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ORIGINAL ARTICLE
Quality issue in the design and use of resources by mathematicsteachers
Jana Trgalova • Ana Paula Jahn
Accepted: 19 July 2013
� FIZ Karlsruhe 2013
Abstract The profusion of resources, mostly on the
Internet, makes the issue of their quality more and more
pressing. Teachers often find themselves unable to choose
from among them those that would be the most relevant to
their educational goal and to the context of their classes. In
our previous work, we claimed that acquiring resource
analysis skills is one of the keys to the teachers’ profes-
sional development supporting the integration of dynamic
geometry systems. Based on this assumption, we have
designed a quality questionnaire for the i2geo repository
aiming at framing the analysis of available resources by the
platform users. The research reported in this paper, which
is a continuation of this work, explores the way the quality
criteria are taken into account in the design and use of
resources by members of the community that has emerged
around the repository and sheds light on possible evolu-
tions of teachers’ and teacher educators’ professional
practices due to their involvement in the resource quality
evaluation.
Keywords Dynamic geometry � Open educational
resource � Dynamic geometry resource quality � i2geo
repository
1 Introduction: open educational resources
For several years now, there has been a growing interest
among the education community in sharing learning
resources (Downes 2007; Johnstone 2005), mostly via
specifically designed web-based repositories. This world-
wide interest is acknowledged by the emergence, in 2002,
of the term open educational resources (OER) coming out
of the UNESCO Forum on the Impact of Open Courseware
for Higher Education in Developing Countries (Johnstone
2005). Numerous benefits from sharing OER are reported.
According to Kanwar and Uvalic-Trumbic (2011), sharing
resources leads to the improvement of their quality:
‘‘experiences clearly demonstrate that this opening of
intellectual property to peer scrutiny is having the effect of
improving quality of teaching and learning materials. This
happens both because educators tend to invest time in
improving their materials before sharing them openly and
because the feedback they receive from peer and student
scrutiny helps them to make further improvements’’ (p.
10). Rolfe (2012) highlights other benefits for teachers and
educators from re-using shared resources, such as saving
time teachers need to devote to the design of new resources
(‘‘save time and money in the long run, although invest-
ment of both would be required initially to develop and
release OER, and to reuse them in a new teaching con-
text’’), finding new ideas for their classroom activities and
new teaching methods to improve their practices (‘‘plenty
of choice for users to find the items they want […] using
resources developed around the world will inspire and
provide new ideas on how to design effective educational
strategies and provide a rich source of analogies and case
studies’’).
A number of OER repositories exist, but little is known
about the way in which available resources are actually
J. Trgalova (&)
S2HEP, Claude Bernard University, Lyon, France
e-mail: [email protected]
URL: http://eductice.inrp.fr/EducTice/equipe/membres/
permanents/jana-trgalova
A. P. Jahn
IME, University of Sao Paulo, Sao Paulo, Brazil
e-mail: [email protected]
123
ZDM Mathematics Education
DOI 10.1007/s11858-013-0525-3
used and how they are modified by the teachers to adapt
them to their educational context. Nguyen (2012) claims
that, in most cases, the teachers modify the downloaded
resources for their personal use, but they do not upload the
modified resources, nor do they report about their usages
and modifications.
In this paper we address the issue of the use of a specific
OER repository, the i2geo platform. This repository of
resources for mathematics teaching and learning with
dynamic geometry (DG) has been developed within the
framework of the Intergeo European project1 (Kortenkamp
et al. 2009). A quality assessment process (presented in
Sect. 2), which aims at allowing a continuous improvement
of the available resources based on users’ reviews and
comments, is a distinctive feature of this repository. The
reported study investigates the impact of the quality
assessment on the design and use of DG resources by the
i2geo community members, as well the effects of exam-
ining resource quality on the community members’ prac-
tices. The theoretical and methodological background of
the study is described in Sect. 3. Sections 4 and 5 present
two case studies from which we attempt to infer elements
of answers to the above-mentioned issues. Finally, general
remarks are provided in the concluding Sect. 6.
2 The i2geo repository
Dynamic geometry systems (DGS) have existed for almost
three decades now and their contribution to the improve-
ment of learning and teaching mathematics has been doc-
umented (Laborde and Capponi 1994; Healy 2000;
Mariotti 2000; Ruthven 2005). However, there has been
little integration of these systems into teachers’ practices,
as Kortenkamp et al. (2009) point out: ‘‘still, the adoption
of DGS at school is often difficult. Despite the fact that a
lot of DGS class material exists, Interactive Geometry is
still not used in classrooms regularly. Many teachers do not
seem to know about the new possibilities, or they do not
have access to the software and/or resources’’ (p. 1,150).
Based on these observations, the Intergeo project aimed at
(1) enabling teachers to easily find suitable resources for
their teaching, (2) providing materials in a format that can
be used with different DG systems, and (3) ensuring
resource quality (Kortenkamp et al. 2009, p. 1,151). More
precisely, the project ambition was to develop a commu-
nity of DG users all over Europe around the i2geo repos-
itory where one can submit resources, tag them with useful
information for their display, view available resources,
analyze them and provide feedback to their authors,
download them for re-using, comment on experiences with
their classroom implementation …In order to help the repository users identify suitable
resources regarding their instructional aim and context of
use, as well as to enable improving the available resources,
two main tools have been developed and implemented into
the repository: (1) a search engine based on mathematical
notions and competencies ontology to help searching for
relevant resources; and (2) a resource quality assessment
process based on a quality questionnaire to help the users
analyse available resources, highlight their weaknesses and
suggest modifications to enhance their quality. In what
follows, the questionnaire and its design process are briefly
presented.
2.1 Dynamic geometry resource quality questionnaire
The questionnaire, which is the main tool for the resource
quality assessment in the repository (Fig. 1), was designed
in a cyclical process consisting in the elaboration of its
successive versions, followed by their testing and sub-
sequent improvements. This methodology can be consid-
ered as design-based research, in which ‘‘development and
research take place through continuous cycles of design,
enactment, analysis, and redesign’’ (DBRC 2003, p. 5),
blending theory-driven design with empirical research. The
group in charge of the design of the questionnaire com-
prised three mathematics education researchers (two of
whom are authors of the present paper) and seven sec-
ondary school mathematics teachers. The first version of
the questionnaire was designed by the researchers drawing
on research results related to the use of DG in mathematics
teaching and learning. It proposed eight general questions
related to eight dimensions of a DG resource considered as
critical with respect to the resource quality, such as tech-
nical aspect, mathematical content validity, instrumental
aspect, and didactical and pedagogical implementation.
Later, a ninth dimension related to the resource ergonomics
was added. Each of these general questions can be devel-
oped into a set of more detailed criteria related to the
corresponding dimension (Fig. 1).
The theoretical considerations underpinning the choice
of the dimensions and the definition of the criteria are
described in some detail in Trgalova et al. (2011).
In order to make the questionnaire accessible to and
usable by teachers, its elaboration was done in close col-
laboration with the seven secondary mathematics teachers
(called the DG-group), according to the schema in Fig. 2.
Each version of the questionnaire was first reviewed by
the DG-group who provided suggestions related to the
relevance and the clarity of the quality criteria. An
improved version was then tested with teachers in various
contexts, such as pre-service or in-service teacher training
1 Interoperable Interactive Geometry for Europe, 2007–2010 (http://
i2geo.net/xwiki/bin/view/Main/About).
J. Trgalova, A. P. Jahn
123
programmes or workshops for mathematics teachers and
teacher educators. The questionnaire was then re-designed
to take into account the outcomes of the tests.
It is important to mention that besides the aim of the
i2geo community benefit consisting in the improvement of
shared resources, the definition of the quality criteria has
also been driven by our ambition to enable each individual
user engaged in the resource analysis to benefit personally
by making her/him reflect on the purpose and the way DG
is used in the resource, which may be different from her/his
own practice. We supposed that the analysis of a resource
would thus have an impact on the user in at least two
aspects: (1) it would help her/him get a deeper insight into
what the resource is about and thus facilitate its
appropriation for a potential implementation in her/his
classroom; and (2) it would contribute to the evolution of
the user’s practices with using DG by gaining awareness of
its possible contributions to the teaching and learning
mathematics and of various ways it can be used.
The empirical studies conducted within the question-
naire design cycle provided some evidence tending to
confirm that teachers perceive the questionnaire as a very
useful tool, specifically in the process of resource appro-
priation and use (Jahn et al. 2008; Trgalova et al. 2011;
Trgalova and Richard 2012). However, these rather short
and controlled experiments do not provide insight into an
‘‘uncontrolled’’ use of the repository. This is what moti-
vated the study reported in this paper.
Fig. 1 Online questionnaire
for reviewing a DG resource in
the i2geo repository
Theory-driven design of the first version of the questionnaire by
the researchers Critical review of the questionnaire by the
DG-group
Test of the questionnaire by
teachers (in France and in Brazil)
Analysis and redesign of the questionnaire by the researchers
Fig. 2 Schema of the resource
quality design methodology
Quality issue in the design and use of resources by mathematics teachers
123
2.2 The i2geo community
Although the i2geo repository offers free access to its
resources, registered members benefit from other tools and
functionalities, such as the possibility to create one’s own
collections from available resources, bookmark selected
resources, create specific interest groups or comment on
available resources. Reviewing resources is also reserved
for registered members.
At present, the i2geo repository has more than 2,100
registered members.2 The community has grown progres-
sively around the Intergeo project partners3 who were its
first members (circle C1), later involving groups of
teachers (circle C2), among which some collaborated with
the project partners on some specific aspects, such as the
resource quality issues, and others were subjects of the
project pilot studies (see Fig. 3).
2.3 Research questions
Now, almost 3 years after the end of the Intergeo project, it
seems legitimate to ask whether the i2geo community
continues to exist and whether and how the repository with
its resources and tools continues to be used. Our study
therefore addresses the following two research questions:
• Is the quality questionnaire actually used in an
‘‘uncontrolled setting’’ and is it useful for improving
the resources available in the repository?
• Does the use of the repository have any impact on the
users’ practices with using dynamic geometry?
The study presented in what follows searches for
answers to these questions by exploring (1) to what extent
the Intergeo project goal to provide tools ensuring a
continuous improvement of the resource quality is fulfilled
and what is the role of the quality questionnaire in it, and
(2) what is the impact of considering DG resource quality
issues on teachers’ practices with the resource design and
use.
3 Theoretical and methodological background
3.1 Methodology
Two case studies have been carried out in order to get
insight into the above-mentioned issues.
The first case study aims at highlighting the impact of
the teachers’ involvement in the Intergeo project research
on their practices with the design and use of DG resources,
and focuses therefore on the teachers belonging to circle
C2 of the i2geo community (see Fig. 3). The group of
teachers concerned in the case study collaborated with the
project partners on the issue of dynamic geometry resource
quality. This group, called DG-group in what follows,
comprised seven secondary mathematics teachers who
started collaborating in 1996 within the Institute for
Research in Mathematics Teaching in Lyon4 as a group of
‘‘users and designers of DG resources’’ (p. 122, authors’
translation) (Bourgeat et al. 2013). In 2008, the group
volunteered to join the Intergeo project and collaborated
until recently with mathematics education researchers on
the resource quality issues. Every year since 2003, the
group has offered training courses aiming at helping other
mathematics teachers master and integrate DG systems into
their practices. All group members together prepare their
courses during their regular meetings and produce various
resources (documents, tools…), although only two or three
of them, in turn, are in charge each time of the imple-
mentation of the teacher training courses.
In order to identify possible evolutions in the design and
use of resources for mathematics teaching and teacher
training by the DG-group members, we gathered teacher
training resources the group has produced since 2003.
Moreover, recently the group was asked to reflect on
changes in their own practices, both as teachers and teacher
educators, which the group members could observe since
their involvement in the Intergeo project. This introspec-
tive activity, conducted in the form of a collective inter-
view, yielded many interesting observations (Bourgeat
et al. 2013) related mostly to the group members’ teaching
Intergeo consortium
(C1)
Teachers involved in the project
(C2)
I2ge
o m
embe
rs
(C3)
Fig. 3 The i2geo community
2 As of April 22, 2013.3 The list of project partners is available at (http://i2geo.net/xwiki/
bin/view/Main/Partner).
4 Institut de Recherche sur l’Enseignement des Mathematiques
(IREM). The IREMs gather together primary, secondary and univer-
sity teachers to conduct research on issues in mathematics teaching
and learning at all school levels, to offer teacher training programmes
based on research results, and produce and disseminate pedagogical
resources.
J. Trgalova, A. P. Jahn
123
practices, some of which are reported below. We have
analysed as well some of the teachers’ reviews and com-
ments on resources in the i2geo repository, which can also
shed light on their views on the usages of DG in mathe-
matics teaching. The data analysis and discussion is
reported in Sect. 4.
The second case study focuses on the use of the i2geo
repository by the i2geo community. We attempt to explore
whether the community members have integrated, at least
to some extent, the quality criteria and whether the quality
questionnaire is used/useful for the improvement of the
resources. We have selected a dozen members from the
most productive ones, that is, those who have contributed a
significant number of resources at various periods of time,
and we have sent them a questionnaire aiming at getting
insight into the processes of the design of resources and the
role of the quality criteria in these processes, the ways of
searching for resources and of re-using them, the ways of
reviewing available resources, and the members’ percep-
tion of the usefulness of the quality questionnaire. Results
of this study are discussed in Sect. 5.
3.2 Theoretical lens used to analyse the collected data
The theoretical background of our study draws mostly on
the instrumental approach and the considerations related to
the potentialities of dynamic geometry.
3.2.1 Instrumental approach
Numerous research studies on information and communi-
cation technologies (ICT) integration adopt an instrumental
approach (Rabardel 2002) as a theoretical framework
specifically designed for studying teaching and learning
phenomena involving technology. The instrumental
approach relies on a distinction between an artefact, which
is a tool available to an individual, and an instrument,
which is the result of a process of appropriation of the tool
by the individual when s/he uses it in order to achieve a
given task. The process of transforming an artefact into an
instrument is called instrumental genesis.
Some of these studies stress the complexity of technol-
ogy integration, which requires a double instrumental
genesis in teachers: a first genesis of an instrument for
achieving mathematics tasks, and a second one of an
instrument for achieving educational tasks (Acosta 2008).
Haspekian (2011) evokes a personal genesis transforming a
given tool into a mathematical instrument, and a profes-
sional genesis transforming it into a didactical instrument.
According to Trouche (2004), ICT integration requires
the teacher to be aware of the potentialities and constraints
of artefacts, which is necessary for designing suitable
mathematical tasks. Moreover, the teacher has to be able to
implement and manage these tasks in the classroom. The
author introduces the term instrumental orchestration to
refer to the didactical management of the artefact in the
classroom. Drijvers et al. (2011) define instrumental
orchestration as ‘‘the intentional and systematic organisa-
tion and use of the various artefacts available in [a] com-
puterised learning environment by the teacher in a given
mathematical task situation, in order to guide students’
instrumental genesis’’ (p. 1,350).
These considerations frame our analysis of resources
produced by the i2geo community members. We look for
elements in these resources showing whether the authors
are aware or not of the necessity of the double instrumental
genesis in teachers wishing to integrate DG. We also try to
highlight the way the activities are orchestrated.
3.2.2 Potentialities of dynamic geometry: the role
of dragging
A dynamic geometry environment is computer-based
software that allows the user to create geometrical figures
and manipulate them into different shapes and positions by
dragging their elements, mostly points. One of the dis-
tinctive features of DG is that, when dragging, the geo-
metrical properties of the figure defined in its construction
are preserved. Three main modalities of dragging have
been identified in the literature (Healy 2000; Laborde 2001;
Arzarello et al. 2002):
1. dragging for verifying consists in dragging to check
the presence of the supposed (known) geometrical
properties in the figure. According to Holzl (2001),
uses of DG are often limited to this modality, in the
sense that students are expected to drag figures to
confirm empirically the properties which are more or
less given;
2. dragging for conjecturing consists in dragging to look
for new properties of the figure through the perception
of what remains invariant when dragging;
3. dragging for validating/invalidating consists in drag-
ging to check whether the constructed figure preserves
its geometrical properties when dragging.
In the analysis of the resources we will focus on the
modalities of dragging in the activities proposed and on
possible changes in the authors’ perceptions of the role of
dragging.
4 Case study 1: the DG-group members’ practices
The analysis of the resources produced by the DG-group
since 2003 shows a significant shift in three main aspects,
presented here.
Quality issue in the design and use of resources by mathematics teachers
123
4.1 Modalities of dragging
Relying on the teachers’ own analysis of their practices
before and after their involvement in the Intergeo project
during the collective interview (Bourgeat et al. 2013), it
appears that with their students, the teachers previously
used DG mostly to obtain robust constructions aiming at
highlighting invariants in geometric figures:
Yesterday, obtaining robust geometric constructions
and highlighting invariants were the main goals
assigned to students: they should construct a figure by
using known properties […] which they could vali-
date by the invariance of the figure when dragging.
Nowadays, they propose new types of activities in which
they ask students ‘‘to explore figures in order to highlight
invariants and/or conjecture new properties’’ (authors’
translation). The teachers seem to have acknowledged the
importance of dragging for conjecturing in students’
learning and they thus propose various and richer tasks
using different modalities of dragging.
The following comment5 written by one of the DG-group
members about a resource in the repository that illustrates,
with a robust construction, the equality of three ratios in a
triangle with a line parallel to one of its sides, shows her
awareness of the interest of soft constructions in geometry
learning: ‘‘several improvements are possible: 1. [The
point] N can be set free, which will allow visualizing the
difference between the case proportional-parallel and the
cases where the ratios are not equal’’ (authors’ translation).
These elements tend to show an evolution in the DG-
group in their perception of the potentialities of dynamic
geometry and especially of the role of dragging: they seem
to have moved from activities where dragging aims at
validating robust constructions toward exploratory activi-
ties in which dragging allows searching for new properties
in soft constructions (Healy 2000). Although it is difficult
to establish a direct link between the questionnaire and the
evolution of the teachers’ awareness of the DG contribu-
tions to the teaching and learning geometry, we can sup-
pose that the numerous discussions about this issue, that
eventually led to the definition of criteria related to the
added value brought by dynamic geometry to the mathe-
matics activity, are at the origin of this evolution.
4.2 Instrumental orchestration
Regarding the classroom management, the teachers confess
to having struggled to combine phases of students’ work on
computers in a computer lab with collective phases of
debate, which often needed to be postponed until the next
session in an ordinary classroom, as they said in the
interview:
Before, the activities with ICT took place in a com-
puter lab in conditions that postponed the debate and
the students–teacher interactions regarding their
observations and manipulations in a digital resource.
Nowadays, the teachers orchestrate their ICT-based
lessons in a more effective way: the use of a video pro-
jector allows articulating individual and collective phases.
Indeed, the teachers say: ‘‘[Now] we observe the interac-
tions in a genuine triangle ‘students–teacher–digital
resource’ ’’ (authors’ translation).
This shift can certainly be related to the criteria related
to the pedagogical implementation of the resource, one of
the nine aspects that we consider critical for determining
the resource quality.
4.3 Awareness of the double instrumental genesis
The analysis of the teacher training resources produced by
the DG-group reveals that the training programmes the
group proposed before 2007, that is, before its involvement
in the Intergeo project, aimed mostly at helping trainees to
master DG environment tools. The training activities con-
sisted in series of exercises to be solved with DG chosen to
illustrate the use of a particular DG tool. Figure 4 shows a
typical training activity: the trainees are asked to solve the
exercise and specify the DG tools they have used.
The focus of the teacher training programmes in this
period was clearly on technical aspects of mastering a DG
environment. In terms of instrumental genesis, the DG-
group accompanied trainees’ geneses of mathematical
instruments.
Since 2009, the teacher training proposals of the DG-
group show a significant shift towards considering didac-
tical and pedagogical aspects of DG integration. Indeed, in
a training programme proposed in 2009, the group
announces the following objective: ‘‘the aim of this train-
ing programme is to accompany the teacher wishing to take
her/his students to a computer lab’’ (authors’ translation).
After a short phase during which the trainees solve exer-
cises aiming at getting them acquainted with the main DG
tools, they are invited to reflect on the types of activities
suitable for the use of DG, the goal being to bring forward
the following aims: introduce a new mathematical concept;
construct figures; and put students into a research activity
with DG.
After having solved a given exercise with DG, the
trainees are asked to explore it in light of possible imple-
mentation in a classroom: envisage possible adaptations,
and anticipate classroom management. Figure 5 shows a
5 (http://i2geo.net/xwiki/bin/view/Coll_cdording/Egalitedes3rapport
savecunedroiteparalleleauncoteduntriangle?bc=&viewer=comments).
J. Trgalova, A. P. Jahn
123
training resource produced in 2011, in which the two
phases, solving an exercise and exploring it from didactical
and pedagogical points of view, are present.
The trainees are also led to create their own activities
related to a mathematical domain of their choice and
adapted to the level of their class. They have to specify the
teaching goals and envisage the classroom implementation
of the activity. The DG-group has developed specific
resources to help the trainees with this task, such as a
description sheet of a session using DG (Fig. 6) or a
checklist with questions to ask before using ICT in a
classroom, for example when to use ICT, do the ICT
contributions favour students’ learning, or how to integrate
an ICT session into an ordinary teaching sequence.
These elements show that the DG-group has become
aware of the necessity to assist the trainees’ professional
instrumental geneses so that they can transform DG software
not only into a mathematical instrument, but also into a
didactical one. The teachers confirm this observation during
the interview saying: ‘‘the shift of emphasis with the gradual
abandonment of the technical aspect in favour of a didactic
one is increasingly important’’ (authors’ translation).
Moreover, the resources produced by the group show signs
of the influence of the quality questionnaire, namely the
consideration of several dimensions such as contributions of
DG, didactical exploitation of DG potentialities or instru-
mental orchestration (see Fig. 6). This seems to confirm a
highly positive impact of the DG-group involvement in the
design of a DG resource quality questionnaire on their
practices with the design and use of DG resources.
5 Case study 2: usages of the i2geo repository
In this section, we first focus on the collection of resources
submitted in the i2geo repository. We address specifically
the following two questions:
• Does the quality assessment process implemented in
the repository lead to the improvement of resources?
• Is there evidence of an impact of the quality criteria on
the resources that are submitted in the repository?
We then study the usages of the repository by a few
i2geo community members.
5.1 Quality assessment and improvement of resources
There are more than 3,700 resources available in the
repository.6 They are written generally in French, German,
English, Czech or Spanish. Among these resources, 175
have been reviewed. In all, 866 reviews have been carried
out.
Exercise n°4:
a) Given a segment [AB], construct a square with [AB] as a side. b) Given a segment [AB], construct a square with [AB] as a diagonal. c) Construct a square with a side [AB] without using « parallel line » and « perpendicular line » tools.
N.B. For each question, verify that the construction remains stable.
Fig. 4 Example of a teacher
training activity proposed by the
DG-group in 2005 (authors’
translation)
3. Studying polynomials 3.1. Relationship between graphical representation and expression of a first and second degree function The trainees open the file “stage1-exo-fct - degre 1 et 2.ggb” They are given the document “stage1-exo-fct degre 1 et 2.odt” Let the trainees solve the exercise. Ask them to reflect on possible adaptationsfor Grade 11 classroom for the next training day.
2nd day: exploitation of the exercise 3.1 solved during the first day: Ask for possible adaptations. A specific attention should be paid to the method used by the students (successive trials without the properties). The need to review this point with them… how? How to manage this activity?
Fig. 5 Excerpt of a training
plan elaborated by the DG-
group in 2011 (authors’
translation)
6 As of April 22, 2013.
Quality issue in the design and use of resources by mathematics teachers
123
To explore possible improvements of resources follow-
ing the quality reviews by peers, we first focus on resources
that have been reviewed at least once. The ‘‘Revision
History’’ tool displays the different versions of the resource
with the date and time of the modifications (Fig. 7), which
allows seeing whether the modifications follow chrono-
logically the reviews or not.
Figure 7 shows an example of a resource created
October 05 2010 and reviewed by two i2geo members,
both reviews being carried out October 08 2010. New
versions of the resource are recorded November 04 2010,
with the author’s comment for the most recent one:
‘‘Improvements have been done!’’
The ‘‘Compare Versions’’ tool shows which elements of
the resource, among metadata, content, attachment and
comment, have been changed from one version to another
(Fig. 8). However, only the modifications that concern the
corresponding resource description fields are tracked;
Fig. 6 DG session description
sheet (authors’ translation)
Fig. 7 Revision history of a
resource
J. Trgalova, A. P. Jahn
123
therefore, the changes in the content of any file composing
the resource are not visible.
Figure 8 shows that none of the fields among metadata,
content, attachment and comment has been changed for
the resource shown. The analysis of the content of the
resource in the light of the reviews suggests that the
improvements mentioned by the author actually follow the
criticisms put forward by the reviewers. Indeed, both
reviewers are mostly critical of the lack of guidance
regarding the didactical and pedagogical implementation
of the proposed activity: for example, no instrumental
orchestration is suggested, the activity duration is not
indicated, and remedial actions with respect to the
expected dead-ends in students’ strategies are not descri-
bed. These elements are now present in the resource, as
can be seen in Fig. 9.
This is an example of a resource that has actually been
improved thanks to the peer reviews. However, our
Fig. 8 Comparing various
versions of a resource metadata,
content, attachment and
comment
Fig. 9 Excerpts from the resource ‘‘le coup du siecle’’. [Translation:
Implementation (use), duration and time course: presentation of the
problem situation: whole class, 15 min. Realisation of the activity:
individual work, 60 min. Focusing back on the activity: whole-class
correction and meta-cognitive phase. Questioning the possibility of
launching a balloon in straight line, 30 min. Material configuration:
computer lab, projector to present the problem situation. Moderate.
Strategies to suggest to students facing difficulties and reorientation
hints: de-contextualise the problem and solve a similar problem
already worked out] (authors’ translation)
Quality issue in the design and use of resources by mathematics teachers
123
analysis shows that this example is rather an exception.
Indeed, the first striking observation is of a relatively small
ratio of resources that have been reviewed at least once:
436 out of 3,354,7 which is around 13 %. Most of these
resources have been reviewed only once. It seems even
more surprising that most of the resources that received
feedback from peers in the form of either a review (i.e.
having a filled-out quality questionnaire) or a comment
have not been modified afterward.
5.2 Usages of the i2geo repository
In order to understand why the reviewed resources have not
been modified further, as well as to get insight into the
usages of the repository by the community members, we
conducted a second case study. We selected a dozen
members from the most productive ones, that is, those who
have contributed a significant number of resources at var-
ious periods of time, and sent them a questionnaire
organised around four aspects:
1. design and submission of resources—the questions
addressed the process of the design of resources, the
role of the quality criteria in the resource design, the
way feedback from peer reviews is taken into account;
2. use of available resources—the questions addressed
the issues of the re-use of resources, the way of
searching for resources, the members’ satisfaction with
the repository offer in terms of resources;
3. resource review—the questions addressed the way the
members carry out the reviews of available resources
and their perception of the usefulness of the quality
questionnaire;
4. professional practice—the questions addressed mem-
bers’ perception of changes in their practices.
We collected six answers from members, whose profile
is shown in Table 1.
The analysis of the responses was completed, when
possible, with analysis of the resources submitted by the
respondents and of the resource reviews they have done, in
order to understand how they use the repository and its
tools, especially the quality questionnaire.
5.2.1 Peer review and resource improvement
Several questions of the questionnaire aimed at gaining an
insight into the perception the resource authors have of the
usefulness of the feedback received from peers by means of
the quality questionnaire. From the answers that have been
collected, several reasons can be inferred that explain why
the authors rarely modify their resources.
5.2.1.1 Fred: time constraints and isolation prevent him
from improving resources Fred claims that he considers
the quality questionnaire as very useful for the improve-
ment of the quality of available resources. Yet, he con-
fesses that he does not modify his resources after a review:
‘‘I don’t have time to return to the criticisms that have been
made, I have not taken the time to analyse the responses. I
am too alone in the production of resources, not inserted in
an educational team where resources are supposed to live
and evolve’’. Despite belonging to the i2geo community
that should represent ‘‘an educational team where resources
are supposed to live and evolve’’, Fred feels alone. When
he was asked if he re-uses available resources, he said: ‘‘I
don’t have secondary school classes so the described usa-
ges are usually not matching mine (training trainers) […]’’.
This remark may suggest that Fred hardly shares resources
with other community members, who are mostly secondary
mathematics teachers, which can increase his feeling of
isolation. But Fred may also be missing tools enabling
communication and collaboration among community
members. Moreover, Fred expresses his dissatisfaction
with the repository content: ‘‘there is almost no resource on
calculus, while it is an important domain for me’’. The lack
Table 1 Profile of the respondents participating in the case study
Nickname Country Profession I2geo circle (see Fig. 3) # of submitted resources/
# of reviews done//
# of submitted resources reviewed
Carl Czech Republic Full professor C1 67/14//11
Fred France Full professor C1 127/29//3
Finn France Secondary teacher C3 46/0//1
Greg Germany Researcher C3 35/0//2
Gael Germany Researcher, teacher educator, programmer C1 71/9//4
Sean Spain Website developer C1 184/2//1
These numbers are indicated in the repository, as of April 22, 2013
7 Various kinds of ‘‘non-reviewable’’ resources, such as national
curricula, are included in the total number of available resources in
the repository, which explains the discrepancy between the total
number of resources (3,701) and the number of ‘‘reviewable’’
resources (3,354).
J. Trgalova, A. P. Jahn
123
of tools supporting a collaborative design of resources, as
well as of adequate resources, may be at the origin of
Fred’s frustration causing him not to take on the evolution
of his resources.
5.2.1.2 Carl and Sean: ‘‘robust’’ resources Questioned
on his way of designing resources, Carl says, ‘‘I usually
adapt existing activities. Most of them I used in my lec-
tures; some come from diploma theses of my students’’.
We can thus suppose that these resources have been care-
fully designed and the experiments showed their sturdiness.
This is perhaps the reason why he does not feel the need to
make them evolve. Indeed, the repository does not show
any modifications of his resources. Nevertheless, Carl
admits that the feedback he received from peers was useful
and he could use it to improve his resources, namely the
text addressed to students: ‘‘I usually changed the text in
order to be more understandable for students’’.
The following observation in the questionnaire filled by
Sean tends to confirm the hypothesis that an author uploads
a resource when it presents certain sturdiness: ‘‘I guess
some people might change the design of the resource after
having filled out a review and having thought about some
questions. But I don’t think this happened often. I would
tend to think that when somebody cares enough to upload a
resource of his own, he has already some experience and
has thought quite enough’’.
5.2.1.3 Finn and Gael: resource improvement based on
peer feedback Finn and Gael are the only two (out of six)
respondents who declare having used the peer feedback to
improve their resources. They have a rather positive
opinion about the usefulness of the questionnaire as a guide
for the design of the resource, but paradoxically, when
asked if they make use of it when they design their own
resources, Gael confesses that ‘‘unfortunately, too little’’
and Finn claims that ‘‘not really; I take it into account, but
a posteriori’’. Finn finds the questionnaire rather useful,
and Gael very useful, for improving the resource’s quality.
Both provide examples of the modifications they made to
their resources following the suggestions provided by peer
reviews: ‘‘for example, I have taken into account a remark
of a reviewer who suggested to me to simplify an activity
by reducing the number of interactive files involved’’
(Finn); ‘‘I had two reviews or comments. […] The other
[…] was rather a set of subtle recommendations which I
could essentially integrate directly’’ (Gael).
5.2.1.4 Greg: sensitivity to criticism of others Greg is the
only respondent who has doubts about the use of peer
review. When he was asked if he found the feedback from
other users helpful, he said: ‘‘partly, but mostly it seemed
like a rant …’’ Surprisingly, this opinion is based on only
two reviews that Greg received for two of his 35 resources.
One of the reviews was only quantitative, without any
qualitative comment. The other pointed out the resource
weakness at the level of an insufficient exploitation of the
dynamic geometry. Greg’s case shows that peer review can
sometimes offend the sensibilities of the author, who will
therefore tend to reject it.
It is worth noticing that the respondents who value the
usefulness of the quality questionnaire for the resource
improvement belong mostly to circle 1 (see Table 1), that
is, they are the first i2geo community members. They seem
to be convinced about the necessity of a peer review of the
resources submitted to the repository to guarantee their
quality, which is not necessarily the case of the circle 3
community members who may not adhere to the commu-
nity spirit. This might explain Greg’s sensitivity to peers’
criticism.
5.2.2 Reviewing resources
A set of questions in the questionnaire submitted to the
i2geo users aimed at investigating how they carry out
resource reviews and gathering the users’ opinions about
the utility and usability of the quality questionnaire.
5.2.2.1 Carl and Sean: ‘‘global’’ and ‘‘fan’’ reviews
Carl’s resources are generally in the form of a dynamic
geometry file proposing a construction task (Fig. 10).
Usually, the file integrates a solution, which is invisible
when the file is open but can be displayed step by step by
moving a cursor.
Interestingly, although the resources do not give any
information about their possible use with students, they are
positively evaluated. For example, the resource shown in
Fig. 10 has been reviewed by seven peers10 and obtained
the best four-star evaluation from six of them. A closer
look at the reviews that give the highest score shows that
these are based on the general questions only. Such a
review, which we called a ‘‘fan review’’ (Trgalova et al.
2011), does not allow highlighting of possible deficiencies
of a resource to enable improvement, for example in this
case a lack of information about its pedagogical and
didactical implementation. This way of reviewing, leading
to either a ‘‘fan’’ or a ‘‘global’’ review, which consists in
responding to the general questions only, seems to be a
shared practice among Carl’s colleagues, as he says when
asked how he carries out the resource reviews: ‘‘mostly
only nine general questions’’. Questioned about the clarity
and the ease of use of the quality questionnaire, Carl claims
that it is rather difficult to understand and rather difficult to
10 (http://i2geo.net/xwiki/bin/view/Coll_Pech/Prouzkovakonstrukce?
bc=;Coll_Pech.Prouzkovakonstrukce).
Quality issue in the design and use of resources by mathematics teachers
123
use since there are ‘‘too many questions’’. And he con-
cludes: ‘‘the questionnaire is useful. In my opinion and also
of my colleagues, it should not be so detailed. A shorter
questionnaire would be better since more people will do the
review.’’
Sean shares Carl’s view of the length of the question-
naire: ‘‘I never filled out all the questions, there are too
many.’’ Nevertheless, he finds the questionnaire rather
useful for improvement of the quality of the available
resources.
It is worthy of note that both Carl and Sean consider that
a resource is not uploaded to the repository until its author
is convinced about its sturdiness. This may explain why
their reviews are either ‘‘global’’ or ‘‘fan’’: they trust the
author as regards the resource details; therefore a review is
for them rather a means to express to what extent they like
or dislike the resource.
5.2.2.2 Fred and Gael: ‘‘expert’’ or ‘‘partially expert’’
reviews Fred and Gael are convinced about the usefulness
of the quality questionnaire for the improvement of the
resources; they both say it is very useful. When reviewing a
resource, Fred attempts to ‘‘be detailed enough’’, claiming
that: ‘‘It clearly helps identify perspectives, viewpoints on
the resource that one must have in mind, both as the author
and as the user.’’ Fred’s reviews can therefore be qualified
as ‘‘expert’’ or at least ‘‘partially expert’’ (Trgalova et al.
2011), meaning that he gives a detailed evaluation of at
least some of the nine dimensions of the resource.
Gael’s reviews are mostly ‘‘partially expert’’. He regrets
not evaluating very often and wishes to be able to evaluate
a resource after its implementation with his students.
It is interesting to note that all the respondents who
have reviewed resources belong to circle 1, whereas the
circle 3 members have not done any resource review. This
suggests that the usefulness of peer review is not shared
within the community, and especially by the circle 3
members.
5.2.3 Impact on users’ practices
When the i2geo community members were asked whether
they feel that their practices have changed due to the use of
the repository, Carl, Finn and Greg were rather, or totally,
negative, while Fred and Gael admitted that they may have
changed their way of choosing classroom activities and
their way of teaching. Nevertheless, the comments of the
respondents suggest that their practices might have been
enriched: ‘‘I don’t think that the usage of a repository really
modifies classroom practices. It contributes to it, for sure’’
Fig. 10 Example of Carl’s
resource (http://i2geo.net/xwiki/
bin/view/Coll_Pech/
Prouzkovakonstrukce?bc=
&viewer=comments). a Given
the points A, B and M, the stu-
dent is asked to construct an
ellipse with A and B as main
vertices and passing through
M. The point in the upper right
corner allows displaying hints
leading eventually to the solu-
tion of the task. b The first hint,
together with the corresponding
construction, appears
J. Trgalova, A. P. Jahn
123
(Finn); ‘‘I don’t think that the usage of i2geo has really
modified my practice, but it has certainly enriched it’’
(Fred).
6 Conclusion
The study reported in this paper focused on the i2geo
repository gathering together dynamic geometry resources
for mathematics teaching and learning and its use by the
community that emerged around it. One of the main pur-
poses of the repository developers was to ensure quality of
the available resources. For this aim, a questionnaire was
designed enabling the repository users to analyse resources
and provide feedback pointing out strengths and weak-
nesses of the resource, so that the author, or any other
repository user, can improve the deficient aspects of the
resource. The study attempted to explore to what extent
this objective has been achieved.
The analysis of the footprints available in the repository
tracing the evolution of resources shows first that only a
relatively small number of resources have been reviewed
and, second, that the reviewed resources are in most of the
cases not modified. The analysis of the responses of six
i2geo community members, gathered by means of a
questionnaire aiming at gaining insight into their repository
usages, suggest some hypotheses to explain this phenom-
enon. Possibly some authors do not submit a resource until
they have carefully thought about the design choices and
tested it in a classroom or in a teacher training course. Such
a resource is considered as robust enough and modifica-
tions suggested by peer reviews can thus be regarded as
pointless. In some cases, it seems that the reviews do not
provide enough information about how to improve the
resource. This is the case of reviews that evaluate only the
general questions, without entering into the detailed criteria
and without providing any qualitative comment (these are
qualified as ‘‘fan’’ or ‘‘global’’ reviews).
Regarding the nature of the reviews, it is interesting to
note that the users who answer the detailed criteria and
provide qualitative comments (‘‘expert’’ or ‘‘partially
expert’’ reviews) have either been directly involved into the
Intergeo project (C1 and C2 members), in which case they
seem to understand the purpose of the assessment process
and therefore adhere to the principle of peer review, or they
provide the review in the framework of a teacher training
programme, in which case their review is supervised by a
tutor. In addition, the lack of communication and collab-
oration tools in the repository may create a feeling of
isolation, which can impact the user’s motivation to
contribute.
Importantly, the review from peers comes usually only
after some delay, so the feedback provided by the review
might not match the author’s need for improving his/her
resource. We can thus conclude that the quality assessment
process has the potential to improve the resource quality,
but it seems not to be fully effective.
The second issue dealt with in this paper is the impact of
the involvement of teachers in the quality resource con-
siderations on their practices related to the design and use
of resources. The case study conducted with seven teachers
involved in the research on the DG resource quality shows
significant evolution of their practices both as teachers and
teacher educators. The teachers manifest a better under-
standing of the potentialities of DG for mathematics
teaching and learning that is evidenced by the design of
richer and more challenging activities for their students
taking advantage of various modalities of dragging. The
teachers declare also that they feel more comfortable in
managing their classes with DG, which is due to their
ability to envisage more adequate instrumental orchestra-
tions of their classroom activities. Finally, in their teacher
training programmes, we could observe a clear shift from
focusing on technical aspects related to the mastery of DG
systems towards a consideration of didactical and peda-
gogical aspects of classroom activity implementation,
showing their acknowledgement of a double instrumental
genesis that is necessary in trainee-teachers wishing to
integrate dynamic geometry in their classrooms.
These results show that the repository and the tools
developed within the Intergeo project can be used effi-
ciently in the framework of teacher training initiatives in
which their appropriation by the participating teachers can
be accompanied and facilitated by tutors’ interventions.
However, an uncontrolled use of these does not seem to
produce the expected outcome. This opens a new per-
spective of searching for the means of accompanying the
processes of appropriation of the repository tools and ser-
vices; in other words, the means of some kind of control of
the repository’s ‘‘uncontrolled’’ use.
Acknowledgments The authors would like to thank the group of
teachers associated with this project, as well as the i2geo repository
users who kindly responded to our questionnaire.
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