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