Rhodes University

Education Department

Research Proposal

Student name: Gugu Bophela

Student Number: 15B3868

Degree: Master’s in Education

Provisional Title: An investigation of Grade 3 teacher experiences of using a

mathematics recovery program focused on progression of early

arithmetic strategies.

Field: Mathematics Education

Type of Thesis: Full Thesis

Supervisor: Professor Mellony Graven

Date of submission: 13 October 2015

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Abstract

The study is an exploration of Grade 3 teachers’ experiences of supporting learner

progression of arithmetic strategies through the implementation of an internationally

researched mathematics recovery program. Initial research will explore teacher current

experiences of supporting learners not progressing according to curriculum expectations.

Additionally the research will conduct a documentary analysis of official curriculum policy

and support documents. This will be followed by an intervention project that focuses on

combining assessment of learner arithmetic strategies with structured activities for enabling

progression of learners towards more efficient and sophisticated strategies. The unit of

analysis will be teacher learning experiences of the implementation of the MR program

which will inform opportunities for possible wider use of aspects of this program for

mathematics teaching, and for pre and in-service teacher education. A multiple case study

approach of five Grade 3 teachers from two selected primary schools in Kwa-Zulu-Natal will

be used to gather rich qualitative data and to enable thick description.

Rationale for the study

My experience of primary mathematics teaching and learning in a range of roles, has afforded

me with an opportunity to engage with teachers’ experiences of curriculum implementation

and the challenges of teaching and learning. I have observed them teaching, conducted

mathematics workshops and lectured pre service Foundation Phase (FP) student teachers.

Across this work teachers articulated their frustrations of the learners’ lack of basic

mathematics concepts and calculation strategies, and the lack of the required grade level

competencies. This resonated with my own frustrations as a FP mathematics teacher. This has

inspired me to conduct research on the possibilities for addressing these gaps within the

South African context. In this respect I have chosen to research the implementation of

Wright, Martland, & Stafford (2006) Mathematics Recovery (MR) programme, particularly

the aspects of the program focusing on early arithmetic strategies. I plan to research the

possible value of this program for improving progression of early arithmetic strategies to

enable better access to the increasingly abstract mathematics in higher grades.

I am also motivated to conduct this research by the chronic low performance levels in

mathematics among South African learners largely attributed to the lack of progression from

1-1 (often concrete) counting methods of calculation even in the upper primary grades

(Schollar, 2008). As an educator I am always concerned about the state of teaching and

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learning and learner performance in South Africa, especially in the FP. I was thus drawn to

the MR programme by the fact that it was developed ‘as a systemic response to the problem

of chronic failure in school mathematics’ (Wright et al. 2006,p.3) and its particular focus on

structured resources to support learner progression up the various stages of mathematical

reasoning was particularly appealing.

Therefore, this study seeks to establish how the MR programme could provide an opportunity

for assessment and remediation to support learners who perform below their grade level

expectations. This in the long term will contribute towards ‘shifting learners out of the

bottom end of the performance spectrum’ as envisaged by Reddy, Zuze, Visser, Winnaar,

Juan, Prinsloo, Arends, & Rogers (2015, p. 38).

Focus and Purpose of study

Firstly the study seeks to understand how Grade 3 teachers currently address the need for

remediation and enabling progress for those learners in their classes who continue to use

concrete inefficient calculation strategies. This will be considered against the background of

the extent to which the department of education’s curriculum policy and teacher support

documents focusing at grade specific curriculum coverage enable or constrain such

opportunities for remediation. Secondly the study seeks to investigate teacher experiences of

the implementation of Wright et al.’s (2006) MR program, which begins with learner

interview assessments, followed by analysis of learner levels of mathematical reasoning and

the implementation of structured activities aimed at progression of learners from the level

they are at.

I have chosen to focus on Grade 3 as this is the exit point in the FP. The expectation is that by

the end of this phase the mathematics foundational concepts are in place so that learners are

ready to progress onto the learning of increasingly abstract mathematical knowledge which is

foregrounded in the Intermediate Phase (IP). The purpose is to expose Grade 3 mathematics

teachers to the MR programme with the aim of implementing it in their classrooms for the

purposes of assisting learners who perform below their grade level expectations. A broader

goal is to help learners develop a strengthened number sense that will help them improve

their mathematics proficiency.

The study is based on the premise that mathematics is a hierarchical subject and that learning

mathematics requires learners to construct knowledge on previously learnt concepts (Graven,

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2015). In this respect it is imperative to identify and remediate learning gaps in the early

years of learning before they expand and become insurmountable in the higher grades

(Fleisch, 2008).

The study is informed by the reports of the chronic low performance levels in numeracy

among most South African learners, which consistently tend to be among the lowest on

comparative international and regional studies such as TIMSS (Trends in Mathematics and

Science Studies) even when compared with other third world countries (Reddy et al, 2015).

Findings of the Systemic Evaluation in 2003 revealed that learners at Grade 3 level appeared

to have a very poor grasp of elementary mathematics, achieving an average score of 30% on

the numeracy tasks. Furthermore, the recent 2012 and 2013 Annual National Assessment

(ANA) analysis conducted by the DBE, show little improvement in Foundation and

Intermediate Phase mathematics learner performance. The mean average percentage for ANA

2011 in mathematics dropped from 63% at Grade 1 to 31% at Grade 6 level. The average

score was 28% at both Grades 4 and 5 (DBE, 2011). In the ANA 2013 Grade 3 learners

achieved an average of 53% but this decreased to 37% in Grade 4 in the following year. The

2013 and 2014 ANA results analysis revealed that learners in Grade 3 and 4 are still

operating far below their grade level in mathematics.

These results concur with other research findings, Schollar (2008) asserts that there is

predominance of 1-1 concrete methods of calculation which become un-useable when

number ranges increase in later grades. Spaull (2013) indicates that by Grade 4, learners are

already 1.8 years below grade level expectations. Thus the majority of South African learners

do not have the basic numeracy skills required to progress mathematically and that with each

progressive year of schooling more and more learners lag behind meeting the basic

requirements for their grade level (Schollar, 2008).

In light of the evidence above, it becomes imperative that FP mathematics teachers be

equipped with much needed competencies to provide remediation and recovery opportunities

to enable learners to cope with increasingly abstract mathematics in the higher grades. This

could be achieved through guiding teachers on how to identify children’s levels of

mathematics reasoning within the framework provided by the MR programme and linking

these with key structured activities that have been reported across a range of international

research to support progression towards higher levels of reasoning.

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Key research question:

What are teachers’ experiences of the use of a structured recovery program, with built in

assessment and progression, in supporting learners who perform below grade level

expectations?

Sub questions:

How do Grade 3 teachers currently provide learners operating at concrete levels of arithmetic

reasoning with opportunities to progress to more efficient strategies, if at all? What

challenges or enablers do teachers encounter in this endeavour?

How does the content of official policy documents and resources provided to teachers (i.e.

curriculum and assessment documents, teacher guides, workbooks, work plans/ schemes of

work) for Grade 3 teaching enable or constrain remediation of inefficient concrete arithmetic

strategies?

Mathematics Recovery (MR) Programme

The MR programme was developed as a result of ongoing research in teaching and

assessment of children’s early mathematics number knowledge. It has two distinct but

interrelated components. One component is concerned with the theory and practice of

developing early number knowledge in young children whilst the other component is

concerned with providing professional development to teachers enabling them to develop

early number knowledge with young children Wright, (2003). The key features of MR are

early intervention, interview-based assessment and teaching and professional development.

My choice of this programme is partly due to its international success. MR has been

implemented across a wide range of countries as well as local research and this points to

successes of teachers as researchers drawing on this work (e.g. Mofu, 2013; Ndongeni, 2013;

Stott, 2014; Weitz, 2012). Additionally the MR provides robust frameworks that are useful

for both research and intervention work. Both international and local researchers report the

success of the programme in terms of progress made by the learners who were involved in the

programme (e.g. Mofu). Across these studies researchers were able to determine learners’

stages and levels, and learners’ progress or absence of progress from one level to the next

could be clearly ascertained. These successes are a motivation to my research of the

effectiveness of this programme in a different context with a different focus i.e. in my case

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the focus of my research is on teacher experiences of the implementation of this programme

while in most research it was on learner experiences.

The MR programme provides a learning and assessment framework which points to the

critical importance of focusing on progression and use of conceptual resources to assist

learner ‘recovery’. The Learning Framework in Number (LFIN) includes early arithmetic

strategies (EAS) which learners must actively construct for themselves through engagement

with key conceptual resources and a more experienced mentor/peer. The framework is

organised into four parts which are further divided into 11 aspects of children’s early

numerical knowledge. Part A of the framework has two aspects which are Stages of Early

Arithmetical Learning (SEAL) and Base-Ten arithmetical strategies. The SEAL has six

stages which are outlined on table one below and Base-Ten arithmetical strategies has three

levels. Part B has three aspects which are Forward Number Word Sequence (FNWS),

Backward Number Word Sequence (BNWS) and Numeral Identification. Part C deals with

structuring number 1 to 20 and has five aspects which are combining and partitioning, spatial

patterns and subitising, temporal sequences, finger patterns and five-based (quinary-based)

strategies. Part D deals with early multiplication and division. It is beyond the scope of this

study to cover all parts of the LFIN hence the focus is on one aspect namely, the SEAL which

is part A of the framework. I have chosen this aspect because SEAL is the most important

aspect of LFIN as it provides the basic mathematics strategies for addition and subtraction

which in turn assist learners as they learn other basic operations and more complicated

mathematics concepts (Wright, et al, 2006). Additionally the SEAL particularly addresses the

problem of 1-1concrete counting strategies that have been identified as the stumbling block to

progression towards abstract mathematics reasoning (Schollar 2008?). The Early

Arithmetical Strategies (EAS) domain in the LFIN encompasses strategies for increasing

efficient counting and the non-calculation in six developmental stages and the framework is

presented below.

Table 1: Early Arithmetical Strategies

Stage

number

Stage descriptor Characteristics (representing increasing levels of sophistication)

0 Emergent counting Cannot count visible items. The child might not know the number words

or might not coordinate the number words with the items.

1 Perceptual counting Can count only visible items starting from 1, including seeing, hearing

and feeling.

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2 Figurative counting Can count concealed items but the learner will ‘count all’ rather than

‘count on’.

3 Initial number

sequence

The child can count on rather than counting from one to solve + or

missing addends. May use the counting-down to solve removed items,

(count back from).

4 Intermediate number

sequence

Count-down-to solve missing subtrahend (e.g. 17-3 as 16, 15 and 14 as an

answer). The child is able to use a more efficient way to count down-from

and count down-to strategies (count-back-to).

5 Facile number

sequence

Uses of range of non-count-by one strategies. These strategies such as

compensation, using a known result, adding to 10, commutativity,

subtraction as the inverse of addition, awareness of the 10 in a teen.

Source: Wright, R.J., Martland, J., Stafford, A.K., & Stanger, G. (2006).

The program integrates both assessment and teaching through specific diagnostic tools of

children’s early number strategies and knowledge, followed by instructional activities that

can be provided to individual learners. Van de Walle & Lovin (2006) support the use of

diagnostic interviews to assess learners. They posit that an interview helps the teacher to

understand how the child thinks about a particular subject, what processes the child uses in

solving problems, how the child constructs concepts or what attitudes and beliefs the child

might have. Interviews have the potential to provide the teacher information about a learner

that he/she cannot easily access in any other way. However, they caution about the fact that

most teachers avoid interviews due to time constraints. Mofu (2013) also concur that

interviews are labour intensive and time consuming to administer to many learners.

Nevertheless, interviews provide crucial information for profiling learners as well as for

enabling teacher reflection on student learning and levels of reasoning generally. I will

negotiate with teachers about this and together we will find strategies for the best use of

diagnostic interviews.

Literature Review

Implementation of the MR programme within the South African context

Most of the research conducted locally on the use of MR programme has been done by

researchers and student researchers from the South African Numeracy Chair at Rhodes and

Wits Universities through the afterschool mathematics clubs. Graven, Stott, Mofu, &

Ndongeni (2015) report on each case of their use of the MR programme in the after school

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clubs context and they commend the usefulness of the programme for planning subsequent

interventions.

Mofu (2013) researched the effectiveness of the MR programme to remediate multiplicative

reasoning in an after school intervention program with a group of six learners and found that

even with an intervention that was conducted over four sessions, all learners showed some

progression at least one level of the LFIN. Mofu noted that learners were beginning to apply

more efficient methods to solve multiplication tasks. Mofu began her research as a teacher,

by the time she was writing up her research she had become a curriculum specialist and

concluded that the MR programme highlighted for her the possibility of the programme to

enable teachers to understand levels at which learners operate when solving mathematics

problems.

Similarly Ndongeni (2013) used the LFIN to establish learner levels of conceptual

understanding in multiplication. Six grade 4 learners were assessed using the LFIN. The

comparison was made between levels of numeracy reasoning and conceptual understanding

with productive disposition as described by Kilpatrick, Swafford, & Findell, 2011. The

researcher noted the usefulness of the LFIN in assessing learner levels of conceptual

understanding.

Stott (2015) researched learners’ numeracy progression more broadly across LFIN aspects

and the role of mediation in the context of two mathematics clubs that ran weekly for a year

using the LFIN as an analytic tool. Although the LFIN interview assessments are not

intended to produce scores (Wright, 2003) but she developed quantitative data in the form of

scores in her study. This was useful for her to compare the overall progress of different clubs

she worked with. From these she identified where learners had achieved high and low scores

and used this information to plan activities to address areas of weakness for the whole club

(Graven et al, 2015, p. 74). Her findings depicted that learners assessed made progress at

different degrees as evidenced by the scores she analysed.

Graven (2012) used the LFIN interviews to identify two learners’ numeracy progression over

a year. The researcher reports on how the analysis of two learners’ interview responses and

assessed levels of numeracy proficiency influenced their opportunity to participate in the

subsequent club activities. The study provides details of learners’ progress and strategies they

used as they progressed from one level to the next.

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Wasserman (2015) conducted research to understand the possibilities and constraints of the

implementation of an adapted maths recovery programme with a class of learners. She

conducted eight recovery sessions with a grade 4 class of 23 learners. The researcher adapted

the programme by administering the interview assessments with groups of learners instead of

individual learners. The researcher shares the challenges relating to working with groups

instead of individual learners. However, she posits that these could be overcome during the

group sessions. Learners were able to progress in terms of their early arithmetic strategies and

conceptual place value, although she noted that a longer recovery period is necessary to

conduct all the assessments.

Weitz (2012) applied the MR programme to get an understanding of the number strategies

used by Grade 2 learners in the ANAs. The LFIN was used as an analytical tool to analyse

strategies used in learner responses. The researcher was able to establish learners’ levels of

operational and structural thinking. The LFIN assessment provided richer information

regarding the learners’ performance in ANA.

In Australia Dineen (2014, p. 31) used the SEAL as a theoretical framework to inform the

advancement in complexity of students’ use of counting strategies to solve addition tasks.

The researcher found that SEAL assisted all learners in the class to progress from perceptual

counting to using grouping strategies. The above research points to different aspects of LFIN

that different researchers focused on and the differences in time and space in which MR was

implemented.

My research will be different since I will be working with teachers who are not researchers

and who might not have the knowledge of the MR programme. The MR programme will be

implemented by teachers in their classrooms and they will share their experiences of the

impact made by the programme on their teaching and learning.

Theoretical framework

This study is framed by Vygotsky (1978)’s socio-constructivist theory which views learning

as a collaborative construction of socially defined knowledge and values and occurs through

socially constructed opportunities. Within this perspective learning and development is a

collaborative activity and it stresses the fundamental role of social interaction towards

development of cognition (Vygotsky, 1978). Learner construction of knowledge is the

product of social interaction, interpretation and understanding (Vygotsky 1962 cited in

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(Adams 2007). Shepard (2000) concurs with Vygotsky’s view and points out that social

constructivist theory emphasises the role for others in the individual construction of

knowledge and views learning as a primarily social process.

The unit of analysis of this study is teacher learning experiences of the use of the MR

program to support and enable progression of learner early arithmetic strategies. This

learning will be enabled, not only by their active experience of using the MR program with a

small group of learners but additionally by their opportunity to engage collaboratively with

other teachers participating in the intervention when attending the MR preparation and

reflection sessions.

A socio-constructive perspective of learning similarly informs the MR program in terms of

how students learn mathematics. Jonassen (1994) posits that constructivist learning is based

on students’ active participation in problem-solving and critical thinking activities which are

relevant and engaging. The MR programme promotes this active participation and critical

thinking by allowing learners to use their own strategies when solving problems and to

explain their reasoning. Vygotsky believed that learning can lead development and he was

concerned with the unity and interdependence of learning and development. Askew (2013)

supports Vygotsky’s idea and asserts that young children possess inherent abstract reasoning

abilities, however, their reasoning is limited due to their lack of worldly knowledge. He

further points out that experience is what is needed to help children expand their range of

abstract reasoning. Development occurs as children learn concepts and principles that can be

applied to new tasks and problems. For children to gain this experience they need more

opportunities to interact with others and with the world around them and to explore their

environment thus constructing their knowledge. The MR programme provides learners with a

wide range of activities according to their stages and levels of the LFIN, these activities

expand their thinking as they construct knowledge and enable them to devise the most

advanced strategies to solve mathematical problems.

Socio-constructivist theory is appropriate for this study as the theoretical origins of the MR

approach are influenced by Steffe’s research methodology called ‘constructivist teaching

experiments’ (Steffe, 1991). This research focused on early number learning and involved

small groups of children in intensive problem-based teaching and observation of the

strategies children used as they engaged in problem solving. Drawing from socio-

constructivism, the MR approach is based on the principles that learning is an active process,

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each child constructs their own mathematical knowledge and they develop mathematical

concepts as they engage in sense-making mathematical activity. It also promotes the idea of

learning assisted by the teacher who helps the child to make sense of what is taught (Wright

et al, 2006). This idea (of learning assisted by the teacher) coheres with Vygotsky’s concept

of ‘the more knowledgeable other’ assisting the child to reach the potential level (Vygotsky

1978.

While the LFIN and the levels of EAS will provide an analytic framework to map learners’

knowledge of early number I will draw on Vygotsky’s idea of artefact-mediated and object-

orientated action (Vygotsky, 1978) in order to analyse teacher experiences. Vygotsky (1978)

posits that people’s thoughts and actions are mediated by external objects (motives or goals).

Action is initiated through mediated artefacts or tools between subject and object. This is

done through cultural means, tools and signs, and language is a special tool that mediates

between understanding and social and cultural action. The motive or outcome of the study is

to find out how the teachers experience the impact of the MR programme in their teaching

and learning. This will be determined through the use of tools that I will provide to teachers.

I will analyse how the subjects (teachers) use the tools for mediation i.e. conducting

assessment interviews, profiling learners, writing their experiences on recovery reflection

sheets, talking about their experiences and viewing video records to stimulate recall during

the reflection and interview sessions. This will involve thematic analysis through which I will

identify emerging themes which are related to the key research question while analysis of

curriculum documents will draw largely on content analysis.

Research design and methodology

Since my research focuses on teacher experiences of implementation of an intervention it is

important to begin with a brief outline of the initial conceptualisation of that intervention and

my role in it. In this study I will wear two hats. On the one hand I will be working with the

teachers to co-ordinate and provide the ‘training’ and resources related to the implementation

of an intervention that may support their teaching and learning (i.e. I will be the co-ordinator

of the development program) while on the other hand I will be a participant researcher in the

process. Of course the MR programme will be adapted in relation to teacher input and so

some aspects might change although the aspect of conducting MR learner interviews and

providing a series of subsequent sessions with learners focused on use of structured activities

informed by the MR program would be central. This would involve the teachers’

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commitment to three monthly afternoon sessions where all teachers involved meet for both

‘MR training’ and MR reflection, feedback and adaptation where necessary.

Time Frame MR aspect ResearchFeb 2016 Invitation of teachers/ schools to participate in

study.Basic explanation of MR and aims of the research.Negotiation time frame and outline.

Permissions and sample selection.

March 2016 Teacher interviews (baseline data on teacher experiences and sub question 1)

March 2016 MR teacher ‘training’ session.Learner assessment interview training.

Learner parent permission.

March 2016 MR learner sessions.Teachers conduct MR interviews on EAS with three learners identified to be operating below grade level expectations.Teachers are supported to identify learner levels of EAS (about 15 minutes per learner interview).

Video record these to enable individual stimulated recall teacher interviews with each of the five teachers.

March 2016 MR teacher ‘training’ session.Teachers bring learner profiles and jointly we select from MR structured activities, those that will be used for subsequent recovery sessions with a group of learners.

Session is recorded to support my journal notes on teacher learning experiences in engaging with MR.

April Teachers conduct five MR sessions (approximately 45 minutes per session) with the three learners.Flexibility on how and when this is done.

Teacher record experiences on recovery reflection sheets at the end of each session and bring these to the following MR teacher session.

Teachers repeat MR interviews with the three learners.

May MR teacher ‘reflection session’Focus: reflection of experiences and opportunities for adaptation.

Session is recorded to enable transcription of session and teacher experiences.

May/June Individual teacher interviews on individual experiences of MR

My questions seek thick description and hence I have chosen a qualitative research design

using a multiple case study approach, will explore five Grade 3 teachers’ experiences of the

use of a structured recovery program with built in assessment and progression in supporting

learners who perform below grade level expectations. Qualitative research is described as a

naturalistic, interpretative approach concerned with understanding the meanings which

people attach to phenomena (actions, decisions, beliefs, values etc.) within their social worlds

(Ritchie, & Lewis, 2003).

I chose the case study design because I will be studying teachers within a specific context,

observing them in their natural environment to gain rich, in-depth, detailed understanding of

their experiences. Through the use of an interpretivist approach, I will use different strategies

for data collection. Qualitative approach will assist me to gather rich descriptive data which

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explains the phenomenon under study in its complexity (Maree, 2007; Henning, Van

Rensburg, & Smit, 2004).)

Sampling

I will use purposive sampling to select my participants. According to Maree (2007) sampling

refers to the process used to select a portion of the population for study. Cohen, Marion, &

Morrison (2000) posit that in purposive sampling the sample needs to be deliberately and

purposefully selected according to their understanding of the phenomenon under study. In

this case five grade 3 mathematics teachers from two primary schools will be invited as

participants. The school in the Pinetown district serves Grade R to 7 learners from the

informal settlements around the area and from different townships and other suburbs. This

school offers English as its LOLT in the FP but most learners’ home language is IsiZulu. This

school has two grade 3 teachers. The other school in the Umlazi district serves Grade R to 7

learners from the township. This school offers IsiZulu as its LOLT in the FP and most

learners’ home language is IsiZulu. This school has three grade 3 teachers. The two schools

are not used for comparative purposes but to enrich findings and provide the opportunity for

at least five grade 3 teacher participants. All grade 3 teachers at these schools will be invited

to participate in the study and it is envisaged therefore that five teachers will form the sample

of the study. Schools were selected according to ‘convenience’ in relation to those that I

already have good working relations with and are relatively easy for me to access in terms of

travel distance.

Data collection and analysis

I will use three main data collection methods (teacher interviews, teacher MR reflection

sheets and researcher observation notes (journal entries). The last two will be used following

each session with teachers enabled by video recordings and transcriptions of sessions for

answering my central question. Individual teacher interviews will be used at the start of the

research, followed by teacher use of MR interviews and at the end of the intervention. I will

use documentary collection and analysis for gathering contextual information.

Initially I will use semi-structured teacher interviews to establish how teachers currently

provide learners, operating at concrete levels of arithmetic reasoning, with opportunities to

progress to more efficient strategies, if at all, and what challenges or enablers teachers

encounter in this endeavour. This will be followed by a teacher training session on the MR

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learner assessment interview as a key tool for gathering diagnostic information on learners’

levels of mathematics reasoning.

Thereafter I will observe each teacher, conducting MR assessment interviews on EAS with

selected learners, this will be video recorded to enable teachers to analyse learner responses

and also to enable me as a researcher to conduct individual stimulated recall teacher

interviews following each teacher’s MR learner interviews.

I will conduct another training session to analyse teachers’ profile of learners according to the

levels of EAS and together we will select the MR structured activities to be used for

subsequent recovery sessions. Subsequent to this, teachers will conduct five MR recovery

sessions with learners and use the teacher reflection sheets for each session wherein they will

have a structured reflection guide to fill in and to reflect on each of the recovery session with

learners, and to record ideas for subsequent sessions. Following these sessions, teachers will

repeat MR learner interviews to analyse progress. I will observe and video- record all the

subsequent MR interviews with learners.

Lastly I will use post teacher interviews to explore the effects of the MR programme on

teaching and learning of mathematics in their classrooms. I will record all training sessions

and use my journal to take notes on teacher learning experiences in engaging with the MR

programme. To analyse this data I will use thematic analysis to identify common phrases,

words and sentences (from transcriptions, field notes and reflection sheets) that are

addressing my research questions and use these to develop themes that capture or summarise

the contents of my data (Thomas, 2009). Each theme will be responding to the research

questions and will provide insight of the meanings that are constructed by the participants.

Semi-structured interviews are relevant to this study because they are best used to gain

insight into people’s opinions, feelings, emotions and experiences (Denscombe, 2010). They

allow for the probing and clarification of answers. As a researcher I will be attentive to the

responses of the participants in order to identify new emerging lines of inquiry that are

directly related to the phenomenon being studied (Maree, 2007). Through semi-structured

interviews, I will be able to explore teachers’ experiences of the use of a structured MR

programme to assist learners who are performing below their grade level in mathematics.

Documentary analysis is relevant to this study (and particularly the second sub-question)

because when a researcher uses documents as a data gathering technique, she or he focuses

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on all written communication that may shed light on the phenomenon under study (Maree

(2007). The documents I will analyse will include: the CAPS mathematics Foundation Phase

(DBE, 2010), assessment and progression policy (DBE, 2011) guidelines on ANA results

analysis (DBE, 2012) and the ANA reports (DBE, 2011, 2012, 2013, 2014). Additionally I

will analyse official teacher support documents provided by districts, namely, the teachers’

work plans/ work schedules and Grade 3 mathematics DBE workbooks (DBE, 2015). In this

case, I will employ a content analysis strategy (Robson, 2002) to analyse the contents of the

curriculum and other related policy documents with the aim of identifying similarities and

differences in text that would corroborate or disconfirm theory (Maree, 2007). Through

content analysis I will be able to investigate how these documents enable or constrain

mathematics recovery and progression opportunities to learners who perform below their

grade level expectations.

Validity and Trustworthiness

Using different data collection instruments i.e. interviews, lesson videos, journal entries,

reflection sheets and document analysis, will support validity and trustworthiness of findings.

It will also provide rich, in-depth collection of data which will be compared and triangulated

to provide a richer picture and to enable consistency and truthfulness.

The teacher participants will be given a transcribed report of their interviews and field notes

taken during observations to enable mutual meanings between the participants and the

researcher, and agreement on the description of events (McMillan, & Schumacher, 2010).

Video records will be viewed with the teacher during the interview to ensure accurate

interpretation of learners’ responses, gestures and strategies used. Video records and

transcripts enable the provision of rich data that will enhance validity. I will ensure

trustworthiness of data by submitting transcripts of interviews and field notes to the

participants to correct errors that might have been overlooked. This will ensure participant

verification of data and to avoid being biased when analysing data.

Limitations

The study is limited to a particular sample of five grade 3 teachers in two schools. Therefore

the research findings will not be generalizable but they should provide insight to the teachers’

experiences of using the MR programme in their context, and point to possibilities for wider

implementation and further research across other samples and context.

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Ethical issues

I will seek informed consent for the participants wherein the information about the purpose,

methods and intended uses of the research will be explained in detail. Participants will be

informed about anonymity and confidentiality of information and their voluntary

participation which they can withdraw at any point. As I work for the Department of Basic

Education I will be particularly sensitive to my positionality as a Departmental official and I

will avoid observing situations from the Department’s perspective.

Video data with learners will only be used for stimulating teacher reflection and recordings of

reflection sessions will not be shown to anyone else and will only be used for research

purposes. Parental permission will however still be obtained to use the video in MR

interviews. I will approach the participants directly for this research in order to avoid

miscommunication. I will seek ethical clearance from the Department of Education as well as

the schools for conducting research. I will also seek permission from the gatekeeper who is

the principal of the school to conduct research. Finally I will avoid any misinterpretation and

misuse of data and I will acknowledge the work of others used in this study.

References:

References:

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