers were
present during data collection and at all times had and have access to the data collected
and its analysis, plus the principal and all teaching staff will share in the findings of the
research at a later convenient time.
Researcher Obligations
The researcher ensured that any commitments made with the participants and teachers
e.g. times, appointments and the like are kept. The researcher has continued some
contact with the school since the research period to keep staff informed of the results.
Because the researcher also believes in ‘giving back’ to the community, inservice on
the research content (mathematical modeling and top-level structure) was offered to all
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interested staff on pupil free day/s in 2006.
Intervention Studies
The project required intervention where the TLS group was initially taught the
strategy: top-level structure. To do this, each author structure, as described in Section
2.3.2, was taught separately throughout a series of lessons which were intergrated with
the teacher’s program. The full lessons: Creating Lists, Comparison, Problem/Solution
and Cause/Effect are outlined in Appendix 1. To balance this, the non-TLS group was
taught the same strategy by the researcher after the initial intervention. These lessons
are outlined in Appendix 5. To continue using and revising the structures during this
time, the TLS group practised using TLS as the teacher incorporated the strategy into
her program and they also participated in activities through the researcher-provided
TLS practice booklet (Appendix 4). It is noted that the non-TLS teacher did not
incorporate TLS into the overall classroom program, and due to time constraints, the
TLS practice booklet was not used by the non-TLS teacher in the class program. Both
groups then participated in a second mathematical modeling activity. This
methodology has been described in Sections 3.3.2.2 to3.3.2.4.
3.4.2 Research Limitations
There were recognised limitations to this research and these are acknowledged by the
researcher in Section 3.4.3 following, as well as in the research results discussion in
Sections 5.1 and 5.1.2. The question of validity is a potential problem with the design
research method (Shavelson et al, 2003). Reliability and validity have been discussed
63
in depth by Burns (1990) because design research is difficult to replicate and is
therefore a ‘one-off’ affair making these difficult to test traditionally. Hence, in this
research, the use of the integration of several methods of collecting data, as detailed in
Section 3.3.2, the involvement of teachers and the openness of the process, plus the
sharing of results of the research allowed for the development of any issues or themes
that may have occurred with the case (Cresswell, 2002), for example in this research,
the issue of key word usage positively affecting students’ ability to express
mathematical reasoning using a structured oral or written form.
3.4.3 Research Issues
There are a number of potential issues with qualitative research and the researcher
considered these throughout the process of this study. Firstly, following on from
validity is the reporting by narrative (Shavelson, 2003), which can run the risk of data
distortion (Cresswell, 2002). The inclusion of teachers as collaborative partners and
the openness of the results to all interested parties and university colleagues was, and
has continued to be in place to counteract any doubt over the honest reporting of
results. Secondly, due to the personal involvement of the researcher with the students,
it was possible that a teacher/student type of relationship could have formed and so
anonymity was a potential issue (Burns, 1990). It has been crucial for careful attention
to be paid to the collecting and analyzing of data in a most professional manner to
respect the privacy of participants.
64
Thirdly the consideration of time was pertinent (Burns, 1990). There were limitations
on time for collecting data, and analysing and interpreting the data, and therefore the
need to strictly keep to the proposed timetable (Section 3.3.2). Time proved to be one
of the greatest limiting factors. Often we had to work around other school activities,
such as, the fathers’ day breakfast, the school carnival, the class assembly presentation,
and class liturgy and all the extra preparations and class activities associated with these
items. This not only affected the timing of the research implementation, but also the
students: (their attention, their behaviour, their disposition), because they were often
excited, tired or restless due to these other activities. So in the everyday life of the
classroom, time management was of utmost importance and keeping to the specified
time allotments was respected. Flexibility was also pertinent. Each episode was set up
in the classrooms early and without undue interruption. Rigorous planning to ensure
episodes ran smoothly and tidying after each episode were crucial.
Unforeseen occurrences, for example, teacher absence and therefore different
personnel or students being called for other curricula activities can create disturbance.
There were times when the class teachers were absent, so the researcher had the
parental information at hand so that visiting personnel could be easily informed. Also,
other staff, such as teacher aides, were informed of the process so that they could also
be involved with students during the process (for instance they were able to assist with
learning disabled students on some occasions Section 3.3.1).
65
As electronic equipment was used, possible risks were anticipated in case of
breakdowns or power failures but there were no such occurrences. There was a
relatively small risk with cords from equipment. These were taped to the floor to avoid
tripping by any participants. To overcome the potential of adverse student reactions to
being video/audio taped, the equipment was introduced during preparatory activities
that is, the comprehension activities before the mathematical modelling investigations
(Appendices 2 & 6) so that they may became accustomed to the equipment. There was
also a risk of human error with the equipment so practice sessions for the researcher
also occurred during the preparatory activities.
3.5 CONCLUSION
The project has been an innovative study that has drawn on my previous background in
literacy and integrated it into the field of mathematics. As such, it contributes to the
fostering of mathematics as a multi-disciplinary field with its own literacy: a literacy
that is learnt through language. This project has focused on the reading, writing, and
language comprehension strategy of top-level structuring and how it affected students’
capabilities in mathematical modeling. It has provided teachers and students with new
skills and rich experiences that are adaptable to an array of real-world contexts both
now and into the future.
The research method was comprehensive to ensure that the aims of the project were
addressed thoroughly and honestly. Clear questions outlining the exact language
66
structures to be assessed have been clearly stated. The project has also taken into
account student histories when considering all outcomes of the study.
This research has built upon current research on mathematical modeling being under
taken by Lyn English and James Watters (2005). Furthermore, it is multidisciplinary
research that responds to the current call to collaborate more than one field in research
inquiries (Alvermann & Reinkiing, 2004). The design for this project has allowed the
researcher to gain deep insights into incorporating top-level structure with
mathematical modelling in the classroom context and to be able to explain thoroughly
possible reasons for the results.
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CHAPTER 4
RESULTS
PREAMBLE
This chapter reports on the results of the research described in the preceding chapters
of this thesis. Firstly, a synopsis of the participants’ literacy and numeracy past results
is given to establish the students’ background and achievements. Next, the students’
thinking processes and their ability to apply mathematics and literacy concepts, as
outlined in Section 3.3.3, are compared between phases 3 and 5. The results of this
comparison are presented within the context of each research question also listed in
Section 3.3.3. The core content of these questions form the four headings under which
the results are conveyed. Finally, the reported results are discussed and concluding
points made in light of the research question: to what extent will mathematical
modelling be changed by the engagement of top-level structuring of text?
4.1 THE HISTORICAL SETTING
It is worth noting that in this particular year level on independently administered tests,
that is, the Queensland Year 3 Aspects of Numeracy and Aspects of Literacy tests,
thirteen students out of fifty-three scored below the middle 50% of students tested in
the state of Queensland in the Numeracy Test. A further five students were in the
lower average range. Notably, seventeen students scored more than 15 % below the
state mean in ‘Measurement and Data” and thirteen were in the lower average range.
Eleven students scored more than 15% below the state mean in ‘Number’ with a
further nine scoring in the lower average score range. In the reading and viewing
68
section of the Literacy test, sixteen students were in the lower 15% range for the state
mean and nineteen were on or below the average score line. In writing, eighteen
students were in the lower 15% range of the state mean and nineteen scored below the
average score.
These student performance data are relevant because they indicate that a significant
number of the students had difficulty both with literacy and with number,
measurement, and data. The teachers of both classes also reported that this particular
year level had continued to experience difficulties in areas of literacy and numeracy.
Furthermore, they reported that these difficulties were exacerbated by behavioural
problems ranging from inattentiveness to tasks, difficulties in concentration, to a
general unwillingness to focus in class. This situation could be due to their personal
family circumstances, their previous classroom experiences, as well as the issues
described in Section 3.3.1. As noted also in Section 3.3.1., both teachers approached
the teaching of problem solving in their class programs similarly.
The generally low literacy and numeracy levels in these classes provided an ideal
situation to explore the efficacy of TLS in supporting mathematical problem solving.
In Sections 2.3.1 and 2.3.2, I discussed the views of Pressley (2000) and Meyer, Brandt
and Bluth (1980) that skilled readers already structure information as they read and
comprehend text. Skilled readers are able to organise textual information, elicit the
main idea/s and extract meaningful content from text. The high probability of the
implementation of TLS being successful with reading-capable students would have
69
tainted the results. Implementing the research with poorer students increased the
probability of reasonable outcomes being demonstrated. As demonstrated in the
Queensland State numeracy and literacy test scores discussed in this Section, a number
of these students had significant difficulties in both areas. Previous studies in TLS
(Bartlett,1979; Meyer & Poon, 2001; Meyer, Middlemiss, Theodorou, Brezinske,
McDougall & Bartlett, 2002), have recognised positive effects of implementing TLS
with students (Section 2.3.2). Therefore, this context provided an ideal situation to
explore the research question because of the high probability that TLS would impact
on comprehension and so position the participants to engage with the mathematical
modelling tasks.
4.2 TOP-LEVEL STRUCTURE AND MATHEMATICAL MODELLING
The data reported in this chapter lend support to the proposition that top-level
structuring changes students’ performance in mathematical-modelling tasks. Through
this study, a positive relationship was noted between mathematical modelling and top-
level structure, which gives credence to the proposition discussed earlier in Section 2.5
of this thesis. The results are summarized in Figure 4 and detailed in Sections 4.2.1 –
4.2.4. This research has revealed six main findings namely:
• Top-level structure has had a positive impact on students’ ability to
participate in the mathematical-modelling process.
• The TLS group used the TLS key words in their discussions for Beans
Investigation 1. Both groups used TLS key words in discussing
Planes problem but neither the TLS group nor the non-TLS group
discussed an author’s plan or appeared to be purposefully
incorporating key words into their language to make predictions for
the Beans Investigation 2.
• Students who had been taught TLS incorporated TLS into their
written and oral communication of mathematical ideas.
70
• Students who had been taught TLS focused on mathematising during
the mathematical-modelling process.
• Top-level structure impacted on students’ acquisition of mathematical
knowledge.
• Top-level structure impacted on peer questioning and responses
resulting in high-level questioning by students and mathematically-
based responses after top-level structure instruction.
The Beans Problem
The Planes Problem
Figure 4. Summary of results.
Clarity
used Key Words in Oral/Written
communication
Used
mathematical reasoning in
explanations and justifications
Use of appropriate
prior knowledge
Relevant
mathematical questions
Used
COMPARISON structure
TLS Beans
Few key words
unclear oral/written
communication
Unclear
mathematical reasoning
Inappropriate prior
knowledge
No questions
Used
no structure
Non-TLS
Beans
Continued use of Key Words in discussion
Continued use of mathematical data in
explanations and justifications
Relevant mathematical questions
Used
Structure in oral/Written
communication
TLS
Planes
Continued use of
Key words in
oral/written
communication
Used Key words in discussion
Use of mathematical data in explanations and justifications
Use of Key Words
in written/oral/ communication
Questions
Used Structure in oral/written
communication
Non-TLS
Planes
71
These findings demonstrate that top-level structure can have a positive impact on
students’ ability to actively participate in the mathematical modelling process. Students
who used TLS were able to analyse the problem situation and plan their solutions
accordingly in contrast to those students who did not apply TLS. They also
demonstrated an ability to reason, explain, and justify their models more clearly after
TLS instruction, and to communicate their ideas orally and in written form. The
evidence of these positive outcomes is discussed in depth in Sections 4.2.1 to 4.2.4.
Also discussed is the fact that although some other positive outcomes in mathematical-
modelling performances were apparent, these were not directly attributable to TLS.
4.2.1 Student Use of TLS Key Words during Discussion
A. Initial discussion: investigation 1 ‘Beans’
As expected, when students were initially presented with the ‘Beans’ problem, there
was a notable difference between the TLS and non-TLS groups. The TLS groups
immediately and spontaneously began exploring the texts for an author’s
organisational structure and discussed possible text structures before ascertaining the
goal of the problem as demonstrated in the following transcript.
Ang.. What author's plan do you think it is?
Megan: I think it's listing/description because what they're
doing, they're actually listing stuff?
However after reading the problem, the non-TLS groups immediately began
questioning what they had to do. A number of these students asked, “So what do we
have to do?” and needed qualification from the researcher or teacher. This behaviour
is significant because the non-TLS group did not have a self-generated starting point
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for the discussion, but needed immediate help whereas, the TLS group had an
immediate decision to make and this seemed to lead them into their mathematical
discussion. This assertion is demonstrated in the text below, taken from a TLS group
that is not one of the focus sample groups being discussed here. This sample is used to
avoid re-citing text which has already been used to demonstrate other issues reported in
these results.
Ang: What author's plan do you think it is?
Megan: I think it's listing/description because what they're
doing, they're actually listing stuff?
Jeff: Well I actually think when you look at the table, it's
comparison. I think they're comparing the weights.
Liam: Yes, they are comparing all the kilograms.
Jeff: I think it's comparison. That's what I reckon it is.
Megan: I think it's comparison.
Liam: It's comparison
Jeff: Yeh! because they are comparing all the weights.
B. TLS and planning the ‘Beans’ solution.
The transcript below demonstrates the TLS students’ engagement of TLS and how they
used it to plan their solution such as, “we're comparing the weights”.
Megan: So we'll put comparison down for our author's
plan.
Megan: OK! We have to take notes from the sunlight and the
shade.
Megan: We need to write down Weeks 6, 8 and 10 and rows
1,2,3,and ,4 for sunlight and then we'll move on to
shade.
Teacher: What is happening here?
Jeff: We're comparing the weights.
Teacher: So what is happening when you compare the weights?
Jeff: We're mainly measuring the weights of butter beans
after they're in sun and shade.
Teacher: What are you comparing - weeks or rows??
Jeff: We're comparing like in row 1, week 1 they have 9
kilos in the sun. They're not growing too well but in
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the shade they are growing heavier.
Teacher: That's row 1 but is that the same for everywhere else?
Jeff: No, not really.
(Students continue to work out and write their results under two
headings: The results of the weights of the butter beans in the
shade/and in the sunlight.)
Jeff: We are comparing the results of the butter bean
plants. After 10 weeks we have some results.
The non-TLS groups also discussed the data, for example:
Lauren: I'd say sunlight and shade.
Tim: I thought it was sunlight because look at this: On row 3
it's 18, row 3 in the shade it's only 12 kgs, row 4 is
17 kgs in the sunlight. In the shade it's only 13kgs.
Lauren: I see what you mean.
Tim continues: Row 2 week 6 it's 8. Row 2 in the shade it's only 5.
Shannon: Guys, could I please talk to you. Wait. In row 1 week 10
it's 13 in the sunlight but in row 1, week 10 in the shade,
it's 15 so it's higher than.
Tim: No, no , no, In row 1 in week 10 in the sunlight it's 9
kilograms.
Tim: So it's probably better to go down. Row 1 in sunlight is
9. Row 2 is 8 in week 6. Row 3 is 9. Row 4 is 10.
(They continued adding in this way for each row and week according to
his way of thinking.)
But their final outcome was incorrect as is shown in their presentation letter and also in
their lack of ability to explain and justify their answers in their presentation.
To Farmer Sprout. We think you should plant your butter beans in the
sun because it helps the beans produce more kilograms. It produces
146kg. We added the numbers up and it came to a bigger number
than we would have thought and more than the shade as well.
Here they show that they have incorrectly added all the kilogram totals of the whole
table to arrive at 146kg. When asked by the researcher to explain how they arrived at
their model, they could not answer. It is conjectured that this outcome was as a result
of not being taught to structurally organise the text. The non-TLS group had had no
74
input to show them how to focus on the table. They were unable to interpret the data
presented on the table.
When participating in Investigation 2 of the Butter Beans problem, neither the TLS
group nor the non-TLS group discussed the author’s plan when examining the data and
neither group appeared to be purposefully incorporating key words into their language.
Students from both the TLS and non-TLS groups systematically looked for patterns in
the data presented on the tables as shown in the text following:
Student: It's because there's 9 kilograms and that goes up in
two's. then there's 13.
Student: But wait, that's not a 2.
Student: Yes it is.
Student: Yeh, but it's 9 and it goes up in two's.
Student: Is there a pattern?
Student: Yes, it's like 13, 14, 15.
Student: Yea, It is too. Look how it's a pattern.
Student: But shouldn't it be 16.
Student: No, this one you don't count the nine.
Student: Yeah it is too. Look how it's a pattern. It goes 9 + 2,
13 +2
It was anticipated that students would use a cause/effect structure or problem/solution
structure to organise their thinking and explanation of the data as outlined in the Beans
booklet notetaking guidelines (Appendix 3). For example, the students could have
discussed the problem that there was not a definite pattern or the effect of no real
pattern in the data on their solution.
C. TLS and the influence of prior knowledge on problem solving
A confounding issue that impacted on students’ engagement with mathematical
modeling was the influence of prior knowledge. A number of groups from both
classes drew on their prior knowledge of the best conditions in which to grow plants
75
before starting to consider the mathematical data.
Ben. (TLS group) I think both sunlight and shade because a plant needs
both sunlight and shade. If it has too much sunlight
and no shade it will die and if it has too much shade it
will die so I reckon that I reckon they might need both.
Put them together. That’s what I need.
Kristy: (non-TLS) I think shade is better. My dad is a gardener.
Eryn: (non-TLS) You get more food and you live longer.
It was observed that some students continued to fluctuate between the data and their
prior knowledge on plants. This particularly occurred in the Non-TLS group.
Isobella: My opinion for shade was because if it got too much
sunlight it might die, but sunlight is right (referring to
the table.).
Kristy: Sunlight is better because it has more kilograms and
you can eat more and it's really healthy.
Isobella: I like shade better because I don't really like the sun
much but I sometimes like the sun because you get to
go to the pool. But if I was a bean I would like shade
better because I like shade better than the sun.
At one stage the teacher directed the following TLS group to use the table:
Matt: I think we should choose sunlight
Ben. So we have to add them all up together and choose
which one is the best.
Kiesha: Well, a plant needs sunlight and shade. If a plant gets
too much shade it will die or if a plant gets too much
sunlight, it will die.
Teacher: What is this (the table) telling you? This is going to
prove your discussion. Why is it saying sunlight is
best?
Matt: Its got more kilos than in the shade.
Teacher. Oh! OK, so it has more kilos compared to?
Matt. The shade. So, sunlight has more kilos compared to the
shade.
The teacher’s intervention was necessary to counteract the students’ reliance on their
76
personal experiences. The teacher was cued to this situation after listening to the
students’ initial discussion which relied on their prior scientific knowledge in
particular, Ben’s statement “I think both sunlight and shade because a plant needs both
sunlight and shade. If it has too much sunlight and no shade it will die and if it has too
much shade it will die so I reckon that I reckon they might need both”. This was
indicative of the focus of their dialogue.
However, the transcript shown below demonstrates that this group went on to use TLS
to interpret the text and plan their solution by comparing the total of kilograms on each
of the tables and justifying their conclusions accordingly “sunlight has more kilos
compared to the shade”.
Taylah: I think Farmer Sprout should plant beans in the
sunlight because on the table it shows that there are
more kilos in the sunlight than in the shade.
Matt: That shade has got less than the sunlight. We looked
all through the weeks and the sunlight is getting more
and more (kilos).
Students: It’s a comparison.
Taylah: That means they are comparing sunlight and shade
together and if it is a list it is listing all the kilos
together. Which one do you guys like best?
Students in unison. Comparison.
Ben: So, sunlight has more kilos compared to the shade.
Teacher: And is that true for all of it? You have to make a
decision and you have to check that information really
carefully.
Ben: I reckon I would choose sunlight because if you
compare with week 6, in the sunlight they got more
kilograms.
Students, once they learned the TLS strategy were using key words to identify the
structure of texts and to organise and subsequently express their ideas. They compared
data while explaining and justifying their reasoning: “I reckon I would choose sunlight
77
because if you compare with week 6, in the sunlight they got more kilograms” and “I
think Farmer Sprout should plant beans in the sunlight because on the table it shows
that there are more kilos in the sunlight than in the shade”.
D. Observed changes in the non-TLS group in the ‘Planes’ problem
The non-TLS group’s discourse taken after they had received TLS instruction for the
Planes problem, shows significant changes in the way the students could express their
thinking. In their justifications, they clearly compared the results between the teams
using mathematical explanations for their decision. The use of key words in
determining the text structure of comparison was demonstrated, for example:
Non-TLS Group 2
Shannon: I think team E will win because the distance is longer.
Sebastian: I think team E should win because if you compared
other teams, you will see that team E has gone further
distance than other teams.
Lauren: I think team E won because the distance was longer
and it did not get scratched through the whole
competition.
Shannon: I think you should go Team E because they have 39
points compared to Team F which has 23 points.
Team E is 16 more than Team F.
The following text from the non-TLS group 1 after the Planes problem also
demonstrates this group’s use of structural key words. Although, this particular group
did not identify the actual structure of comparison, their discussion was focused on
examining the data and reasoning about the data. There was an order consistent with
knowledge about TLS in how the students went about discussing the data:
Isobella: I chose it (Team E) because it did three attempts in ----
seconds and it did the most metres.
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Isobella: Look at the chart. OK. Look at the seconds. Then the
first team goes up and the second goes backwards
(12,7, 8 metres) and the third…
Eryn: What about Team D?
Kristy: Yea, but it has scratches.
And so on …
Eden: I chose Team E because its scores were higher than
the others and it didn’t get scratched and it goes for the
longest time.
This discussion can be compared with the discussion for the Butter Beans problem
where the non-TLS students continued to fluctuate between prior scientific knowledge
on ‘gardening’, plant needs and health etc (as outlined in this Section above) and the
actual data:
Eden: Looking at this, I think sunlight is just a bit better. The
results say 15. in row 1, it’s 15, that’s for shade and in
sunlight it’s 13 which is a bit less but as you go
down…Well, I forgot!
Isobella: Why did you pick sunlight?
Eryn: Because they grow bigger and better. Way Better.
Eden: My answer is that it grows more and you get to eat
more of the beans.
Eryn: You get more food and you live longer.
Isobella: My opinion for shade was because if it got too much
sunlight it might die, but sunlight’s right.
Kristy: Sunlight is better because it has more kilograms and
you can eat more and it’s really healthy.
4.2.2 TLS and Written and Oral Communication of Mathematical Ideas
The following transcripts illustrate samples of written text from the first problem
‘Beans’ and the second problem ‘Planes’ taken from the TLS group. Key words which
indicate the TLS are highlighted. The TLS students showed that they were well aware
of organising the textual information when they confronted the ‘beans’ problem and
were clearly comparing the two scenarios. They did include a chart with the
79
mathematical evidence to prove their stance. They could define their justification
clearly and succinctly.
Sample letter transcripts from the TLS group
Group 2 To Farmer Sprout. We arrived at the decision by reading the
page of information and deciding it was comparison. We
chose comparison because it (the bean plant) grows much
better. It can grow higher and faster but shade is still good for
the beans. The beans in the sunlight grew bigger in three
weeks. On the other hand, the beans in the shade grew
lower. So grow them in the sunlight. That’s our decision.
Group 3 Dear Farmer Sprout, We recommend as a group that you
should plant your butter beans in the sunlight because on the
chart sunlight has a bigger rate of kilograms than shade.
We worked it out by doing a sum. (Students demonstrated
sums of all the rows)
Although the non-TLS students gave the reasoning behind their decision, their
explanation that they were comparing sunlight and shade results for the bean crops was
unclear.
Group 1 To Farmer Sprout, We think you should plant your butter
beans in the sun because it helps the beans produce more
kilograms. It produces 146kg. We added the numbers up and
it came to a bigger number than we would have thought and
more than the shade as well.
These students have incorrectly summed each weight listed on the table to gain a total.
The other sample demonstrates an over-reliance on prior knowledge:
Group 2 Dear Farmer Sprout, I think sunlight is the best choice of light
because beans are supposed to grow in a warm place and in
the sunlight the beans grow quicker. The beans are bigger and
the beans are heavier for example: In week 6, row 1’s sunlight
was 9kg and the shade had 5kg.
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The TLS group continued applying the strategy to the Paper Planes modelling activity
as is shown in the following example accompanied by the students’ chart in Figure 5:
Group 2. Dear Judges. We chose listing and description because my
text has lots of listing in it. You can choose your winners by
who ever has the longest metres and centimetres for example,
team E would get the first prize and then if you had two with
the same scores, you would go back to the seconds. That’s
how our group chose the winners.
Seconds Metres
Team A 2, 1, ½ 11, 12
Team B 1, ½, ½ 12, 7, 8
Team C 1, 1, 2 9, 11, 11
Team D 2, ½, 1 12, 8
Team E 1 1/2, 1, 2 9, 10, 13
Team F 1, 2 9, 11
Figure 5: Student Chart
This group had differing opinions of the author’s structure so submitted another idea as
shown below:
We chose comparison because we thought it is comparing all
of the teams. The winner we chose was team E because they
had the most amount of metres gained and the same amount
of attempts.
These particular members saw it as important to include their structural plan name in
their writing. However, this is not necessary, so further teaching on TLS to correct this
misconception is necessary. They were comparing the length totals as well as taking
into account the time spent in the air.
Written work sample from the Non-TLS group after TLS instruction
Group 1 Dear Judges. We heard about the paper planes contest.
However, we thought they all did well but E did better. To
solve this, we compared the other teams’ scores and realised
that its last score in seconds was 2, but flew 13 metres and
didn’t get scratched at all.
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Our Profile
Team A 12
Team B 12
Team C 11
Team D 12
Team E 13 Best Number
Team F 11
Figure 6: Student Chart
Group 2 Dear Judges, We think you should decide the winner by the
distance, height, speed and by time. We also think that Team
E will win because if you compare other teams with team
E, you will see that team E has gone further distance than
other teams. We think team E won because it did not get
scratched at all during the competition. We think you should
go for team E because they had higher points.
Both the samples for the TLS and non-TLS groups for the ‘planes’ problem illustrate
the students’ use of textual organisation in planning their responses. Both groups used
key words to signal the organisation plan for their thinking for example, “comparing
the teams”, “but E did better”, “To solve this, we compared…”
4.2.3 TLS, Mathematising and Constructing Mathematical Knowledge
A. Phase 3: Approaches to solving ‘Beans’ investigation 1: Oral communication
Students from the TLS group approached the Butter Beans discussions, written tasks,
explanations, and justifications in a different manner than the non-TLS group. The
TLS students were aware of finding textual structure from the outset. “We arrived at
the decision by reading the page of information and deciding it was comparison”.
The TLS students were able to decide on their approach to the problem, reason about
the data and explain their solutions sensibly using the data.
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Ben: I reckon I would choose sunlight because if you
compare with week 6, in the sunlight they got more
kilograms.
Students: It’s a comparison.
Researcher: What sort of solution are you coming up with for the
problem so far?
Matthew: That shade has got less than the sunlight. We looked
all through the weeks and the sunlight is getting more
and more (kilos).
Taylah: I think Farmer Sprout should plant beans in the
sunlight because on the table it shows that there are
more kilos in the sunlight than in the shade.
On the other hand, although the non-TLS groups centred also on obtaining totals for
the rows and comparing the totals they confused prior knowledge and factual data
knowledge more often. Predominantly they alternated between the two reasoning
factors in their explanation attempts.
Isobella: My opinion for shade was because if it got too much
sunlight it might die, but sunlight’s right.
Kristy: Sunlight is better because it has more kilograms and
you can eat more and it's really healthy.
Isobella: I like shade better because I don't really like the sun
much but I sometimes like the sun because you get to
go to the pool. But if I was a bean I would like shade
better because I like shade better than the sun.
After such discussion, this non-TLS group decided on adding rows to find totals but
their approach to solving the problem lacked initial certainty of purpose and was less
ordered: “Looking at this I think sunlight is just a bit better. The results say 15. In row
1, it’s 15 that’s for shade and in sunlight it’s 13 which is a bit less but as you go
down…well, I forgot”. Some confusion and lack of correct focus was also
demonstrated in non-TLS Group 2 when Tim looked at week 6 of the table while
Shannon was looking at week 10:
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Tim: … row 2, week 6 it’s 8. Row 2 in the shade it’s only 5.
Shannon: Wait. In row 1, week 10 it’s 13 in the sunlight but in
row 1, week 10 in the shade, it’s 15 so it’s higher than.
Tim: No, no no. In row 1 in week 10 in the sunlight it’s 9
kilograms. So it’s probably better t go down. Row 1
in sunlight is 9. Row 2 is 8 in week 6. Row 3 is 9.
Row 4 is 10. (he continued adding in this way for each
row and week)
Even though the TLS groups did engage prior knowledge in their explanations, their
discussions were more semantically ordered and focused on interpreting the data as is
demonstrated in the transcripts cited in Section 4.2.1 above.
B. Investigation 2 ‘Beans’
In making the predictions regarding the growth of beans for week 12, both TLS and
non-TLS groups looked for patterns in the data and despite the anomalies they found
still regarded that some sort of pattern existed as justification for their predictions:
TLS Group:
Ryan: What do you think it’s going up in? Seems to be going
up in twos to me
Hayley: Ones
Jason: I think twos.
Non-TLS Group:
Isobella: Is there a pattern?
Eden: Yes, it’s like 13, 14, 15.
Kristy: Yeah. It is too. Look how there’s a pattern.
Eden: But shouldn’t it be 16”.
Isobella: No, this one you don’t count the nine.
This last statement by Isobella makes little sense. It appears she could be attempting to
justify her pattern by ignoring data that does not fit her conclusions.
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The only evidence that TLS was considered in part B of the investigation was the fact
that Jason (TLS Group 2) made reference to TLS by indicating that the group needed
to give a reason for their decision: “We need to put: ‘We think this because it’s going
up in two’s’ or something like that it’s not necessarily two’s...”. Jason realised the
need to explain their prediction mathematically. Otherwise, both TLS and non-TLS
groups worked on interpreting data according to patterning to make their predictions.
C. Written communication: ‘Beans’
The TLS students expressed their written, mathematical explanations clearly: “If you
look at our results in sunlight week 6 and compare to shade week 6 row 1, you will
see that the sunlight weighs more … than the shade.” Matthew’s TLS group
introduced the concept of ‘rate of kilograms’ in their justification: “We recommend as
a group that you should plant your butter beans in the sunlight because on the chart,
sunlight has a bigger rate of kilograms than shade. We worked it out by doing a
sum.” They then showed how they aggregated the totals to obtain their model.
Isobella’s non-TLS group also justified their explanation in their letter: “We think you
should plant your butter beans in the sun because it helps the beans produce more
kilograms.” But, it was this group which was confused and totaled every weight on the
table to 146 kilograms. They explained: “We added the numbers up and it came to a
bigger number than we would have thought and more than the shade as well.”
Non-TLS group 2 gave a mathematical justification for their model: “The beans are
bigger and the beans are heavier. For example, in week 6, row 1 sunlight was 9
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kilograms and the shade had 5 kilograms.” However, in the first part of their letter the
students were also influenced by prior knowledge as evidenced by the use of
“supposed” in the following statement: “Sunlight is the best choice of light because
beans are supposed to grow in a warm place and in the sunlight the beans grow
quicker.” They ended their report with a picture depicting Farmer Sprout on the farm.
There were no mathematical data given.
The TLS groups appeared more sophisticated in their written explanations and
justifications. They relied on mathematically sound comparisons of data and their
justifications were mathematically correct. However, the non-TLS groups had not
applied structure to help their organisational thinking. The evidence is persuasive that
their incorporation of prior knowledge and incorrect aggregation may be as a result of
not interpreting the main idea of the data in a structured manner.
D. Phase 5: After the Planes Problem
Once the non-TLS groups had been taught the TLS strategy, it was evident that they
began to focus on mathematical reasoning in an organised fashion:
Seb: I think Team E should win because if you compared
other teams, you will see that Team E has gone further
distance than other teams.
Lauren: I think Team E won because the distance was longer
and it did not scratch through the whole competition
Tim: I think you should decide the winner by speed and
time.
Shannon: I think you should go Team E because they have 39
points compared to Team F which has 23 points which
(Team E) is 16 more than Team F. This is my proof –
Team A – 16, Team B…
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The students now had structure in their discussion using words such as, because, if you
compared, compared to, in ways that suggested a sound comprehension of the problem.
They focused on the mathematical concepts of distance speed and time as justification
for their ideas and also incorporated teams’ scratches into their justifications.
Therefore, they were now drawing together the mathematical data in planning their
model and the evidence of this is shown in their letter:
Dear Judges, we think you should decide the winner by the
distance, height, speed and by time. We also think that team
E will win because if you compare other teams with team E,
you will see that Teams E has gone further distance than
other teams.
We think Team E won because it did not get scratched at all
during the competition.
We think you should go for Team E because they had higher
points.
When questioned by the teacher and their peers, these students were now able to
mathematically justify their explanations as is outlined in Section 4.2.4 below.
Non-TLS group 1 began their Planes Investigation metacognitively by focusing on
what they needed to do:
Kristy: Isn’t it when we have to see which team is the best?
Eden: What we think is the best and why we choose it to win
the contest.
Isobella: What you have to do is you have to pick any team you
like and why you chose that team to win.
Compared to the Butter Beans investigation when they relied to an extent on prior
knowledge for their discussion, in the Planes investigation, the group with the
exception of Eryn, was able to focus on mathematically analysing the data as is
apparent in the following extract: “I chose it (Team E) because it did three attempts in
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---- seconds and it did the most metres.”
When Eryn chose Team E because it “started with the same letter as” her name,
Isobella was able to explain to her what she needed to be doing: “It doesn’t matter that
it starts with you name Eryn…Look at the chart. OK. Look at the seconds. Then the
first team goes up and the second goes backwards (12, 7, 8 metres) and the third …”
The group continued to focus on their discussion mathematically:
Eryn: What about Team D?
Kristy: Yeah, but it has scratches.
Eden: E doesn’t have any scratches.
Kristy: Neither did C and neither did B.
Isobella; I chose E because it has 13, the highest number out of
all of them and that’s why I chose E.
Kristy: What about C? It goes 9, 11, 11
Isobella: Eden, why did you choose E?
Eden: Because there were no scratches. It had the highest
number in metres and because its seconds were more
and so…
At this point the class teacher interrupted and stopped all groups. He wanted the class
to think individually about their decisions and then share with the rest of their group.
As a result the ongoing discussions were interrupted. When students returned to their
discussion, they began to read out what they had written for example. Isobella read out
“I chose E because it goes for a long distance. It goes for longer seconds and it has no
scratches.” Eden read “I chose Team E because its scores were higher than the others
and it didn’t get scratched and it hoes for the longest time.” Both girls reasoned with
time, distance and took scratches into account. At this point, the teacher asked this
group to show him the proof for what they were claiming. He asked a number of
questions in a row such as:
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Teacher: How do you know? Where did you work it out? Show
me how you worked that out. Show me the numbers.”
Students: The numbers?
Teacher: Show me the best number from the others. Make sure you can
prove it.
The students were then confused:
Kristy: I don’t get it though.
Eden; What are we meant to do?
Kristy: I don’t get what he said.
Isobella: Well, we’re not doing it right because he told me to
pick the number of each that would be the best one so I
circled 13 because it was the biggest out of all of them
so that’s why I chose E.
The group then continued to check the highest score of each team such as 13 was the
highest score listed for any team which was in Team E’s results. Finally, Kristy
decided to add the scores of the teams such as “9 plus 10 plus13” to find which team
had scored the longest distance overall.
The group used top-level structure to organise their thoughts when writing. Their letter
shows how they knew they were comparing data and, despite the confusion after the
teacher’s interruption above, the group incorporated distance, time and scratches into
their justification:
Dear Judges, We heard about the paper plane contest. However,
we thought they all did well but E did better. To solve this, we
compared the other teams’ scores and realized that its last score in
seconds was 3 but flew 13 metres and didn’t get scratched at all.
Both TLS Groups 2 and 3 began their Planes investigation by metacognitively
planning what they needed to do. Taylah (Group 3) says: “What do we have to do
here? List what we have to do. Let’s read what we have to do.” Jason (Group 2)
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stated “What’s the first thing we have to do? We have to help them choose the
winner. You have to write down what they need to do meaning help them choose a
winner. Here, the students have recapped on the facts they already know about how
they need to go about the problem-solving process.
The students went on then to list what the judges needed to do:
Ryan: Do we need to count the metres? Do we need to count
the seconds?
Jason: They need to count the number of metres recorded on
the data. OK that’s the first thing they need to do.
Now what’s the second thing they need to do? Do they
need to count the number of seconds?
Hayley: Yes
Jason: OK so we’ll write that. They need to count the number
of seconds recorded on the data.
Ryan: And then for the third one write ‘make sure they have
the right number of attempts.
This group then discussed the data of distance and time in depth but did not refer to the
scratches. They saw that as they compared these results, two teams had the same
distance but they could differentiate between these two teams by considering the time
factor, as Hayley demonstrates here: “You know how there’s two 20’s. I put D as…
and F as next because D in the air has 3 ½ seconds.” “E is first cos it has longer
seconds (4 ½).” Hayley clarifies “I decided that you could choose the winner by
whoever had the longest metres and seconds.”
TLS Group 3 also neglected the scratches (see also Section 3.3.2.3) using distance and
time as reasoning for their decision: “E is the winner because the distance is 32 and
the seconds is 4 ½.” They discussed that they were “comparing the planes, the
distance and if they go in a straight line.” This showed that they were using structure
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to analyse the data.
4.2.4. Top-Level Structuring, Peer Questioning and Responses
After the Butter Beans presentations, the TLS groups’ peers were able to question the
presenters mathematically: “Can you tell us on your graph (table) the estimates that
you came up with?” Ryan, TLS Group2 responded: “well, we counted up like in a
pattern and it’s going up by a number so we just added the number because it seems
to be going up instead of down so we put higher numbers. We put higher numbers as
well because we thought it would make it more interesting and if it was going down
say---7, 6, 5 and we put 15, you wouldn’t really get that but if it was going up, we
would keep going up as well so that it makes more sense.” Ryan has attempted to
give a mathematical justification to the group’s patterning method.
When questioned by the teacher as to why the group chose sunlight, Jason from the
TLS group answered using his prior knowledge on plants’ needs (sunlight and rain)
rather than giving a mathematical justification. As the teacher probed further about the
‘graph’ they had drawn, Jason explained that it showed how much the beans grew:
Teacher: Can you tell us about that graph?
Jason: We did it because we thought it would make it easier
because we were explaining it to Farmer Sprout and we
wanted to make it easier so he would know what one to
grow it in.
Teacher: So which is the best one to grow it in?
Jason: Sunlight
Teacher: How does your graph back that up?
Jason: Because it shows how much it grew…
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Hayley expanded this explanation with: “the beans are heavier and if they are heavier,
they must have grown taller and they would be healthier too.” Peer group questions
continued after other TLS group presentations as well for example Group 3 had shown
additions across the rows to help verify their reasoning and were asked what these
‘sums were for’. They answered that ‘the sums’ made it easier for them to work out
(the model).
TLS Group 3 appeared more confident after their Planes presentation and faced further
mathematically-based questioning from their peers. The group was able to justify their
position in mathematical terms:
Jeff: Why did you do sums?
Matthew: Because it makes it easier to work it out. We can just
write it instead of working it out by ourselves.
Ryan: Why did you choose E?
Matthew: Because we looked on the chart and we added it all up
and E had the biggest total.
Teacher: How do you mean the biggest total—Total of what?
Matthew: Well, metres and seconds.
Teacher: How do you mean?
Matthew: We looked on the chart and we looked at just say C
and then we looked at E and E had a greater rate, a
bigger total than C, the most seconds and metres.
TLS Group 3 was not questioned to any great extent on their Planes presentation.
They were asked why they drew a ‘graph’ to which they responded “to show how
much each team got.” They demonstrated this to the class showing their table. They
were then asked if they had displayed the totals of all groups and which team had the
most scratches after which they again referred to the table.
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After the non-TLS groups’ Butter Beans presentations, no members of the class peer
group asked any questions to any presenters. When questioned by the researcher, these
students had difficulty in answering. Non-TLS Group 2 had totalled every number in
the table and when questioned by the researcher on this, responded with silence after
each question. When questioned further by the researcher on their prediction Tim
responded:
Tim: Well Shannon, she helped us decide on all different
things so we all kind of wrote it.
Researcher: How did she decide?
Tim: She added the numbers from week 10 in the um. In this
she, she um. For this she did that and then she thought
oh, and plus 1 cos that was plus 1 that it would be 14.
The whole group appeared confused and was unable to explain their position.
After the Planes problem, questioning was open-ended requiring presenters to justify
their decisions. Both the TLS and non-TLS group peers questioned presenters. The
non-TLS group showed significant changes in their ability to question and in the way
the students could express their thinking. In their justification, they compared the
results between the teams and were able to give a clearer, mathematical explanation for
their decision. They showed that they took into account distance, time, and the number
of scratches for the team. They justified their position by listing the criteria on which
they based their explanation and by stating the cause for their decisions. For example:
Question: Why did you choose Team E?
Shannon: Cos the distance was further.
Patrick: Where’s you proof?
Shannon: Team E has scored higher points. It didn’t get
scratched. They had higher points and the
distance was further.
Lauren: We also got it because we added up all the
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scores. We added up all the teams.
Teacher: Which columns?
Seb: We added up metres, time, distance as well.
Callum: What about the seconds? Did Team E win with
seconds as well?
Lauren: No, not exactly because it got 1 ½ for the first,
and 2 seconds for the second and for number
three—1 ½.
Non-TLS Group 1 had mistakenly aggregated a total for all data in the whole of both
tables for sunlight and shade in the Butter Beans investigation. When questioned by
the researcher, they were unable to explain what they had done:
Researcher: So the last one altogether is 112 kilograms.
Tell me how you got that number.
No Response.
Researcher: So you added all the number in one box
together, which one was the shade. What about
the sunlight? What does that tell you?
No Response.
However after their Planes presentation, this group was questioned firstly on providing
proof for their claims to which they responded by pointing to their chart and relaying
the totals of the distances travelled. They were further questioned on the highest total
and how many points the teams achieved. Again, they read out the points and noted
the highest score. They were questioned by one peer as to why they had not used
seconds in their model and they responded they thought distance was better. Although
this group may not yet have demonstrated they were able to account for all
mathematical variables in their oral justifications, they showed confidence in their
answering but they only focused on distance.
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CHAPTER 5
DISCUSSION, IMPLICATIONS AND CONCLUSION
This chapter summarises the findings of the research and discusses the main
observations attained from the study. It argues that the study has ascertained positive
outcomes for the application of top-level structure to mathematical modelling
problems. Implications of these outcomes for mathematical modelling are given, as
are the implications for further research in mathematics. Finally, concluding points are
made.
5.1 DISCUSSION
This study was located in a naturalistic setting and hence the conclusions are limited by
the idiosyncrasies of each classroom. There were subtle differences in the learning
environments brought about by the personalities of the classroom teachers. In
addition, opportunities and constraints, such as time and class current curricula meant
there were differences in the implementation of top-level structure (Section 3.3.2.4).
Such differences would need to be addressed in future studies of TLS and
mathematical modelling.
Two main observations were recorded in this study. Firstly, there were fundamental
differences between the TLS and non-TLS groups during the process of the Butter
Beans problem and secondly, the non-TLS group showed positive changes between the
Butter Beans problem and the Planes problem. Before beginning the detailed
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discussion on the main findings deemed from this research, possible factors
contributing to the children’s responses need to be noted.
As outlined in Sections 3.3.2.3 and 3.3.2.5, both classes participated in comprehension
activities prior to participating in both problems. However, for the butter beans
problem, the TLS group had been taught to take notes from the information using the
top-level structure they had chosen for the text. The majority chose ‘comparison’.
Only a couple of individual students chose ‘listing’. Comparison was the better choice,
but listing was sufficient to provide an organisational structure. Taking organised
structural notes would have contributed to students viewing the information and data in
an organised fashion as they investigated the problem.
The next factor is the way in which the teaching of TLS to both groups occurred. As
described in Section 3.3.2.4, the intervention with the TLS group occurred with ten
TLS lessons taking place once a week over a period of one term. This was at the class
teacher’s request as she felt this would be more beneficial for the particular class.
Between the two modelling problems, this class teacher endeavoured to incorporate
TLS into her teaching as much as possible. It is also noted that she had not been
specifically trained in the strategy, but had learnt it as she team-taught her science
program with the researcher during which the researcher implemented the TLS
strategy.
The non-TLS group was taught the strategy during ten daily, successive lessons over a
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period of two weeks prior to the Planes problem. They were taught solely by the
researcher at their class teacher’s request. Therefore, the researcher had complete
autonomy with the class so the dynamics were naturally different. Personally, having
autonomy with the class impacted positively on my teaching as students responded to
me as their teacher rather than as a visitor. The lessons for both classes were basically
the same topics but the non-TLS class was not completing a ‘Plants’ unit at the time
but were studying a unit with their class teacher on “Planes”. Therefore, the context
differed to some extent. However, it was decided that for continuity in TLS instruction
for both classes, it was better to keep the lessons the same as much as possible.
Then, there were the fundamental differences between the two classes in terms of
behaviour, attitude, listening, and although both classes had about the same number of
students with learning disabilities there were apparent differences in problem-solving
abilities. The non-TLS group appeared more proficient in problem solving. Their
attitude was more positive. However, the mathematical-modelling problems were
quite different to their previous problem-solving experiences in mathematics. The
non-TLS group also grasped the TLS strategy and its application more readily than the
TLS group perhaps due to the intensive implementation of the TLS strategy over the
two week period.
The main findings listed in Section 4.2 are now discussed in the light of the
observations noted above in this section. The discussion outlines the effects of top-
level structure on mathematical modelling.
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5.1.1 The effects of key word usage during mathematical modelling
During the Beans problem, the TLS groups deliberately used words of comparison, for
example; more than, so, compare as they considered the task, discussed the data, and
wrote about their model. The use of such words indicates greater awareness of text
structure and applying structure to text. The evidence demonstrated that these students
were conscious of using structural key words to help them analyse the data and explain
their ideas both orally and in writing. This finding supports claims by Bartlett (2001)
that after being taught TLS, students become more engaged by text and more effective
communicators about the text. The students had a method by which to focus their
discussion and begin the planning of their model. They showed that they knew the
importance of justifying their ideas by the use of statements like: “We have to say
why…” and “because on the chart…”
Where the TLS group did engage some prior knowledge on plants, this did not detract
from their mathematical discussion. It did to some extent substantiate their decision
for sunlight but was used in conjunction with the mathematical data. They progressed
to reliance on the data during the discussion.
There was no evidence of the students deliberately using key words to structure their
approach to Investigation 2 of the Beans problem where they needed to make
predictions. It seemed that all groups, TLS and non-TLS relied on prior mathematical
knowledge and decided that to make a prediction it made sense to look for a pattern
and continue the pattern. Perhaps due to this, the mathematics overrode the fact that
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the table was still a text. The students could have used a cause/effect or
problem/solution structure to organise their thoughts, promote discussions and then to
make predictions. With more experience in applying structure to a variety to texts,
students could learn to use this procedure in future circumstances. This could also
have helped Jason when he noted that there was not an exact pattern. Students did not
know how to deal with this situation so made their predictions as if there was a pattern.
Using key words played a major part in the way students were able to structure their
letter writing. It was observed that TLS students were able to express ideas in writing
more easily than non-TLS students who questioned within their groups: “What do we
write?” Top-level structure provides a strategy by which writing can be organised
according to a set structure, and sentences can then be structured incorporating key
words, thus improving the semantics and syntax of the overall written text. Significant
improvements in students' writing after being taught TLS has also been reported in
Bartlett and Fletcher (1997) and Bartlett (2003).
On the other hand, the non-TLS group showed no major use of structure as they
approached the Beans problem. Other than some natural use of words such as,
‘because’ in their usual speaking, they did not strategically use key words to plan how
they were investigating the problem. There was an over-reliance on prior knowledge
for example: “My Dad’s a gardener.” or on plant needs rather than the data. This
seemed to lead to confusion between what they already knew and the factual data so
discussions lacked focus. Significantly, the TLS class was simultaneously studying a
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science unit on plants, so one would have expected more prior knowledge to come into
their discussion rather than the non-TLS groups’ discussions.
It was observed that most non-TLS groups were less sure of the task and required more
assistance from the teacher or researcher to understand the task. Several groups
appeared overwhelmed and needed more individual direction. They did not know
where to start. This confusion was also evident in their approach to the writing
requirement. Their letters were not structured as well as those of the TLS group and
they did not contain as much mathematical justification, rather, they relied on prior
knowledge to substantiate their arguments.
Notably, after the non-TLS group was taught the TLS strategy, they applied structure
to their oral and written language. The use of key words was more prominent and the
evidence in their oral and written communication showed that they structured their
thinking by comparing the data and actually stating that they were comparing such as:
“because if you compared other teams…” and “Team E…compared to Team F…”
They became focused on mathematical data and were able to use it in analysing,
explaining and justifying. So, using structure helped the students to compare their
ideas, to be discerning and to communicate their ideas as stated by Bartlett, Barton and
Turner (1989).
Non-TLS group 1 particularly demonstrated a significant progression in their ability to
focus their discussion and writing on mathematics after TLS instruction. They were
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able to use mathematical justifications rather than depending on prior knowledge.
Notably, at the time of undertaking the Planes problem, the non-TLS group was
concurrently studying a science unit on Planes. As with the TLS group studying Plants
during the Beans problem, it might have been expected that students would rely more
on prior knowledge gained from science investigations rather than focus on the
mathematical ideas but in both instances that was not the case. Rather, in both
incidents, after being taught TLS, students could focus on the task at hand and the
supporting mathematical data. This observation suggests that TLS instruction helped
students to extract the main idea/s of text information (Pressley & McCormick, 1995).
5.1.2 The effects of TLS on mathematising and constructing mathematical
knowledge
During the Beans investigation, the TLS groups focused more fully on the
mathematical data. They took the approach of either adding the data of the rows
horizontally or looking at individual rows and weeks. This is demonstrated in their
notes and their final representations used as mathematical justifications. This approach
was also seen in the non-TLS group but their discussions and letters reveal a higher
dependence on prior knowledge as is shown in Group2’s letter in Section 4.2.2. The
TLS group discussed the comparison of weight and looked across the data on the tables
to determine trends; “We need to write down weeks 6, 8, and 10 and rows 1, 2, 3 and 4
for sunlight and then we’ll move on to shade.”; “We’re mainly measuring the weights
of butter beans after they’re in sun and shade.”
With the non-TLS groups, one group was confused as they added each amount on the
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tables to gain overall totals of 112 kilograms and 146 kilograms. These groups relied
more on prior knowledge than mathematical data for reasoning. Both non-TLS groups
initially looked only at week 10 results where they saw a definite difference between
sunlight and shade data. The second group went back to week 6, rows 3 and 4 only.
Shannon did notice a discrepancy where in some instances shade recorded more than
sunlight. Although there was this evidence where the non-TLS groups considered data
to some extent, their discussions were interspersed with their prior knowledge. These
students had difficulty focusing on the mathematical data to substantiate their claims.
There is evidence that both the TLS and non-TLS groups gained the mathematical
knowledge of comparing data, aggregating data and measuring weights in Investigation
1 of the Beans problem, but the TLS group were less confused. They were able to
make connections between the data, analyse, explain and justify their ideas
mathematically. The TLS group communicated more effectively because they were
more aware of the main idea of the problem and the text. This was evident in the
structure they used for oral and written communication. It further reflects Bartlett’s
(2003) claims that planning enables beneficial interaction and discussion, and that TLS
can help readers/writers to make sense of problems by identifying relationships within
texts.
As stated in Section 4.2.1 and discussed in Section 4.3.1, both TLS and non-TLS
groups focused on patterning for Investigation 2 of the Beans problem. There was no
specific evidence that TLS played a significant role in this problem.
102
Further evidence that TLS was beneficial in focusing student learning of mathematical
knowledge was gained after the non-TLS group was taught the strategy prior to the
Planes problem. The subsequent development of the non-TLS groups’ ability to focus
on mathematical reasoning throughout the process of this problem (discussed in
Section 4.2.3) provides evidence of positive effects of TLS on mathematical
modelling. Students immediately used the language of TLS to state that they were
comparing the teams. They focused on the mathematics of distance and time and
accounted for the variable of ‘scratches’ as they analysed the data. They gave sound
mathematical reasoning for their decisions; for example, “Because they have 39 points
compared to Team F.” This structure demonstrated in their oral language also emerged
in their written language shown in their letter to the judges in Section 4.2.3: “We think
you should decide…by distance, height, speed and by time…because if you compare
the other team…”
It is acknowledged that the ‘Planes Problem’ was the second mathematical-modelling
problem for both groups therefore both groups were familiar with the requirements of
mathematical modelling. This familiarity would have had some impact on the
outcomes for the Planes problem for both groups but, it is difficult to gauge the exact
extent. Nevertheless, the aspects of structured language appeared to emerge as a result
of TLS instruction.
Students set up the goal of the problem metacognitively using structured language:
“First, we have to…” They were able to distinguish personal knowledge and problem-
solving knowledge, and know when and how to apply each during the mathematical-
103
modelling process (English &Watters, 2004). This would be partly due to their
previous experience but the structured language of comparison shows that TLS has
played some part. Non-TLS group 1 particularly showed positive progression in their
ability to analyse, explain, justify and reason about the data throughout the process.
Their demonstrated outcomes from the Beans problem show they were very confused
compared to their demonstrated outcomes from the Planes problem (see Section 4.2.3).
They showed that they progressed from an over-reliance on prior knowledge and
inability to distinguish their prior knowledge with the task knowledge to interpreting
data and using time, distance and the ‘scratches’ variable to justify their position. It is
noted that as this group was confidently participating in the Planes problem, they were
interrupted by the teacher. Their latter conversation showed that his questions led to
some confusion in the group as they stated they did not understand what he had said
and felt they were on the wrong track. This incident was unfortunate. It demonstrates
that we as teachers need to listen carefully to student interaction. Their letter
demonstrates that they were able to re-focus and concentrate on their mathematical
justifications for their decisions.
5.1.3 Top-level structuring and questioning
The data reported in Section 4.2.4 show that after the Beans problem only the TLS
peers asked high-level questions of the presenters and that these presenters were able to
mathematically justify their positions. No peer questioned the non-TLS group after the
‘beans’ presentations and this group also had difficulty answering the researcher’s
questions. After the Planes presentations, both TLS and non-TLS peers asked relevant
104
questions requiring groups to justify their positions with mathematical proof. Both
groups of presenters could justify their positions mathematically.
Perhaps the role that TLS played here was an indirect one in that students who used the
strategy were more mathematically focused on the tasks and therefore this focus
influenced the questioning stage of the process. Part of the explanation for the non-
TLS groups’ positive development in questioning/answering stage of the process
would be their prior experience with the Beans problem. The non-TLS groups’ active
participation in the questioning segment was much greater that the TLS groups’. They
were much more enthusiastic. This could be due to their positive response to TLS
instruction, the intense TLS implementation over the shorter period, or to their more
positive attitude to the presentation section. It could also be due to the fact that they
had simultaneously completed the science “Planes” unit of work, which could have
contributed to their attitude and confidence.
105
5.2 IMPLICATIONS FOR FURTHER RESEARCH
5.2.1 Implications for mathematical modelling
The problems used in this research contained expository texts, namely:
• factual information on growing beans
• factual information related to flying
• background information establishing the settings for the two
problems
• instructional information for the two problems
Both problems also contained graphical texts in the form of mathematical tables
containing relevant data for the problems. These problems are representative of
mathematical modelling problems. However, other mathematical modelling problems
could contain a range of different text types, for example, mathematical representations
in diagrams, graphs, manipulatives, or other written text types. To engage in
mathematical modelling, students must be able to gain meaning from the information
and work with the information (Sections 2.3; 2.3.1; 2.4; & 2.5).
Consequently, this research has demonstrated positive aspects of applying TLS to
mathematical modelling through its indications that students were helped to construct
mathematical knowledge and to express that knowledge both in written and oral forms.
This gives rise to further research being conducted with mathematical modelling and
TLS to ascertain the extent of the positive effects over longer periods of time, with
students of different ages, both younger and older and with students who are higher
achievers, as well as lower achievers.
Furthermore, it would be desirable for students to apply TLS to mathematical
106
modelling problems containing a wider variety of mathematical representational texts,
such as, graphs of different types. An examination of students’ ability to obtain, recall,
interpret, discuss, and analyse such information using TLS, and also students’
application of TLS to explain models using their own diagrams, graphs, manipulatives,
or other symbolic language, etc. is also of interest.
5.2.2 Implications for mathematics
As has been identified in this thesis, mathematics is not an entity that stands alone, but
rather is set within, and requires its own literacy (Sections 1.1 & 2.4). This study has
shown that there is potential for further research in incorporating TLS with
mathematical texts, such as, word problems in the traditional sense (Section 2.2) where
information could be contained in price lists, menus, advertisements etc., along with
the problem instructions. But, the research could go much further than this, to
examining the structure of mathematical language, for example, something as simple
as ‘two plus two equals four’, has its own structure and its own semantic make-up as
do more complex mathematical statements in numeracy, algebra, measurement, and so
on. Therefore, investigations into the linguistics of these fields and how TLS could
benefit these fields of mathematics could enhance mathematical teaching.
From a multi-disciplinary perspective, the intergration of other curriculum areas with
mathematics is also of interest. As was seen in the mathematical modelling problems
presented in this study, scientific textual settings were used. Other curriculum strands
bring with them their own language and literacy, so when they are intergrated with
107
mathematics, there is yet another level of literacy to be investigated.
5.3 CONCLUSION
Fundamental to children gaining any mathematical knowledge from textually-based
mathematical-modelling problems, is their ability to read and comprehend the text in
which these problems are embedded. Literacy does play a major part in mathematics
learning (Cobb, 2004). Kiewra (2002) argued structural strategies are means of
teaching students how to learn. The present results indicate that young students can be
taught to identify structure in texts (Bartlett, 1979) and that this skill can make positive
changes to their mathematical-modelling outcomes. Through TLS, students have been
taught to thoughtfully structure textual information on two levels: firstly the text/s they
need to read, comprehend, analyse and discuss (ingoing information) and secondly, the
oral and written text that they use to communicate, explain and justify their ideas
(outgoing information).
The research explored the question: ‘to what extent will mathematical modelling be
changed by engaging to-level structuring of text? Regarding the three components of
design methodology: (Section 3.2) the results of this research have established firstly
how TLS effectively changed mathematical modelling. The results indicate that
through incorporating TLS with mathematical modelling, students were able to focus
on:
• the main goal of the problem,
• the mathematical content of the textual information and
• using TLS key words to organise their thinking in order to
communicate through oral and written language.
108
As a result, the students could mathematise more efficiently after TLS instruction and
gain the necessary mathematical knowledge to communicate their understanding
effectively. Having strategic knowledge about how to use text effectively gave
students confidence and encouraged persistence with texts (Meyer, 2003). Therefore,
TLS acted as a springboard to mathematical modelling (Section 2.6). Students had a
starting point, as well as an organisational strategy to apply throughout the modelling
process in their ongoing thinking and oral and written communication. TLS influenced
all areas of mathematical modelling. Rather than a bottom-up strategy with which to
approach problem soling, TLS provided students with a top-down strategy, a meta-
language with which to investigate the problems.
As previously acknowledged in Sections 4.3.2 and 4.3.3, there would have been
transfer of learning from the first problem to the second and so the impact of TLS
would have been affected by this to some extent. I see the questioning stage of the
process as particularly affected by this. Additionally, the implementation of TLS over
the intensive two week program with the non-TLS students (Sections 3.3.2.4 & 4.3)
could have had a more dynamic impact on the students. However, the evidence is clear
through the language used by the non-TLS students that they did engage TLS and it did
aid them in analysing, comparing, explaining and justifying information. When
comparing TLS students to non-TLS students, the latter were not mathematically
focused in the Beans problem. They did not demonstrate the same degree of
mathematising and as a result did not demonstrate a construction of mathematical
knowledge to the same degree. However, this changed after the Planes problem when
109
the non-TLS group did demonstrate mathematising and also construction of
mathematical knowledge.
Secondly, the appropriate design of this research enabled the study to take place in a
real classroom context, to develop the learning environment and to test in that practical
environment (Section 3.2). As a result, this design has allowed the study to
demonstrate clearly that TLS has influenced positive changes to the outcomes of the
mathematical modelling process by addressing the literary nature of mathematical
modelling. The evidence is non-conclusive as to the extent of these changes because it
is not possible to measure the impact of transfer of learning or the TLS implementation
method.
Nevertheless, TLS has complemented the mathematical-modelling process by
equipping students with an organisational strategy with which to discriminate relevant
information and convert textual information to a logical form. In doing so, TLS
extended the potential for thinking mathematically that is, interpreting and
communicating, making sense of powerful mathematical ideas. Therefore in answer to
the final component question of design methodology: ‘when is it appropriate to employ
the strategy?’ - the research has demonstrated that TLS has been able to positively
change mathematical-modelling by instigating a literary tool to support active student
participation in the mathematical-modelling, problem-solving process. Therefore, it is
evident from this research that TLS is an appropriate and beneficial tool to use in
conjunction with the investigation of mathematical-modelling. The research has
opened the way to further investigations of TLS with mathematical modelling and
110
indeed with other mathematical foci requiring mathematical literacy.
111
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education design studies. Educational Researcher, 32(1), 25-27.
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(Eds.), Handbook of research design in mathematics and science education
(pp. 487-512). Mahwah, New Jersey: Lawrence Erlbaum Associates.
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120
APPENDIX 1
LESSON PLANS
TERM 3
121
LESSON OUTLINES
TOP-LEVEL STRUCTURE
The following top-level structure lessons were implemented in conjunction with the
classroom teacher’s integrated program. The texts used were mainly those that were
readily available in the classroom and that the teacher uses as part of her program. Any
other texts that have been devised by the author and are included in this appendix.
Only the outcomes from Language and Literacy have been restated here.
INTRODUCTION TO TOP-LEVEL STRUCTURE
OUTCOMES
Reading and viewing:
Cultural Strand: Making meanings in contexts; Cu 3.2
To demonstrate these reading and viewing outcomes students should know:
Subject matter
• In narratives, main ideas are developed through connections between plot, setting
and descriptions of characters/people, places, events and things.
• In reports and expositions, main ideas are developed by elaborating on ideas and
information with supporting details
Mode and medium
• Ideas and information are organised and linked to guide the audience
Operational Strand: using language systems Op 3.2
To demonstrate these reading and viewing outcomes students should know;
Mode and medium
• Clauses can be combined, using conjunctions to form compound and complex
sentences that elaborate subject matter.
Writing and shaping:
Cultural Strand: Making meanings in contexts Cu 3.3
To demonstrate these writing and shaping outcomes students should know:
Subject matter
• In narratives, main ideas are developed through connections between plot, setting
and descriptions of characters/people, places, events and things.
• In reports and expositions, main ideas are developed by elaborating on ideas and
information with supporting details.
122
Operational Strand: Using language systems Op 3.3
When writing and shaping, students:
• Organise and link ideas using generic structure, layout, and text connectives,
conjunctions and referring words.
• Use noun groups, circumstances, compound and some complex sentences to
develop subject matter.
123
LESSON 1: CREATING LISTS: the following activities are extracts of the class
science program taken directly from the class teacher’s program.
Top level structuring was introduced through these activities. The language of top
level structuring was emphasized throughout the activities.
Learning Activities
(Teacher’s program)
TLS Component Resources
What is soil?
Think, pair, share – What is
soil made of? What is in
soil? How do people and
other living things use soil?
Students (with teacher) list
responses on class concept
map.
Collect soil samples. Use
magnifying glass to observe.
Record findings in lists.
Investigate: soil contains
water, air, organic waste,
living organisms, rocks,
minerals.
Investigate: 3 soil types –
sandy, loamy, clay soils.
Discuss:
1. Authors organise text
in different ways.
2. The students will
become detectives; their
task will be to identify
the different ways that
text is organised.
3. The first example is
listing- find lists around
the room- draw
attention to the class
concept map made up of
several lists.
Use the soil samples to
create lists on types of
soils.
Read “What is Soil”.
As detectives,
investigate the text and
use the information to
create a list about soil.
Introduce the KEY
words (helping words)
that help to identify the
author’s plans. Find the
key words in the text.
Text: Investigating our
world- What is Soil?
Soil samples, magnifying
glass, observation sheet
Rock samples
TLS detective poster: This
lists the key words for the
listing plan.
124
LESSON 2: COMPARISON: Note that as we moved through the lessons, we kept
referring back to the plans that have been previously taught. This was because
there is usually more than one plan represented in a whole text, but one usually
stands out as the overwhelming plan of the whole text. Ultimately, students put a
plan on to the text they encounter. While one particular plan may be best, it does
not really matter if the student does not choose this plan. The important thing is for
the student to apply a structure so that he/she can organise the information. As the
students gain experience, they become more competent in choosing the best plan.
Learning Activities
(Teacher’s program)
TLS Component Resources
What is rock?
Investigate different types
of rocks.
Sedimentary, igneous,
metamorphic.
Revise listing.
Investigate posters: Create
two lists describing the
soil types evident in the
posters.
Revisit the key word
detective poster.
Read the text: What is
rock? Be detectives.
Look for the key words.
Note that we are reading a
description. Listing is also
known as description..
Continue reading the text
on sedimentary, igneous
and metamorphic rocks.
Discuss the attributes of
each rock type. Look for
similarities and
differences.
Introduce the concept of
comparison.
Introduce the new
comparison detective
poster.
Be detectives: look for
comparison key words.
Demonstrate how these are
used in a comparison text.
Posters:
Farming
Bush scene
Investigating our world –
What is rock?
Rock samples
TLS detective poster:
Comparison key words.
125
LESSON 3: PROBLEM/SOLUTION: This lesson was independent of the class
teacher’s program but complemented her maths program and continued the science
conceptual framework of plants.
The students continued playing the part of detectives throughout the following
lessons whenever they search for key words and authors’ plans.
TLS Activity Resources
Refer back to the plans already
introduced: listing/description,
comparison.
Discuss different types of texts: written
texts, diagrams, tables, pictures etc.
Refer to texts we have already
investigated i.e. the soil posters, concept
maps/diagrams, written information.
Investigate the different plans we can
apply to the different texts and why a
particular plan is chosen.
Introduce information presented in tables.
Present the ‘flower farm’ problem. Work
through this with the children.
Focus on the problem and solutions
offered.
Note the key words.
Refer to the Problem/Solution detective
poster.
Previously used resources: pictures,
concept maps, written texts
Problem solving sheet: Farmer Bill’s
Flower Farm.
TLS detective poster: Problem/Solution
Key Words.
126
PROBLEM SOLVING YEAR 4
FARMER BILL’S FLOWER FARM
Bill has a flower farm and sells flowers to the markets in most months of the
year. What seems to be the best season for Bill to make the most money in
2005?
First, think about the question.
The problem is_______________________________________________
__________________________________________________________.
What information can I use to help me find a solution? _______________
__________________________________________________________.
Bill’s flower totals for 2004
Month Total of Flowers Sold
January 1600
February 536
March 815
April 612
May 588
June 350
July 0
August 0
September 4150
October 6400
November 2285
December 2260
127
Now, think about the Table:
Which months show there is a problem growing flowers?____________
__________________________________________________________
___________________________________________________________
Why do you think there is a problem during these months?
_____________________________________________________________
________________________________________________________Where
on the table can you see a solution for the problem?
___________________________________________________________
*Go back and read the original question at the top of Page 1.
Using the information from the table, write your solution for Bill?
_____________________________________________________________
_____________________________________________________________
_______________________________________________________Why
have you decided on this solution?_________________________
_________________________________________________________
_________________________________________________________
Show your proof below:
MY FINAL SOLUTION
The best season for Bill to make the most money is _________________
Because ____________________________________________________
128
LESSON 4: CAUSE/EFFECT
Learning Activities
(Teacher’s program)
TLS Component Resources
How we use plants –
Discuss objects that have
plant origins.
Plants are Living Things-
Explore ways plants move
using microscope
What do plants need to
grow? – Nutrients, soil,
water, sunlight.
Growing plants:
All about seeds. Reading
information page.
Planting seeds
Characteristics of a flower.
Listing plant needs.
Introduce cause/effect
Observe plants from the
classroom.
What are the possible
causes of particular plants
growing well/not growing
well?
What are the possible
effects of not providing:
1. The right soil
2. Water
3. Sunlight
Look for key words as the
information page is read
and discuss the plans used.
Note the key words for
cause/effect on the poster.
Complete the cause/effect
sentences on the sheet with
the students.
Investigate the hibiscus
flowers and list the
components of a flower.
Earth & Life Science
Series – Plants.
Terrific Topics – Book 2
Plants p. 82
Containers, soil, cotton
wool, seeds.
Soil samples – sandy,
loamy, clay.
Magnifying Glasses
Sketch paper
Hibiscus flowers
TLS detective poster:
Cause/Effect key words.
TLS Cause/Effect sheet:
Complete the sentences –
Based on Information Page
‘All about seeds” Ready-
Ed Publications.
129
AUTHORS’ PLANS
CAUSE AND EFFECT
Use your information sheet: ALL ABOUT SEEDS to complete the
sentences on the following table. The first one is done for you.
CAUSE KEY
WORD
EFFECT
Some seeds have little spikes or a
sticky glue
that makes them stick to an
animal.
so they stick to birds as they
eat the fruit around the seed.
Pollen is a golden dust that attracts
bees and other insects
so
if a seed has enough water and
sunlight.
A seed will not grow if
A seed may not grow because
130
LESSON 5: LISTING/DESCRIPTION AND COMPARISON
Learning Activities
(Teacher’s program)
TLS Component Resources
Observation of plant
characteristics:
Types of plants: nature walk: take observations on
size, shape, colour, other
distinguishing features.
Collect samples.
Magnifying glass
investigations.
Comparison: Children fill
in their observations as
lists on their sheet thus
forming a table of
comparisons.
Children compare the
features of plants.
Continue to make
comparisons according to
the various attributes using
magnifying glasses
Use key words while
listing and comparing.
Observation sheet- size,
shape, colour,
distinguishing features.
Samples of leaves,
flowers, twigs, bark
Magnifying glasses.
Sketch paper.
LESSON 6: PROBLEM/SOLUTION AND CAUSE/EFFECT
Learning Activities
(Teacher’s program)
TLS Component Resources
Investigate global
warming:
What is global warming?
Oxygen/Carbon dioxide
The oxygen cycle
Investigate the information
on the cause/effect
diagram and list the causes
and effects.
Discuss: What are the
problems that contribute to
the greenhouse effect?
Create posters
demonstrating a chosen
problem and a possible
solution for that problem.
?????
A4 poster card: one sheet
per child.
Diagram: causes of carbon
dioxide in the air.
Sheets: cause/effect
diagram
131
As a culmination to these learning experiences, children were given an Authors’
Plans practice book. This also formed part of the assessment for the students.
The following activity was given to the students to complete for their class portfolios.
This was requested by the teacher so that she would also have a student example of
work for her own records.
132
APPENDIX 2
Beans, Beans, Glorious Beans
133
Beans are a very popular vegetable crop because they are easy to grow and healthy to eat. There are many types of beans around, which have different uses. Farmer Ben Sprout is delighted to discover that beans are the vegetable to grow. So that he can make the right decision, Farmer Sprout finds out more on beans. He discovers that beans grow as either bush plants or climbing plants.
1. Bush bean plants are low growing and need no support. They will grow up to 30cm high.
2. Climbing bean plants start reaching for the
sky as they grow. They grow very tall, some up to 200 cm high and need to have a trellis to climb up. This is so that they don’t lie on the ground and get eaten or damaged.
The main kinds of beans available are Green Snap beans, Yellow beans, Butter beans, Shell beans and Broad beans. Green Snap beans grow as either bush or climbing bean plants. These are picked just as the beans reach full size, but before the pod gets too fat. If the pod gets too fat then the bean will lose its sweetness and become bitter. Yellow beans only grow as a bush plant. Most agree that it is better tasting and tenderer than green beans. Butter beans grow as either climbing or bush plants. They are flat and rounded beans with a distinct flavour. Broad beans are grown for the big, fat beans that taste great in soups. These beans prefer a cool growing season and do not like our hot summer weather. Shell beans are grown for the bean inside the pod. The most common one is the Navy bean, which is used to make baked beans.
In fact, you could say that there is a bean for everyone.
The Sprout family tasted many kinds of beans and all voted that the best tasting beans are the Butter beans. Now that Farmer Sprout has made his decision to grow Butter beans, he needs to choose whether to grow bush beans or climbing beans. Here are some more important facts to consider. Climbing beans produce more beans and continue to bloom for a longer period than bush beans. Ground bugs won’t bother climbing beans as much as bush beans and any pests that need to be removed are easier to see on climbing beans.
All beans prefer good soil that is warm, well fertilised and not too dry. Too much moisture in the soil will rot the seed and plant. After learning about the differences between climbing beans and bush beans, Farmer Sprout decided to grow climbing Butter beans
134
Readiness Questions
1. What is the difference between bush beans and climbing
beans?
2. Why are climbing bean plants better to grow than bush bean plants?
3. What kinds of conditions would you test to find good ways to grow bean
plants?
4. What are some things climbing bean plants need to grow well?
135
Butter Beans Problem
Farmer Sprout is trying to decide which light conditions are best for growing
Butter beans.
To help Farmer Sprout make his decision, he went to visit the Farmers’
Association who are growing climbing Butter bean plants using two different
light conditions. The two light conditions being tested are: -
a) Growing Butter beans out in the full sun with no
shade at all, and
b) Growing Butter beans underneath shadecloth.
The Farmers’ Association measured and recorded the weight of Butter beans
produced after eight weeks. They grew 3 rows of Butter bean plants using each
type of light condition.
Sunlight Shade
Butter
Bean
Plants Week 6 Week 8 Week 10
Butter
Bean
Plants Week 6 Week 8
Week
10
Row 1 9 kg 12 kg 13 kg Row 1 5 kg 9 kg 15 kg
Row 2 8 kg 11 kg 14 kg Row 2 5 kg 8 kg 14 kg
Row 3 9 kg 14 kg 18 kg Row 3 6 kg 9 kg 12 kg
Row 4 10 kg 11 kg 17 kg Row 4 6 kg 10 kg 13 kg
136
Your first investigationYour first investigationYour first investigationYour first investigation
Using the data above, determine which of the light conditions is suited to
growing Butter beans to produce the greatest crop. In a letter to Farmer Ben
Sprout, outline your recommendation of light condition and explain how you
arrived at this decision.
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
137
Your second investigationYour second investigationYour second investigationYour second investigation
Predict the weight of butter beans produced on week 12 for each type of light.
Explain how you made your prediction so that Farmer Ben Sprout can use it
for other similar situations.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
138
APPENDIX 3
Beans, Beans, Glorious Beans WITH TLS NOTE TAKING GUIDELINES
139
Beans, Beans, Glorious Beans
USE YOUR AUTHOR’S PLANS!
140
Beans are a very popular vegetable crop because they are easy to grow and healthy to eat. There are many types of beans around, which have different uses. Farmer Ben Sprout is delighted to discover that beans are the vegetable to grow. So that he can make the right decision, Farmer Sprout finds out more on beans. He discovers that beans grow as either bush plants or climbing plants.
3. Bush bean plants are low growing and need no support. They will grow up to 30cm high.
4. Climbing bean plants start reaching for the
sky as they grow. They grow very tall, some up to 200 cm high and need to have a trellis to climb up. This is so that they don’t lie on the ground and get eaten or damaged.
The main kinds of beans available are Green Snap beans, Yellow beans, Butter beans, Shell beans and Broad beans. Green Snap beans grow as either bush or climbing bean plants. These are picked just as the beans reach full size, but before the pod gets too fat. If the pod gets too fat then the bean will lose its sweetness and become bitter. Yellow beans only grow as a bush plant. Most agree that it is better tasting and tenderer than green beans. Butter beans grow as either climbing or bush plants. They are flat and rounded beans with a distinct flavour. Broad beans are grown for the big, fat beans that taste great in soups. These beans prefer a cool growing season and do not like our hot summer weather. Shell beans are grown for the bean inside the pod. The most common one is the Navy bean, which is used to make baked beans.
In fact, you could say that there is a bean for everyone.
The Sprout family tasted many kinds of beans and all voted that the best tasting beans are the Butter beans. Now that Farmer Sprout has made his decision to grow Butter beans, he needs to choose whether to grow bush beans or climbing beans. Here are some more important facts to consider. Climbing beans produce more beans and continue to bloom for a longer period than bush beans. Ground bugs won’t bother climbing beans as much as bush beans and any pests that need to be removed are easier to see on climbing beans.
All beans prefer good soil that is warm, well fertilised and not too dry. Too much moisture in the soil will rot the seed and plant. After learning about the differences between climbing beans and bush beans, Farmer Sprout decided to grow climbing Butter beans. Group Work:
1. Underline the key words. 2. Decide on your authors’ plan. 3. Discuss the reasons why you chose that
particular plan. 4. Write the author’s plan you have chosen
on the line below. ______________________________
141
Readiness Questions
5. What is the difference between bush beans and climbing
beans?
6. Why are climbing bean plants better to grow than bush bean plants?
7. What kinds of conditions would you test to find good ways to grow bean
plants?
8. What are some things climbing bean plants need to grow well?
142
Butter Beans Problem
Farmer Sprout is trying to decide which light conditions are best for growing
Butter beans.
To help Farmer Sprout make his decision, he went to visit the Farmers’
Association who are growing climbing Butter bean plants using two different
light conditions. The two light conditions being tested are: -
c) Growing Butter beans out in the full sun with no
shade at all, and
d) Growing Butter beans underneath shadecloth.
The Farmers’ Association measured and recorded the weight of Butter beans
produced after eight weeks. They grew 3 rows of Butter bean plants using each
type of light condition.
Sunlight Shade
Butter
Bean
Plants Week 6 Week 8 Week 10
Butter
Bean
Plants Week 6 Week 8
Week
10
Row 1 9 kg 12 kg 13 kg Row 1 5 kg 9 kg 15 kg
Row 2 8 kg 11 kg 14 kg Row 2 5 kg 8 kg 14 kg
Row 3 9 kg 14 kg 18 kg Row 3 6 kg 9 kg 12 kg
Row 4 10 kg 11 kg 17 kg Row 4 6 kg 10 kg 13 kg
143
CHOOSING YOUR AUTHOR’S PLAN
1. Look carefully at the tables: There are two tables:- one for sunlight and
one for shade.
2. What author’s plan is being used?
3. Author’s Plan = ________________________________________________
4. Use the author’s plan you have chosen to organise the information you
read on the tables.
144
YOU MAY WISH TO WRITE MORE NOTES HERE.
SUNLIGHT NOTES
1.
2.
3.
SHADE NOTES
1.
2.
3.
145
Use the notes to write the information that you have learnt from the tables.
Remember, use an author’s plan when you write.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
__________________________________________
Your first investigationYour first investigationYour first investigationYour first investigation
Using the data above, determine which of the light conditions is suited to
growing Butter beans to produce the greatest crop. In a letter to Farmer Ben
Sprout, outline your recommendation of light condition and explain how you
arrived at this decision.
REMEMBER USE AN AUTHOR’S PLAN TO HELP ORGANISE YOUR
LETTER.
Choose EITHER 1. cause/effect 2. problem/solution 3. comparison or 4.
listing/description.
IT’S GREAT TO USE KEY WORDS FROM YOUR AUTHOR’S PLAN WHEN
YOU WRITE.
146
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
_________________________________________
147
Your second investigationYour second investigationYour second investigationYour second investigation
Predict the weight of butter beans produced on week 12 for each type of light.
Explain how you made your prediction so that Farmer Ben Sprout can use it
for other similar situations.
USE AN AUTHOR’S PLAN TO HELP YOU ORGANISE YOU
EXPLANATION.
(THINK ABOUT CAUSE/EFFECT OR PROBLEM/SOLUTION)
148
APPENDIX 4
TLS PRACTICE BOOK
149
AUTHORS’ PLANS PRACTICE BOOK 1 Listing / Description Listing / Description Listing / Description Listing / Description
Comparison Comparison Comparison Comparison PPPPrrrroooobbbblllleeeemmmm //// SSSSoooolllluuuuttttiiiioooonnnn Cause / Effect Cause / Effect Cause / Effect Cause / Effect
Name: ______________________
Year 4. KATHERINE DOYLE
QUEENSLAND UNIVERSITY OF TECHNOLOGY
KELVIN GROVE CAMPUS
150
Author’s Plans and Key Words
Listing / Description Comparison
And
Also
Include
Besides
First, second, third
Lastly
Finally
For example
Such as
That is
Namely
Characteristics are
But
In contrast
However
On the other hand
Whereas
The same as
Different
Compared to
Instead
Problem / Solution Cause / Effect
Problem
Question
Solution
Answer
Puzzle
To solve this
As a result
Because
So
Since
Caused
Led to
Consequence
Thus
This is why
The reason is
Therefore
151
TEXT: THE CYCLE OF PLANTS
Notice that the diagram relates to our investigations on plants. We have
already looked at seeds sprouting in our worm farm. The information that
we have discovered is in the diagram so the diagram is our text. Let’s use
the diagram to write about what we have been learning.
Author’s Plan: ____________________________________________
Main Idea: ________________________________________________
Now write some sentences about the main idea.
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
Katherine Doyle
seeds
shoot
roots leaves
stem
flower
152
TEXT: THE DANDELION
Write the parts of the dandelion on the lines provided.
(Inset manual drawing of dandelion)
Author’s Plan: _____________________________________________
Main Idea: _____________________________________________
Write some sentences about the main idea.
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
Katherine Doyle
153
TEXT: PLANTS
There are many types of plants in the world. They have special needs so that
they can grow well. Firstly, they need nutrients. Plants also need soil. As
well they need water and sunlight.
Key Words:
Author’s Plan __________________________________________________
Main Idea: _________________________________________________
Use your notes to write about plants.
___________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
___________________________________________________________ Katherine Doyle
Main Idea
Note 1 Note 2 Note 4 Note 3
154
1.
2.
Compare / Contrast
Main Idea:___________________________________________________
Complete the sentence:
In picture 1, the flowers have long stems and narrow heads but in picture 2,
the flowers have _______________________________________________.
Katherine Doyle
Picture 1
Note 1 Note 2 Note 3
Picture 2
Note 1 Note2 Note 3
155
SOILS:
Think of two different soil types we have investigated at school. What was
the same and what was different about them?
Write the headings for the soil types:
Now list the points about each soil type:
Now, you have written your notes. Use these notes to help you to write a
comparison about the two soils. Some of the key words are there to help
you.
Soil Types at School
The _________________soil is _______________________but the other
soil is ___________________________. The ___________________soil is
different from the ___________________________ because it has________
_________________________________________________________in it.
However, the ________________________ soil does not seem to have
these properties. I think plants would grow well in the ______________soil.
On the other hand, I do not think plants would grow well in the __________
soil.
• Go back and underline all the key words that help you to know that this is a
COMPARISON about soils.
Katherine Doyle
156
Read the following text. Underline the key words.
PLANT FACTS
Plants live and grow all over the world. Most plants need plenty of fresh
water to grow but some plants live where there is very little water --- in the
desert. Other plants grow where there is only salt water ----in the ocean.
Author’s Plan ---- ___________________________________________
Text from: Go Facts --- Plants
Main idea
_________________
Note 1
_________________
_________________
_________________
Note 2
_________________
_________________
_________________
Note 3
_________________
_________________
_________________
____
157
Read the text. Underline the key words.
PLANT HOMES
Flowering plants live in many different parts of the world. Rainforests,
deserts and cold mountains are all places where different flowering plants
grow.
Rainforests get plenty of rain, warmth and sun so lots of plants grow well
there. Trees, vines and other tropical plants grow in the rainforest.
However, deserts are hot, dry places with not much water. Plants that grow
in the desert need to store water in thick, fleshy stems. Cactus plants like the
desert.
In contrast to these places, there are the high mountain areas called alpine
areas. Alpine areas have long cold winters when the ground is frozen, short
summers and strong winds. Plants need to grow during the short summers.
They must flower and make seeds quickly.
Author’s Plan = ________________________________________________
Main Idea = __________________________________________________
_____________________________________________________________
Now use the diagram on the next page to take your notes from the passage.
Reference: Go Facts ---- Flowers
158
MY NOTES. Plant Homes
Katherine Doyle
Heading 3
-----------------
Note 1
------------------
------------------
------------------
Note 2
------------------
------------------
------------------
Note 3
------------------
------------------
------------------
Heading 2
-----------------
Note 1
-------------------
-------------------
-------------------
--------------
Note 2
-------------------
-------------------
-------------------
---------
Note 3
-------------------
-------------------
-------------------
----------------
Heading 1
----------------
-
Note 1
----------------
----------------
----------------
----------------
Note 2
----------------
----------------
----------------
----------------
Note 3
----------------
----------------
----------------
----------------
159
Now use your notes to write about plant homes. Remember to use good
sentences. Use some key words in your writing.
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
160
THE LIFE CYCLE OF A BEE
Read and follow the life cycle of the bee.
Underline the Key Words. LIST THE KEY WORDS IN THE BOXES BELOW.
Which author’s plan would you use on the text?________________________________
Why did you choose this plan? ______________________________________________
_______________________________________________________________________
1. First the queen
bee lays all the eggs.
Each egg is inside a
honeycomb cell.
3. Next the larva
grows into a pupa
and the pupa grows
into a bee.
4. Finally, the adult
bee breaks out of the
honeycomb.
Growing from egg to
adult takes about
three weeks.
2. Then each egg
grows into a larva
and the worker bees
feed and care for the
larva.
161
Text from Go Facts --- Insects
Write your notes in the boxes.
Put your title in the main rectangle. Think about the main idea.
Now use your notes to write your own text about bees.
________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
162
Katherine Doyle
THE QUILTING CLUB
May, Tess, Bob and Frank have all go to quilting club. They’re making honeycomb
patchwork quilts. They all have the same selection of fabrics with patterns and
colours. Their problems are that none of them are allowed to use the same fabric
side by side in their quilt and none of them are allowed to use the same design as
anyone else in their quilt.
AUTHOR’S PLAN = _______________________________________
In groups of four use the information in the table to help them work out four
different designs so that each person will have their own unique quilt. Each
person in your group can colour a different design on the honeycomb above.
COLOUR PATTERN
FABRIC 1 WHIITE * * * * * * * * * *
* * * * * * * * * *
FABRIC 2 BLUE
FABRIC 3 ORANGE
FABRIC 4 PURPLE
Katherine Doyle
163
Photo: Katherine Doyle
THE GIANT’S CAUSEWAY
In Northern Ireland there is a special place called “The Giant’s Causeway”. There
are some 40 thousand columns of volcanic basalt rock jutting out to sea. These were
formed as a result of volcanic action. The columns were formed by the slow and
even cooling and contraction of molten lava.
UNDERLINE THE KEY WORDS IN THE INFORMATION ABOVE.
164
NOW, COMPLETE THE TABLE BY WRITING YOUR OWN SENTENCE ABOUT
THE GIANTS CAUSEWAY.
CAUSE KEY WORD EFFECT
______________________
______________________
______________________
__________________
__________________
_________________
_________________
__________________
The sentence you have written is the main idea of the text.
More information on THE GIANT’S CAUSEWAY:
The rock formations are amazing! About half of them are hexagonal. Others have
four, five, seven or eight sides. There are also some really fun structures like: the
Wishing Chair, the Keystone, the Honeycomb, the Giant’s Loom and the Giant’s
Organ, the King and his Nobles, the Horse Back, the Harp and others as well.
UNDERLINE THE KEY WORDS.
WHAT AUTHOR’S PLAN ARE YOU GOING TO USE? ______________
WHAT IS THE MAIN IDEA OF THE TEXT? ___________________________________
_______________________________________________________________________
The Chimney Tops is another formation. Because of erosion, it is separated from
the surrounding cliffs. In the 16th
century when the Spanish Armada was passing
by, some of the sailors thought these rock formations were actually a castle so they
opened fire at the rocks.
UNDERLINE THE KEY WORDS.
165
WHAT AUTHOR’S PLAN IS USED IN THIS INFORMATION TEXT?
_____________________________________________________________________
THE MAIN IDEA IS: ___________________________________________________
______________________________________________________________________
______________________________________________________________________.
USE THE INFORMATION IN THE ABOVE TEXT TO COMPLETE
THE SENTENCES IN THE TABLE BELOW.
Effect Key Word Cause
The Chimney Tops are
separated from surrounding
cliffs
__________________
______________________
Cause Key Word Effect
so
Information on the Giants Causeway from: Readers’ Digest “Illustrated Guide to Ireland”.
166
THE LEGEND OF FINN MACCOOLTHE LEGEND OF FINN MACCOOLTHE LEGEND OF FINN MACCOOLTHE LEGEND OF FINN MACCOOL
Long ago on the northern coast of Ireland Long ago on the northern coast of Ireland Long ago on the northern coast of Ireland Long ago on the northern coast of Ireland ------------ around about 300 BC roamed a giant called Finn around about 300 BC roamed a giant called Finn around about 300 BC roamed a giant called Finn around about 300 BC roamed a giant called Finn
MacCool . He was about 16 metres tall which is not really tall for a giant. But, across the nMacCool . He was about 16 metres tall which is not really tall for a giant. But, across the nMacCool . He was about 16 metres tall which is not really tall for a giant. But, across the nMacCool . He was about 16 metres tall which is not really tall for a giant. But, across the narrow arrow arrow arrow
sea of Moyle in Scotland lived a rival giant called Benandonner. The two giants would yell across the sea of Moyle in Scotland lived a rival giant called Benandonner. The two giants would yell across the sea of Moyle in Scotland lived a rival giant called Benandonner. The two giants would yell across the sea of Moyle in Scotland lived a rival giant called Benandonner. The two giants would yell across the
sea to each other arguing about who was the strongest. sea to each other arguing about who was the strongest. sea to each other arguing about who was the strongest. sea to each other arguing about who was the strongest.
Finn had a great idea! He decided to build a type of bridge Finn had a great idea! He decided to build a type of bridge Finn had a great idea! He decided to build a type of bridge Finn had a great idea! He decided to build a type of bridge ------------ a causeway a causeway a causeway a causeway –––– so that Benandonner so that Benandonner so that Benandonner so that Benandonner
could come across to Ireland and they could test their strength. So, Finn began to tear down great could come across to Ireland and they could test their strength. So, Finn began to tear down great could come across to Ireland and they could test their strength. So, Finn began to tear down great could come across to Ireland and they could test their strength. So, Finn began to tear down great
pieces of volcanic rock and stood the rocks side by side to make pillars. The pillars spread out across pieces of volcanic rock and stood the rocks side by side to make pillars. The pillars spread out across pieces of volcanic rock and stood the rocks side by side to make pillars. The pillars spread out across pieces of volcanic rock and stood the rocks side by side to make pillars. The pillars spread out across
the sea to Scotland. Now, Bthe sea to Scotland. Now, Bthe sea to Scotland. Now, Bthe sea to Scotland. Now, Benandonner had a pathway to Ireland. enandonner had a pathway to Ireland. enandonner had a pathway to Ireland. enandonner had a pathway to Ireland.
As Benandonner stepped across the causeway moving closer to Ireland, he was spotted by Finn’s wife As Benandonner stepped across the causeway moving closer to Ireland, he was spotted by Finn’s wife As Benandonner stepped across the causeway moving closer to Ireland, he was spotted by Finn’s wife As Benandonner stepped across the causeway moving closer to Ireland, he was spotted by Finn’s wife
Oonagh. Oonagh saw that he was really gigantic which caused her to worry about herOonagh. Oonagh saw that he was really gigantic which caused her to worry about herOonagh. Oonagh saw that he was really gigantic which caused her to worry about herOonagh. Oonagh saw that he was really gigantic which caused her to worry about her Finn. Finn Finn. Finn Finn. Finn Finn. Finn
was not nearly as huge as Benandonner and he was tired after moving all the rocks! Consequently, was not nearly as huge as Benandonner and he was tired after moving all the rocks! Consequently, was not nearly as huge as Benandonner and he was tired after moving all the rocks! Consequently, was not nearly as huge as Benandonner and he was tired after moving all the rocks! Consequently,
she had a very brainy idea. She dressed Finn up in a nightgown and bonnet and told him to have a she had a very brainy idea. She dressed Finn up in a nightgown and bonnet and told him to have a she had a very brainy idea. She dressed Finn up in a nightgown and bonnet and told him to have a she had a very brainy idea. She dressed Finn up in a nightgown and bonnet and told him to have a
sleep.sleep.sleep.sleep.
Benandonner came booming in looking forBenandonner came booming in looking forBenandonner came booming in looking forBenandonner came booming in looking for Finn. Oonagh whispered “Be quiet or you’ll wake the Finn. Oonagh whispered “Be quiet or you’ll wake the Finn. Oonagh whispered “Be quiet or you’ll wake the Finn. Oonagh whispered “Be quiet or you’ll wake the
baby.” Benandonner looked at the sleeping Finn and his face went pale with panic. If this is just the baby.” Benandonner looked at the sleeping Finn and his face went pale with panic. If this is just the baby.” Benandonner looked at the sleeping Finn and his face went pale with panic. If this is just the baby.” Benandonner looked at the sleeping Finn and his face went pale with panic. If this is just the
baby, how huge is his father Finn? baby, how huge is his father Finn? baby, how huge is his father Finn? baby, how huge is his father Finn?
Since the thought of this was so scary, Benandonner turned Since the thought of this was so scary, Benandonner turned Since the thought of this was so scary, Benandonner turned Since the thought of this was so scary, Benandonner turned around in fright and ran across the around in fright and ran across the around in fright and ran across the around in fright and ran across the
causeway as fast as he could to hide away from the mighty Finn.causeway as fast as he could to hide away from the mighty Finn.causeway as fast as he could to hide away from the mighty Finn.causeway as fast as he could to hide away from the mighty Finn.
Story adapted from: http://www.giantscausewayofficialguide.com/once01.htm
167
COMPLETE THE FOLLOWING SENTENCES.
1. Comparison:
Finn MacCool was about 16 metres tall but __________________________________
_______________________________________________________________________.
2.Cause / Effect
________________________________________________________________so that
Benandonner could come across to Ireland.
3. Cause / Effect
Finn decided to tear down great pieces of volcanic rock so _____________________
4. Cause / Effect
__________________________________________________________________which
caused Oonagh to worry.
5. Comparison
_____________________________________________________________as huge as
Benandonner.
5. Cause / Effect
____________________________________________________________consequently
Oonagh had a brainy idea.
7. Cause / Effect
Benandonner ran back to Scotland since ____________________________________
_______________________________________________________________________.
Katherine Doyle
168
CONGRATULATIONS! You now know the Authors’ Plans and the key
words that help you decide which plan an author uses on information text.
Now it’s your turn to show off how clever you are!
First, read the following text.
What is a Plant?
Plants are living things that use energy from the sun to make their own
food. Plants are the only living thing that can make their own food.
Leaves are like food factories. Plants take in sunlight, air and water
and change them into food. Since plants make food in their leaves, they
are the basis for all other life on Earth.
Plants can live in the sea and on the land. They come in all shapes and
sizes, from tiny water plants to huge forest trees. Plants grow anywhere
there is light and water.
Think about what you will do now. Remember:
• You need to decide on the main idea of the text
• You need to take some notes in an organised way. Use an author’s
plan.
• Use your notes to write your own text.
Text from Go Facts – Plants
169
___MY NOTES_
(you can draw diagrams or take your notes in any way that helps you to organise
your writing)
170
MY TEXT
___________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
171
APPENDIX 5
TERM 4 LESSON OUTLINES
(NON-TLS GROUP)
172
TLS IMPLEMENTATION LESSON OUTLINES:
NON-TLS GROUP
TERM 4
Lesson 1 Introduction
Discuss:
1. Authors organise text in different ways. Identify text types
2. Students will become detectives; their task will be to identify the
different ways that text is organised according to the author’s plan.
3. First example – listing: Identify lists around the room and in
everyday life.
4. Continue to investigate lists and ‘key words’ that help identify
something as a list.
Lesson 2 Soil
• Investigate soil samples: Clay, Sandy etc
• Create lists to describe the samples
• Read “What is Soil”. Investigate the text and use the information to
create a list on soil.
• Identify any key words in the text.
• Discuss: the list forms our notes taken from the text. We can use
these notes to write our own information that we have learnt from
reading this text.
Lesson 3
• Introduce detective poster of key words.
• Revise listing.
• Read “What is Rock” - a description.
• Make lists re: sedimentary, igneous and metamorphic rocks
Lesson 4 Comparison
• Introduce Comparison
• Detective poster – comparison
• Refer back to text on Rocks.
• Use the text to make comparisons about the rocks.
• Discuss the fact that it is important to put an author’s plan on the
text. Sometimes one plan is better that another. What would be
the best plan for the “rocks” text? Why?
173
Lesson 5 Problem/solution
• Revise listing/description and comparison
• Introduce problem/solution: show dead plant in the pot:- What
could be the problem here? What could be the solution here?
• Detective poster:- problem/solution
• Read problem/solution passages: pollution and early settlers and
identify the key words and structure.
Lesson 6
• Discuss different text types: expository, graphic and narrative
examples.
• Refer back to the Beans Problem and the ‘table’ from which we
gathered our information.
• Investigate the comparison on the table.
• Introduce the ‘flower farm’ problem.
• Work through with the children.
• Identify ‘key words’ and structure.
Lesson 7 Cause/Effect
• Introduce cause/effect.
• Discuss key words – poster
• Read “All About Seeds” and investigate structure of text.
• Complete the accompanying sheet.
Lesson 8
• Investigate the cause/effect pollution poster
• List the causes and effects
• Complete the ‘Plants and Global warming sheet
Following these lessons the students will work through the TLS practice
booklet.
174
Pollution:
Pollution is a problem for our rivers. Polluted rivers are eyesores.
They are also health hazards. One solution is to stop the dumping of
industrial waste.
Key Words: ______________________________________________
Author’s Plan: ____________________________________________
PROBLEM SOLUTION
Now, write a sentence of your own:
___________________________________________________________
___________________________________________________________
Text 2:
When the early settlers first came to Australia, they did not know which
Australian plants could be used as bush tucker. The question they thought
about was: how would they get enough food? To solve this, they brought
out many different types of seeds from their homeland. They then planted
these seeds and grew their own food here in Australia.
Key Words: ________________________________________________
__________________________________________________________
Author’s Plan:- ____________________________________________
175
Read the following text and use the key words to help you find the author’s plans.
PLANTS AND GLOBAL WARMING
When plants make food, they take up carbon dioxide and give out oxygen. Animals, on
the other hand, take up oxygen and give out carbon dioxide. Other natural processes on
earth also add carbon dioxide to the air, for example plant and animal death, pollution
from industry and motor vehicles as well as volcanoes and burning wood and coal.
UNDERLINE THE KEY WORDS IN THE PARAGRAPH YOU HAVE JUST READ.
NOW, COMPLETE THESE SENTENCES AND WRITE THE AUTHOR’S PLAN FOR
EACH SENTENCE.
1. Plants give out ____________________________, on the other hand, animals
give out _________________________________.
THE AUTHOR’S PLAN IS __________________________________
2. Plants take up carbon dioxide and give out oxygen so that they can make
____________________.
THE AUTHOR’S PLAN IS __________________________________.
3. Natural processes that add to carbon dioxide include ________
_____________________________________________________________
_________________________________________________________
THE AUTHOR’S PLAN IS ___________________________________
READ THE FOLLOWING TEXT.
Some of the gases in the earth’s atmosphere trap the sun’s heat and help
keep the earth warm. This is called the greenhouse effect. Carbon dioxide
176
is the main greenhouse gas. Although this effect is useful in keeping the
earth warm for us, lots of processes in our modern world are releasing too
much carbon dioxide into the air.
Because of this, the world is gradually heating up. This is called global
warming. Scientists think global warming is likely to cause droughts in
some parts of the world and perhaps flooding in other parts of the world as
polar ice-caps melt.
UNDERLINE THE KEY WORDS.
NOW CHOOSE ONE AUTHOR’S PLAN THAT YOU WOULD LIKE TO PUT ON
THIS TEXT.
MY AUTHOR’S PLAN = ____________________________________
NOW WRITE THE MAIN IDEA OF THE TEXT USING THE AUTHOR’S PLAN
YOU CHOSE.
THE MAIN IDEA OF THE TEXT IS
________________________________________________________________________
________________________________________________________________________
177
APPENDIX 6
THE PAPER PLANES CONTEST
178
THE OLW TIMES
Students fly away in the Annual Paper Airplane
Contest at local school
If the Wright Brothers,
pilots, and aircraft
engineers can do it,
surely the students in
our school’s year four
classes can do it.
What will you be doing,
that a couple of
inventors, some of the
best pilots in the world,
and the brightest minds
in the world do
everyday? Fly!
You will attempt to be
like the Wright Brothers
and design an airplane
that will meet today’s
airplane standards.
However, you won’t be
using aluminium,
various metal parts or jet
engines for these planes.
All you will need are
pieces of paper – or any
other craft materials –
and a whole lot of
imagination.
You have the
opportunity to design
planes that will be able
to fly long distances. In
the contest, you will
need to design a plane
that will travel in a
straight path.
However, with every
contest there is a set of
rules that you must
follow to try to win the
contest’s grand prize.
Some of these rules are:
1. no cuts can be made
in the plane’s wings,
2. parts may be cut off
from the plane entirely
and
3. you must build your
own planes.
You will be working in
groups to design and test
your planes before
contest day. Each group
gets three attempts.
Scratches may occur in
this contest. A scratch
means that the plane did
not travel in a straight
path for any of the
flight.
I have heard that some
of you are getting way
into this – someone said
that you are bringing in
the in-flight
refreshments! This will
be an interesting contest.
Let’s check out the
information in this
text.
Underline any key
words.
What author’s plan
can you see?
_________________
My Notes:
*________________
_________________
_________________
_________________
_________________
_________________
_________________
*________________
_________________
_________________
_________________
_________________
_________________
_________________
_________________
179
Reflection Questions:
1. What is the Annual Paper Airplane Contest about?
2. What needs to be done to design an airplane that will be successful for the
contest?
List what you need to do:
3. What does it mean if your plane is scratched in one of your attempts? What is the
cause?
Cause =
4. What units of measurements are used in contests in which distance and time are
measured? Make a LIST.
__________________________________________________________________
180
The Annual Paper Airplane Contest
This year, our school will hold their annual paper airplane flying contest on the 25
th of November.
Students in year four will be working in groups and will design one plane.
All planes will be designed to fly for as long as possible in the air (time) and over a long distance
from a target. The plane will need to travel in a straight-line path.
Three awards will be given at this contest. One will be given to the group whose plane stays in
the air the longest – another to the group whose plane travels the longest straight-line path – and
the final award is an overall award given to the group who wins the contest.
LIST THE THREE AWARDS TO BE GIVEN: ________________________________
________________________________
________________________________
Results from the Annual Paper Airplane Contest 2004
Team Attempts
Time in the
Air
(seconds)
Distance
traveled in a
straight path
(metres)
1 2 11
2 1 ½ 12 Team A
3 scratch scratch
1 1 12
2 ½ 7 Team B
3 ½ 8
1 1 9
2 1 11 Team C
3 2 11
1 2 ½ 12
2 scratch scratch Team D
3 1 8
1 1 ½ 9
2 1 10 Team E
3 2 13
1 1 9
2 2 11 Team F
3 scratch scratch
181
Investigation
In the past years, the judges have had problems with deciding how to select a
winner and how to judge the contest. Using the given data from the previous
years, find a way to help the judges decide on the overall winner of the contest.
LIST THE TWO THINGS YOU NEED TO DO:
______________________________________________________________
______________________________________________________________
NOW READ THE TEXT BELOW:
Write a letter to the judges of the contest explaining to them how to determine
who wins each of the categories (time in the air and distance traveled in a
straight-line path) and how to decide the winner of the overall award for the
contest.
LIST WHAT YOU NEED TO DO:
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
Go back and check the data.
What author’s plan will you use to examine the data?
_____________________________________________________________
Use that author’s plan to write your notes about the data and work out
what you want to say in your letter. (Use a separate sheet of paper to
write your notes.)
What author’s plan will you use to write your letter?
____________________________________________________________
182
APPENDIX 7
INFORMATION FOR PARENTS
183
RESEARCH PROJECT
MATHEMATICAL MODELLING THROUGH TOP LEVEL STRUCTURING
Dear Parents/Guardians,
My name is Katherine Doyle. I am a postgraduate student and a primary teacher with
over twenty years teaching experience. I am conducting a research project as part of my
studies to attain a Master of Education (Research) at the Queensland University of
Technology.
Project Background
The research brings together literacy and mathematics. As I have a prior degree in
reading, I am interested in investigating the relationship of students’ literacy
comprehension to students’ ability to actively participate in mathematical problems
which require them to comprehend a variety of written texts.
MATHEMATICAL MODELLING is a problem-solving process which enhances
mathematical knowledge, reasoning processes and learning processes. Top Level
Structuring is a strategy whereby students learn to organise texts so that they can extract
the main idea from the text and remember facts from the text.
For the purposes of the project, my research observations must be documented.
Consequently, I seek your consent to video and audio tape your child/children while they
participate in the activities.
Details of the Study
The study will involve the two year four classes participating in problem-solving
activities during Term 4. The regular teachers will be cooperatively teaching with me as
we implement the activities which conform to the requirements of the Queensland
Mathematics Syllabus. The lessons will routinely be video and audio taped. Students’
work samples will also be collected for data analysis.
Confidentiality
Your child’s confidentiality will be assured. In reporting the results of the study, there
will be no identification of the school, individual teachers or students. Audio tapes,
transcripts, video data and work samples will be accessible only to the research team.
Data collected will be used solely for research and educational purposes and will be
stored for 5 years in a lockable cabinet before being destroyed.
184
Participation
Your child’s participation is entirely voluntary. Participation however does mean that
your child will be videotaped or audiotaped. This may be as a member of the whole class
or as an individual engaged in some learning task.
Benefits
The project will enable the students to access new and meaningful mathematical learning
experiences as well as access learning opportunities in text comprehension.
The project also enables the exploration of the relationship of literacy and mathematics.
Risks
No significant risks can be foreseen. Students will be performing normal learning tasks
and will not miss any basic mathematics content. Any stress induced by the presence of
cameras and other personnel will be monitored and support provided by the teachers.
Experience shows that students are highly accepting of video cameras and enjoy the
opportunity to be video taped.
Questions/ Further Information/Concerns
You are advised that if you have any concerns or complaints about the ethical conduct of
the project you may contact QUT’s Research Ethics Officer on 38642340.
If you wish to discuss any further information or have questions about the project, you
are welcome to contact me or one of my supervisors directly.
Yours faithfully
Katherine Doyle Professor Lyn English
Centre for Maths, Science & Technology Centre for Maths, Science & Technology
Queensland University of Technology Queensland University of Technology
Victoria Park Road Victoria Park Road
Kelvin Grove QLD 4059 Kelvin Grove QLD 4059
Telephone: 38643646 Telephone: 38643329
Email: [email protected] Email: [email protected]
Associate Professor Jim Watters
Centre for Maths, Science &Technology
Queensland University of Technology
Victoria Park Road
Kelvin Grove QLD 4059
Telephone: 38643639
Email: [email protected]
185
APPENDIX 8
PARENTAL CONSENT FORMS
STUDENT CONSENT FORM
186
PARENTAL CONSENT FORM
RESEARCH PROJECT
MATHEMATICAL MODELLING THROUGH TOP-LEVEL STRUCTURE
I/We have read and understood the information package regarding the research project.
I/We consent to my child being videotaped and audiotaped while participating in
mathematical problem solving activities.
I/We consent to the use of my child’s work in publications about this research.
In giving consent, I understand that:
1. My child’s identity and that of the school will remain confidential.
2. Only Katherine Doyle, Professor Lyn English and Associate Professor Jim
Watters will have access to the tapes and will retain them in a locked filing
cabinet at QUT’s Kelvin Grove campus for 5 years after which time they will
be destroyed.
3. I/We can withdraw consent at any time without further comment or
explanation.
Child’s name ...…………………………………………………………..
Parent’s/Guardian’s name ………………………………………………………….
Parent’s/Guardian’s signature …………………………………………………………
Date ………./…………/2005
Katherine Doyle Professor Lyn English
Centre for Mathematics, Science Centre for mathematics, Science
& Technology & Technology
Faculty of Education Faculty of Education
Queensland University of Technology Queensland University of Technology
Kelvin Grove Kelvin Grove
Telephone: 38643646 Telephone: 38643329
Email: [email protected] Email: [email protected]
Associate Professor Jim Watters
Centre for Mathematics, Science
& Technology
Faculty of Education
Queensland University of Technology
Kelvin Grove
Telephone: 38643639
Email: j.watters@ qut.edu.au
187
29/08/05 PARENTAL CONSENT FORM
PRACTICE FOR RESEARCH PROJECT
Dear Parents/Guardians,
You would have received last week an information package on the research project to be
conducted in Term 4 with the year four children. I would like to video/audio the children
during class time prior to undertaking the research. This would allow the students to be
familiar with the video and audio taping process. These tapes will be viewed by the
students only and then be destroyed.
If you have any objection to your child participating in this taping, please sign and return
the form below by this Friday 2nd
September, 2005.
Thankyou.
Katherine Doyle.
I/We object to my child being videotaped and audiotaped prior to the research taking
place.
Child’s name ...…………………………………………………………..
Parent’s/Guardian’s name ………………………………………………………….
Parent’s/Guardian’s signature …………………………………………………………
Date ………./…………/2005
Katherine Doyle
Centre for Mathematics, Science
& Technology
Faculty of Education
Queensland University of Technology
Kelvin Grove
Telephone: 38643646
Email: [email protected]
188
Project Title:
Mathematical modelling through Top Level Structure
Katherine Doyle Professer Lyn English Associate Professor JimWatters
38643646 38643329 38643639
[email protected] [email protected] [email protected]
STUDENT CONSENT FORM
You are invited to participate in this research project. Your involvement is entirely
voluntary and your parent or caregiver will also be asked to complete a consent form for
you to be involved in this research project.
Your parents/caregivers have an information package on the project that you can discuss
with them.
Your participation in the study will provide you with opportunities to work in small
groups on tasks designed to help your problem solving abilities.
The activities will be audio taped and video taped. Your group will give presentations to
the class after each activity which will be video taped. At the end of the year we will be
flying planes on the oval as part of our presentations.
There are no apparent risks to you if you participate in the project. The activities are part
of your classroom maths program.
Everything you say or write is confidential.
Your participation is voluntary. If you have questions or concerns you can contact any of
the researchers or the Research Ethics Officer on 3864 2340.
If you are willing to participate in this research project, please sign your name below.
Thank you.
Katherine Doyle
Name: _______________________________________________________________
Signed: ______________________________________________________________
Date: _______________________________________________________________
189
APPENDIX 9
ETHICAL CLEARANCE FORMS
190
Date: Wed, 10 Aug 2005 15:28:40 +1000 From: Wendy Heffernan <[email protected]> Subject: Confirmation of Level 1 ethical clearance - 4186H To: [email protected] Cc: [email protected], [email protected] Dear Katherine I write further to the application for ethical clearance for your project, "Mathematical Modelling Through Top-level structure" (QUT Ref No 4186H). On behalf of the Chair, University Human Research Ethics Committee (UHREC), I wish to confirm that the project qualifies for Level 1 (Low Risk) ethical clearance. This is subject to:
• provision of a child friendly information sheet and consent form for the student participants; and
• provision of a copy of approval from the school principal.
However, you are authorised to immediately commence your project on this basis. This authorisation is provided on the strict understanding that the above information is provided to the Research Ethics Office prior to the commencement of data collection. The decision is subject to ratification at the 20 September 2005 meeting of UHREC. I will only contact you again in relation to this matter if the Committee raises any additional questions or concerns in regard to the clearance. The University requires its researchers to comply with:
• the University’s research ethics arrangements and the QUT Code of Conduct
for Research;
• the standard conditions of ethical clearance;
• any additional conditions prescribed by the UHREC;
• any relevant State / Territory or Commonwealth legislation;
• the policies and guidelines issued by the NHMRC and AVCC (including the National Statement on Ethical Conduct in Research Involving Humans).
Please do not hesitate to contact me further if you have any queries regarding this matter.
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Regards Wendy. Date: Thu, 11 Aug 2005 16:27:35 +1000 From: Wendy Heffernan <[email protected]> Subject: Response - 4186H To: <[email protected]> Dear Kathy I write further to the response received in relation to ethical clearance provided for your project, "Mathematical Modelling Through Top-level structure" (QUT Ref No 4186H). On behalf of the Chair, University Human Research Ethics Committee (UHREC), I wish to confirm that the response has addressed the additional information required for ethical clearance, subject to a copy of approval from the school principal. I look forward to receiving this in due course. However, I reconfirm my earlier advice that you are authorised to immediately commence your project. Please do not hesitate to contact me further if you have any queries regarding this matter. Regards Wendy
