An exploration of grade 4 teachers' understanding and practice of 

formative assessment in Mathematics. 

By 

Jacob Mark Anthony Tripp 

Submitted in partial fulfillment of the requirements for the degree 

Master in Education  

In the 

Humanities Faculty 

At the 

University of the Witwatersrand 

Supervisor 

Dr Preya Pillay 

Submission date 

 March 2024 

 

 

 



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DECLARATION 
 

I, Jacob Mark Anthony Tri, hereby declare that this research report titled An exploration of 

grade 4 teachers’ understanding and practice of formative assessment in Mathematics, is my 

own work, and that it has not been submitted for any degree or examination to any other 

University. I declare that all the sources I have used or quoted have been referenced and 

acknowledged. 

 

Signed:   

Date: 15 March 2024. 

 

 

 

 

 

 

 

 

 

 

 

 

 



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ABSTRACT 
 

This qualitative case study examined grade 4 teachers' understanding and implementation of 

formative assessment in mathematics at a South African private school. The study employed 

semi-structured interviews with three teachers and observations of nine lessons to develop 

insights into how educators conceptualize and apply formative assessment strategies. 

Thematic analysis revealed that while teachers demonstrated strong theoretical knowledge of 

formative assessment during interviews, classroom practices showed inconsistencies and 

missed opportunities for effective integration. Key findings indicated gaps in translating 

conceptual understanding into consistent, high-quality formative routines. Instruction often 

conflated formative and summative purposes, with an over-reliance on teacher judgments 

rather than eliciting student thinking. Despite recognizing the value of descriptive feedback, 

crucial opportunities were missed to provide specific guidance to advance learners' 

mathematical comprehension. 

Challenges in implementing formative assessment stemmed from time constraints, difficulties 

managing differentiation, and determining appropriate pedagogical responses based on 

assessment insights. The overarching issue was the struggle to operationalize theoretical 

understanding into routines that unveil and responsively scaffold students' emerging 

mathematical proficiencies. 

The study highlights the need for ongoing professional development, collaborative planning, 

and coaching to bridge the theory-practice divide. Leveraging technology and resources could 

alleviate logistical constraints. Recommendations aim to foster a culture of continuous learning 

and responsiveness to students' evolving needs. Effective formative assessment has the 

potential to enhance engagement, conceptual understanding, and achievement in mathematics. 

 

 

 

 

 



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ACKNOWLEDGEMENTS 
 

Finishing my Master's Thesis is a significant achievement for me. I owe a debt of gratitude to 

several individuals who have supported me along this journey. 

Firstly, I want to express my heartfelt thanks to my late grandmother, Patsy Tripp, whose 

consistent love and honest encouragement continue to be a compass that guides me. 

Also, I am also grateful to my family for their constant support and understanding throughout 

the challenges of my academic life. 

Besides, I extend my appreciation to the school where I work for providing funding that has 

eased the financial burden of pursuing my studies. 

Lastly, I want to acknowledge the invaluable guidance and support of my supervisor, Dr. Preya 

Pillay, whose expertise has been instrumental in helping me complete this thesis. 

To all those who have contributed to my journey, thank you for your belief in me and for 

helping me reach this milestone. 

 

 

 

 

 

 

 

 

 



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LIST OF FIGURES 

 

Figure 1: Assessment of learning loop …………………………………  page 46 

Figure 2: Thematic analysis Phases ………………………………………page 73 

LIST OF TABLES 

Table 1: Five key activities of formative assessment …………………….. page 48 

Table 2: Classroom Observation guide……………………………………page 62 

Table 3: Observation record………………………………………………  page 66 

Table 4: Participant information ………………………………………….page 73 

 

 

 

 

 

 

 

 

 

 

 

 



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ACRONYMS & ABBREVIATIONS. 

 

CAPS –Curriculum and Assessment Policy Statement  

DBE- Department of Basic Education 

OBE- Outcomes Based Education 

C2005- Curriculum 2005 

RNCS- Revised National Curriculum Statement  

DOE- Department of Education  

IEB - Independent Examinations Board (IEB) 

ISASA- Independent Schools Association of Southern Africa 

 

 

 

 

 

 

 

 

 

 



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TABLE OF CONTENT 

 

DECLARATION .................................................................................................................................... 2 

ABSTRACT ............................................................................................................................................ 3 

ACKNOWLEDGEMENTS .................................................................................................................... 4 

LIST OF FIGURES ................................................................................................................................ 5 

LIST OF TABLES .................................................................................................................................. 5 

ACRONYMS & ABBREVIATIONS. .................................................................................................... 6 

TABLE OF CONTENT .......................................................................................................................... 7 

CHAPTER ONE ................................................................................................................................... 11 

ORIENTATION TO THE STUDY ...................................................................................................... 11 

1.1 Introduction ................................................................................................................................. 11 

1.2 Background and contextualisation of study ................................................................................ 11 

1.3 Statement of problem .................................................................................................................. 15 

1.4 Rationale ..................................................................................................................................... 16 

1.5 Key research questions ............................................................................................................... 17 

1.6 Aim of the study .......................................................................................................................... 17 

1.7 Significance of the study ............................................................................................................. 19 

1.8 Context of study .......................................................................................................................... 20 

1.9 Overview of the research design and methodology .................................................................... 21 

1.9.1 Paradigm .............................................................................................................................. 21 

1.9.2 Sampling .............................................................................................................................. 21 

1.9.3 Data collection strategies ..................................................................................................... 22 

1.10 Overview of the chapters ...................................................................................................... 23 

CHAPTER 2 ......................................................................................................................................... 24 

LITERATURE REVIEW ..................................................................................................................... 24 

2.1 Introduction ................................................................................................................................. 24 

2.2 Types and purpose of assessment in Mathematics ...................................................................... 24 

2.3 South African National Assessment Policies .............................................................................. 27 

2.4 Principles of formative assessment ............................................................................................. 29 

2.5 Impact of formative assessment on learning ............................................................................... 31 

2.6 Teaching, Learning and Assessment in Primary Mathematics ................................................... 36 

2.7 Assessment challenges in Mathematics education ...................................................................... 38 

2.8 Translating policy into classroom practice ................................................................................. 41 

2.9 Assessment in private schools..................................................................................................... 45 

2.10 The gap and conclusion ............................................................................................................ 48 



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2.11 Theoretical framework .............................................................................................................. 48 

2.12. Conclusion ............................................................................................................................... 54 

CHAPTER 3 ......................................................................................................................................... 55 

RESEARCH METHODOLOGY .......................................................................................................... 55 

3.1 Introduction ................................................................................................................................. 55 

3.2 Research paradigm: Interpretivism ............................................................................................. 55 

3.3 Qualitative research approach ..................................................................................................... 57 

3.4 The Research design ................................................................................................................... 58 

3.5 Data collection instruments ......................................................................................................... 59 

3.5.1 Semi-structured interviews .................................................................................................. 59 

3.5.2 The Pilot study ..................................................................................................................... 60 

3.5.3 Process for conducting the semi-structured interviews ........................................................ 61 

3.5.4 Classroom observations ....................................................................................................... 62 

3.5.5 Advantages of using classroom observations ...................................................................... 63 

3.5.6 Procedure for classroom observations ................................................................................. 63 

3.6.7 Conducting the classroom observations ............................................................................... 68 

3.5.8 Challenges encountered during classroom observations ...................................................... 69 

3.6 Measures to ensure the trustworthiness of the study ................................................................... 70 

3.7 The Sampling approach .............................................................................................................. 71 

3.8 Selection of participant criteria ................................................................................................... 74 

3.9 Data analysis ............................................................................................................................... 74 

3.10 Research ethics .......................................................................................................................... 77 

3.11 Chapter summary ...................................................................................................................... 78 

CHAPTER 4 ......................................................................................................................................... 79 

DATA ANALYSIS ............................................................................................................................... 79 

4.1 Introduction ................................................................................................................................. 79 

4.2 Research question 1: What are grade 4 teachers’ understanding of assessment as it relates to the 

mathematics learning area? ............................................................................................................... 79 

4.2.1 Theme 1: Practical applications and real-world connections ............................................... 80 

4.2.2. Theme 2: Formative assessment for monitoring and guiding conceptual understanding ... 84 

4.2.3 Theme 3: Difficulties in applying formative assessment ..................................................... 87 

4.3 Research Question 2: How do grade 4 teachers' understanding of assessment influence their 

practice of classroom assessment as it relates to the mathematics learning area at a private school?"

 .......................................................................................................................................................... 89 

4.3.1 Theme 1: Strong conceptual understanding, inconsistent practice ...................................... 90 

4.3.2 Theme 2: Assessment for learning vs assessment of learning ............................................. 93 

4.3.3. Theme 3: Over-reliance on teacher observation versus learner articulation ....................... 95 



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4.3.4 Theme 4 - Good understanding of descriptive feedback but missed opportunities for 

descriptive feedback ...................................................................................................................... 98 

4.4 Conclusion .................................................................................................................................. 99 

CHAPTER FIVE ................................................................................................................................ 101 

SUMMARY OF FINDINGS, CONCLUSION AND RECOMMENDATIONS ............................... 101 

5.1. Introduction .............................................................................................................................. 101 

5.2. Summary of the chapters.......................................................................................................... 101 

5.3 Discussion of findings ............................................................................................................... 104 

5.3.1 Theme 1: Practical applications and real-world connections ............................................. 104 

5.3.2 Theme 2: Formative assessment for monitoring and guiding conceptual understanding .. 107 

5.3.3 Theme 3: Challenges in implementation............................................................................ 109 

5.4.1 Theme 1: Strong conceptual understanding, inconsistent practice .................................... 110 

5.4.2 Theme 2: Assessment for learning vs. assessment of learning .......................................... 112 

5.4.3 Theme 3: Over-reliance on teacher observation versus learner articulation ...................... 113 

5.4.4 Theme 4: Good understanding of descriptive feedback but missed opportunities. ............ 115 

5.5. Limitations of the study ........................................................................................................... 116 

5.5.1 Snapshot in time ................................................................................................................. 116 

5.5.2 Single school context ......................................................................................................... 117 

5.5.3 Lack of student perspectives .............................................................................................. 117 

5.6. Recommendations .................................................................................................................... 117 

5.6.1 Ongoing professional development.................................................................................... 117 

5.6.2 Collaborative planning and learning communities ............................................................ 118 

5.6.3 Using technology and resources ........................................................................................ 118 

5.6.4 Ongoing Training and Feedback Cycles ............................................................................ 118 

5.7 Recommendations for future research ...................................................................................... 119 

5.7.1 Longitudinal studies ........................................................................................................... 119 

5.7.2 Impact on student learning and achievement ..................................................................... 119 

5.7.3 Comparative studies ........................................................................................................... 119 

5.7.4 Teacher beliefs and mindsets ............................................................................................. 120 

5.7.5 Technology integration and digital tools ............................................................................ 120 

5.8 Conclusion ................................................................................................................................ 120 

REFERENCE LIST ............................................................................................................................ 122 

APPENDIX A ..................................................................................................................................... 149 

ETHICAL CLEARANCE CERTIFICATE .................................................................................... 149 

APPENDIX B ..................................................................................................................................... 150 

LETTER TO THE PRINCIPAL ..................................................................................................... 150 

APPENDIX C ..................................................................................................................................... 152 

LETTER OF CONSENT: PRINICPAL ......................................................................................... 152 



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APPENDIX D ..................................................................................................................................... 154 

INFORMATION SHEET: LETTER TO TEACHER..................................................................... 154 

APPENDIX E ..................................................................................................................................... 156 

TEACHER’S CONSENT FORM ................................................................................................... 156 

APPENDIX F...................................................................................................................................... 158 

PERMISSION LETTER: SGB CHAIRPERSONS. ....................................................................... 158 

APPENDIX G ..................................................................................................................................... 160 

CONSENT FORM: SGB CHAIRPERSON ................................................................................... 160 

APPENDIX H ..................................................................................................................................... 162 

PERMISSION LETTER: PARENT ............................................................................................... 162 

APPENDIX I ...................................................................................................................................... 164 

CONSENT FORM: PARENT ........................................................................................................ 164 

APPENDIX J ...................................................................................................................................... 165 

FORMAT OF INTERVIEW ........................................................................................................... 165 

1. Introduction ............................................................................................................................. 165 

2. Questions: ............................................................................................................................... 165 

3. Closure: ................................................................................................................................... 165 

APPENDIX K ..................................................................................................................................... 166 

BIOGRAPHICAL INFORMATION FOR TEACHERS................................................................ 166 

APPENDIX L ..................................................................................................................................... 168 

INTERVIEW SCHEDULE FOR GRADE 4 TEACHERS ............................................................ 168 

APPENDIX M .................................................................................................................................... 170 

OBSERVATION SCHEDULE....................................................................................................... 170 

APPENDIX N ..................................................................................................................................... 174 

PLAGARISIM REPORT ................................................................................................................ 174 

APPENDIX O ..................................................................................................................................... 176 

EDITORS LETTER ........................................................................................................................ 176 

 

 

 

  



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CHAPTER ONE 

ORIENTATION TO THE STUDY 

1.1 Introduction  

The goal of this research was to understand the perceptions and practices of grade 4 teachers 

in the context of formative assessment, specifically in the mathematics learning area at a private 

school in Gauteng province. This introductory chapter aimed to orient the reader to the study 

by providing background information, contextualising it, and discussing the key concepts 

relevant to this study. This chapter included the problem statement, research objectives, key 

research questions, research methodology, and study structure. The chapter concluded by 

providing an outline of the chapter that follows. 

1.2 Background and contextualisation of study 

Until 1994, the focus of the South African educational system was on summative assessment 

through tests and examinations. Assessment was different from pedagogy, in that it assessed 

discrete, isolated or fragmented “knowledge” and “skills” (Lubisi, 1999). As a result, teaching, 

learning and assessment were viewed as separate activities, such that teachers did not consider 

assessment until after they had taught everything. Traditional, testing-based assessment 

practices came under heavy criticism, for not emphasising higher-order thinking skills, or 

valuing the learners’ contributions (Lubisi, 1999, Andrade, 2010). Primary school mathematics 

also used summative assessment. The grading and ranking of students in class mainly utilised 

mathematics assessments. This meant that this type of assessment was regularly done through 

tests and examinations. Many teachers considered it important for pupils to memorise formulas 

as the chief aim in primary school mathematics because it was largely viewed as a subject 

where rote memory of formulae instead of conceptual understanding was key. Critics attacked 

the traditional method of teaching mathematics because it was excessively prescriptive, 

algorithmic, and memory-dependent (Lubisi, 1999, Andrade, 2010). 

After 1994, the thinking of assessment had to change. Scholars had opposed calls for increased 

standardised testing in primary school mathematics with research on models that integrate 

assessment seamlessly within everyday pedagogy (Andrade, 2010). In this regard, Black and 

Wiliam (2003) asserted that if assessment is tied to learning, then assessment becomes more 

powerful than if it were mainly for accountability. This idea of “assessment for learning” 

formed the basis of what current scholars refer to as formative assessment thus assessment with 



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prospects that inform and shape teaching and learning in time (Bennett, 2011). Unlike 

summative testing which evaluates achievement at the end of pedagogy, formative assessment 

provides real-time insight into student thinking that allows teachers to identify and respond to 

gaps in understanding (Earl, 2013). Embedded interactively within pedagogy, it functions as a 

rich feedback mechanism for both learners and teachers, illuminating progress towards goals 

(Andrade, 2010).  

Researchers emphasised that motivating students as self-regulated learners analysing their 

thinking via metacognitive self-assessment enhances motivation and autonomy (Clark, 2012). 

Scholars argue for teachers to adopt formative assessment strategies that provide windows into 

students’ thinking, such as rich questioning, facilitating explanations of problem-solving 

processes, and other techniques revealing student reasoning. This focus echoes calls for 

reforming rigid initiation-response-evaluation dialogue patterns that limit insights into 

mathematical understanding (Emanuelsson & Sahlström, 2008). Overall, research 

resoundingly critiques assessing primary students through fact-based tests alone without 

dynamic assessment facilitating deeper learning. Progress relies on assessments that activate 

higher-order cognition and inform pedagogy responsive to demonstrated understanding, not 

just scores (Emanuelsson & Sahlström, 2008). 

The idea of a vision in terms of assessment being an essential part of learning rather than just 

as a tool for accountability has been the basis of South Africa’s curriculum adjustments since 

apartheid. In 1997, the introduction of Curriculum 2005 saw it advocating for continuous 

assessment, to be used formatively as part of OBE principles (Chisholm, 2005). The notion 

that assessment is intricately tied to how teachers teach and not only about holding learners 

accountable is at the heart of Curriculum 2005 (Chisholm, 2005). Curriculum 2005 (C2005) 

ambitiously promoted learner-centred education oriented towards competency development 

rather than rote learning (Jansen, 1999). It endorsed continuous assessment embedded within 

classroom activities to promote meaningful learning aligned to outcomes (Department of 

Education, 1997). This vision resonated philosophically with shifting global assessment 

perspectives centred on “assessment for learning” models (Kellaghan & Greaney, 2001). 

However, scholars highlight that C2005 adoption was severely constrained by a lack of teacher 

preparation and capacity building (Jansen & Taylor, 2003; Kanjee & Moloi, 2014). Teachers 

struggled to shift from deeply embedded notions of assessment as mainly periodic grading 

through formal examinations. Envisioned classroom-based assessments demanded conceptual 

and technical shifts that simply failed to materialise at scale (Lubisi & Murphy, 2002). 



13 
 

In 2002, the following revised National Curriculum Statement (RNCS), however, continued to 

advocate for formative assessment embedded in classroom activities rather than predominantly 

summative examinations (Department of Education, 2002). This is built on philosophical 

convergence with emergent global views on fluid modes of ‘assessment for learning’ and not 

only ‘assessment of learning’ (Kellaghan & Greaney, 2001). Yet, academic scholars emphasise 

that policy rhetoric was swifter than the real transformation of pedagogical processes in 

classrooms (Jansen, 1999). 

Fleisch (2008) argued that without fundamental shifts in educator concepts and competencies 

around classroom-based assessment, well-intentioned reforms made little headway in 

transforming entrenched assessment cultures. Despite curriculum vision statements, prevailing 

mindsets continued focusing assessment on periodic grading and promoting learners based on 

grades (Kanjee & Moloi, 2014). Teachers lacked strategies for integrating interactive formative 

assessment strategies as a seamless teaching-learning process centred on advancing 

understanding (Suurtamm & Koch, 2014). Scholars like Lubisi and Murphy (2002) suggested 

infrastructure barriers like large class sizes and limited resources also constrained the 

enactment of continuous assessment. However, underlying issues of teacher capacity and the 

need to reshape beliefs and practice persisted as the deepest challenges (Jansen & Taylor, 2003; 

Dunne et al., 2010). Without addressing these root factors, Fleisch (2008) argued that top-down 

assessment policy reforms had floundered in permeating classroom change. 

The Curriculum and Assessment Policy Statement (CAPS) reiterated the importance of 

formative assessment as a fundamental classroom procedure (DBE, 2011). Introduced in South 

Africa in 2011, the CAPS curriculum took note of the shift in global assessment perspectives, 

with models that favour a deeper connection to pedagogy. The vision of CAPS diverged from 

a narrow concentration on periodical grading and classifications based on end-of-term 

examinations (DBE, 2011). Instead, CAPS suggests that assessments should become an 

integral, frequent component of the education and development process. CAPS underscores the 

significance of formative assessment in mathematics at primary school level. It suggests that 

teachers use informal, day-to-day checks that are diverse to help them determine their learners’ 

engagement with content, identify learning gaps, and enhance pedagogical practices. Some 

examples of formative assessments include “classroom discussions, oral questions, mini 

classroom quizzes, homework exercises, and feedback on practical tasks” (DBE, 2011, p. 4). 

The policy advises teachers to use assessment to “identify problems and misconceptions early, 

rather than just issuing marks” (DBE, 2011, p. 5). It also suggests giving learners "second 



14 
 

chances and allowing them to learn from their mistakes” (DBE, 2011, p. 5). Teachers can adapt 

their teaching and provide help to learners who are not doing well by using formative 

assessments. The incorporation of formative assessment in CAPS has the goal of improving 

mathematics learning by making teaching more adaptive to learner demands. As far as the 

conceptualisation and role of classroom-based assessment were concerned, this was a 

significant policy shift at the level of curriculum development in South Africa through CAPS. 

The document states that rather than being thought about as distinct things, assessment and 

teaching must be seen as one and thus woven together with formative assessment practices as 

guiding principles towards understanding and implementing curriculum expectations. 

However, while policies and curricula have advanced, actual changes in teachers' classroom 

assessment practices have often been very gradual and uneven across different schooling 

contexts in South Africa. After 1994, two different types of schools came into existence because 

of historical and socio-political factors; public and private ones. These groupings were 

established to cater for the diverse requirements of the population while still recognising 

inequalities of the past. Sapire and Sorto (2018) and Dhurumraj (2013) found that assessment 

methods in many public township and rural schools remain centred on summative testing aimed 

more at accountability purposes rather than providing formative information to strengthen 

teaching and learning because of resource constraints, teacher habituation, and cultural norms 

emphasising summative rankings. Even when teachers attempt more continuous assessment, 

Kanjee and Moloi (2014) found that these often take the form of informal observations rather 

than systematic documentation and analysis. The uneven translation of curriculum mandates 

on classroom assessment into practice remains an implementation challenge. 

In contrast, assessment practices in private schools catering to more affluent populations are 

frequently considered to be more progressive, as Lelliott et al. (2000) found in comparisons of 

schooling contexts. Private schools are renowned for offering top-tier education and often 

follow globally recognised curricula like the Cambridge International Curriculum or CAPS 

curriculum. The CAPS curriculum emphasises that assessment is an ongoing process of 

assessing learners’ understanding through various assessment methods beyond traditional 

examinations (DBE, 2011). Private schools prioritise a broader range of assessments, including 

formative assessments that focus on providing feedback and tracking student progress 

throughout the learning journey (Shepard, 2000). Teachers in private schools, similar to those 

in South African public schools, are expected to have a deep understanding of assessment 

principles and strategies. They must align their assessments with frameworks set by bodies like 



15 
 

the Independent Examinations Board (IEB) or Cambridge Assessment International Education 

to ensure they meet educational standards and reflect the school's ethos (ISASA). These 

assessments should not only gauge academic knowledge but also evaluate skills, attitudes, and 

values crucial for holistic development. 

Formative assessment has gained increasing prominence in educational discourse as a powerful 

tool for enhancing teaching and learning (Black & Wiliam, 2018). Unlike summative 

assessment, which evaluates learning outcomes at the end of an instructional period, formative 

assessment is an ongoing process that provides real-time insights into student understanding, 

allowing teachers to adapt their instruction responsively (Wiliam, 2011). In the context of 

mathematics education, formative assessment holds significant potential for promoting 

conceptual understanding, problem-solving skills, and mathematical reasoning (Cotton, 2021; 

Santos & Semana, 2021). 

However, despite growing recognition of its value, the effective implementation of formative 

assessment in mathematics classrooms remains a challenge for many teachers (Kanjee & 

Moloi, 2021). This is particularly evident in the South African context, where traditional, 

testing-based assessment practices have long dominated the educational landscape (Lubisi, 

1999; Andrade, 2010). The shift towards more learner-centered, formative approaches has been 

advocated in post-apartheid curriculum reforms, yet translating policy into practice has proven 

difficult (Kanjee & Sayed, 2019). 

1.3 Statement of problem  

While private schools in South Africa are often assumed to have more progressive classroom 

assessment practices aligned with post-apartheid reform initiatives that emphasise continuous, 

competency-based assessment, arguably, there is little empirical evidence regarding how 

teachers in these well-resourced schools understand and enact assessment approaches, 

particularly within key subject areas like mathematics (Botha & Coetzee, 2020). As researchers 

like Brijlall and Ndlovu (2015) discuss, mathematics has historically prioritised procedural 

knowledge and rote assessment methods misaligned with the critical thinking and conceptual 

grasp focus of reforms. Furthermore, Kanjee and Moloi (2014) note that even when teachers 

espouse reformed curricula, their classroom assessment often remains informal and lacks 

rigorous documentation and analysis of learning gaps. 

This study aimed to explore the perspectives and practices of grade 4 mathematics teachers in 

a private school regarding assessment within the mandated curricula. The research delves into 



16 
 

how these teachers conceptualise and implement assessment daily, focusing on the integration 

of formative assessment practices into their teaching routines. Specifically, in what ways do 

their enacted assessments reflect or contradict prevalent assumptions about superior assessment 

capacity and progressive formative assessment practices catering to higher-order outcomes in 

well-resourced private institutions? Grasping this issue has implications for substantiating 

claims used to market such schools as well as understanding translational gaps between policy 

and classroom practice. It also facilitates the comparison of the assessment classroom between 

contrasting schooling contexts. 

1.4 Rationale  

As a mathematics teacher in a well-resourced private school, I decided to undertake this study 

because I wanted to deeply examine how my own conceptions and enactment of classroom 

assessment align with mandated curriculum reforms oriented around continuous, formative 

approaches. Private schools are often assumed, both publicly and within the independent school 

community, to be further along in adopting progressive assessment anticipated by post-

apartheid policies - utilising formative assessment like projects, oral questioning, and 

diagnostics to gauge higher-order thinking beyond content knowledge. 

However, as a self-reflective practitioner teaching a subject like mathematics, which has 

traditionally prioritised procedural knowledge and standardized testing over conceptual grasp 

and critical analysis, I question my peers' assessment capacity. Do their daily assessments 

indeed capture the depth of understanding and skill application expected of reformed 21st  

century curricula? Do they remain focused on the reinforcement of mathematical operations 

and repetitive drill assessment? I believe that as teachers in a well-resourced, high-capability 

school context, we have a responsibility to enact assessments that prepare our students for 

competitive global tertiary environments. Hence out of curiosity, this personally-driven study 

will facilitate a deep examination of my fellow teachers' assessment conceptions and practices 

related to the mandated mathematics curriculum, using empirical qualitative techniques. The 

findings can validate strengths, reveal areas of practice not aligning to reforms, and inform the 

design of assessment-focused professional development catering to discipline-specific needs 

within my private school setting. 

Professionally, as an education researcher seeking to inform assessment policy and teacher 

professional learning in South Africa, I undertook this study to help address critical knowledge 

gaps regarding how teachers in well-resourced private schools understand and enact classroom 



17 
 

assessment. While private schools are often portrayed as having better assessment capacity and 

practices more attuned to post-apartheid reform expectations, debatably, there is strikingly little 

empirical evidence to substantiate these claims that influence public perceptions and school 

choice. 

In particular, the assessment translational capacity of teachers within key subjects like 

mathematics remains unexamined, despite the historically outdated practices in this discipline 

and calls for greater attention to higher-order conceptual assessment rather than procedural 

fluency. As the country continues investing in reformed curricula, understanding practice 

realities in schools with high self-perceived capability has policy and teacher training 

implications. It facilitates more targeted capacity building where espoused and enacted 

assessment may show gaps between public rhetoric and classroom reality. 

As Kanjee and Moloi (2014) argue, there is a need for an in-depth qualitative study of how 

contemporary reforms manifest in assessment perspectives and routines across diverse 

schooling contexts. Focusing this exploration specifically on assumed high-functioning private 

sites will provide a strategic point of comparison for strengthening system-wide assessment 

capacities intended to unlock learner potential and advance equity of outcomes. 

1.5 Key research questions  

To provide direction and focus to the research study, the following research questions were 

outlined: 

• What are grade 4 teachers’ understanding of assessment as it relates to mathematics? 

• How does grade 4 teachers’ understanding of assessment influence their practice of 

classroom assessment as it relates to the mathematics? 

1.6 Aim of the study  

This study aimed to gain insight into teachers’ understanding of formative assessment and to 

explore the extent of alignment between their understandings and practices. 

The research delved into variations in teachers' understanding and application of formative 

assessment, influenced by their professional contexts and experiences. A central focus was on 

understanding the transition of teachers from traditional summative assessment models towards 

the principles of formative assessment advocated in current educational reforms. Additionally, 

the study analysed the alignment between teachers' professed beliefs about effective formative 

assessment and their actual classroom assessment practices. 



18 
 

To address the aims, the study drew on several key concepts central to the topic: 

Formative Assessment  

Formative assessment is a continuous process of gathering evidence about student learning 

during instruction to inform and adapt teaching. Unlike summative assessment, which 

evaluates learning at the end of an instructional period, formative assessment is ongoing and 

integrated into the teaching and learning process. In this study, formative assessment refers to 

the various strategies and practices that grade 4 mathematics teachers use to monitor student 

understanding, provide feedback, and adjust their instruction accordingly. 

Assessment for Learning  

This term is closely related to formative assessment but emphasizes the use of assessment to 

support and enhance learning rather than merely evaluate it. In this research, assessment for 

learning refers to the ways in which teachers use assessment information to guide their teaching 

and help students understand their own learning processes. This includes strategies such as 

sharing learning goals with students, providing descriptive feedback, and encouraging self and 

peer assessment. 

Grade 4 Mathematics  

This term refers to the specific context of the study - the mathematics curriculum and 

instruction for students typically aged 9-10 years in the South African education system. Grade 

4 mathematics often includes topics such as number operations, fractions, geometry, 

measurement, and basic data handling. 

Private School Context  

In this research, the private school context refers to the specific educational setting where the 

study took place. Private schools in South Africa often have more resources, smaller class sizes, 

and greater autonomy in curriculum and assessment practices compared to public schools. This 

context is important for understanding the specific conditions under which the teachers in the 

study were implementing formative assessment practices 

 

 



19 
 

1.7 Significance of the study  

The study focused on understanding how primary school mathematics teachers perceive and 

apply formative assessment strategies. First, it addressed a gap in empirical insight int 

assessment capacity, specifically within private school contexts, often assumed to be more 

progressive yet under-studied (Kanjee & Sayed, 2013; NELP, 2008). Generating evidence on 

how well-resourced private school teachers understand and implement continuous 

competency-based assessments has implications for substantiating or challenging public 

perceptions and tailoring professional development. Second, focusing specifically on 

mathematics assessment is strategically valuable given the subject’s historical challenges 

aligning with the critical thinking goals of reforms (Brijlall & Ndlovu, 2015). Developing a 

nuanced understanding of assessment integration in mathematics classrooms within supportive 

private environments can illuminate needs and models for wider improvement. 

Third, the study will facilitate a strategic comparison of assessment integration between 

resourced private sites and documented challenges in public schools. This may reveal common 

struggles or spotlight effective practices for wider emulation (Lelliott et al., 2000). Fourth, 

examining how national assessment policies translate to classrooms in schools with the greatest 

agency for change provides rare insight into strengthening reform communication and 

implementation (Pryor & Lubisi, 2001). Finally, as a mathematics teacher, this study holds 

significance for advancing my professional knowledge and capacity to engage with cutting-

edge issues in assessment theory and practice. Conducting an in-depth inquiry into grade 4 

teachers' conceptualisations and enactment of classroom assessment will expand my 

understanding of current debates regarding effective assessment principles and integration. 

Gaining firsthand insight into how assessments operate in primary classrooms will strengthen 

my ability to prepare teachers through nuanced training attuned to real-world complexities. 

This research will facilitate critical self-reflection on my own assessments and pedagogy as an 

educator. Additionally, focusing specifically on mathematics will enrich my subject-specific 

assessment literacy. 

Overall, this research study will help address empirical gaps, which will elevate understanding 

of classroom assessment realities in the under-studied private school sector, with wider 

implications for practice, policy, training, and public perception. It carries significance for 

educational quality, innovation, and advancement reflective of 21st century global priorities. 

Further, this research will assist my growth as a knowledgeable, competent teacher. It will 

expand my ability to substantially contribute to academic and policy conversations regarding 



20 
 

classroom assessment reform and innovation in South Africa's evolving educational landscape. 

This research comprises an invaluable opportunity to advance both my practices and capacity 

to improve mathematics assessment nationwide as findings are disseminated. 

1.8 Context of study  

This research was carried out at a private primary school in Johannesburg, s "Greenwood 

Academy" for confidentiality, serving students from affluent backgrounds. Greenwood 

Academy has cultivated a reputation for high academic performance, quality teaching, and 

utilising progressive approaches aligned with national curriculum reforms. With class sizes of 

around 20 students and well-qualified teachers, the school touts its focus not merely on content 

knowledge and test scores, but on holistic development, including critical thinking, creativity, 

and problem-solving. 

The official discourse around classroom assessment at Greenwood Academy - such as in the 

school's pedagogical philosophy documents, assessment policy frameworks, mathematics 

department instructional guidelines, and statements from school leadership/administration - 

emphasises enabling “deep learning” over “surface learning” through continuous diagnostic, 

competency-based formative assessments rather than over-reliance on traditional pen-and-

paper testing focused solely on content knowledge. Documents like Greenwood Academy's 

teaching guidelines, assessment policy frameworks, mathematics department assessment 

planning templates, and promotional brochures emphasise enabling “deep learning” over 

“surface learning” through continuous diagnostic, competency-based assessments rather than 

traditional pen-and-paper testing. These documents indicate that assessment practices should 

analyse student work, guide instructional adjustments using learning data, and engage learners 

in self-assessment. School assessment guidelines explicitly mandate variety, including projects, 

simulations, open-ended writing, presentations, and other techniques meant to provide 

multifaceted data and feedback while gauging higher-order understanding. 

Greenwood Academy highlights its assessment approaches as aligned with key post-apartheid 

expectations like the National Protocol on Assessment (2011) which accentuates tracking 

conceptual grasp and skill application through continuous, competency-based models. CAPS 

outlines varied assessment types analysing critical thinking and problem-solving. 

Specifically, within mathematics, CAPS, the South African Mathematics Teaching Handbook, 

and the Gauteng Province Mathematics Assessment Framework guide, for example, these 

documents focus assessment on mental mathematics, mathematical modelling, development of 



21 
 

“number sense”, and open-ended writing and questioning to gauge mathematical 

comprehension rather than only computational fluency. 

Provincial initiatives like the Annual National Assessments (ANAs) and Gauteng Mathematics 

Benchmarking Tests, which Greenwood Academy participates in, also mandate demonstrations 

of applied mathematical skills. This study took Greenwood Academy as a site where these 

national and provincial assessment policy aspirations emphasising diagnostic, skill-based 

evaluations with attention to conceptual understanding appear concentrated; examining how 

grade 4 teachers enact expectations provides insight into reform realisation. 

 1.9 Overview of the research design and methodology  

This section provided a preliminary overview of the research design. A more detailed 

discussion of the research design and the rationale for the choice of methodology was presented 

in Chapter 4.   

1.9.1 Paradigm 

This study was situated within an interpretivist paradigm that seeks to understand the subjective 

meanings individuals construct through their lived experiences and interactions (Bailey, 2007; 

Cohen et al., 2007). In line with this paradigm, the research adopted a qualitative approach 

aimed at capturing the nuanced perspectives of participants regarding the issue under study 

using real-world contexts (Henning, 2004; Lichtman, 2006). The goal was to elucidate how 

individuals make sense of phenomena through the meanings they attach to them. Specifically, 

this enquiry utilised a qualitative case study design to explore in-depth how mathematics 

teachers in their school settings conceptualise and apply formative assessment strategies in 

their practices (Merriam, 2007). The intent was to gain insight into teachers' assessment 

knowledge, beliefs, and behaviours as they experience and engage with this approach. By 

taking an interpretive qualitative approach situated in real school contexts, the study aimed to 

construct an understanding of formative assessment from the point of view of teachers and their 

implementation of formative assessment in their classrooms. 

1.9.2 Sampling  

This study utilised purposive and convenience sampling to identify information-rich cases for 

in-depth investigation (Patton, 2015). The sample consisted of three purposively selected 

mathematics teachers in grades 4 from a single private primary school, selected based on their 

extensive experience with the subject area. This aligned with qualitative case study guidelines 

to select a small sample that can provide detailed insights into the phenomenon of interest 



22 
 

(Creswell & Poth, 2018). The specific school site was chosen due to having multiple 

mathematics teachers available to participate and facilitate the investigation of the research 

topic across educators within the same educational context. This purposeful sampling approach 

provided the opportunity to deeply explore formative assessment perspectives and practices 

from knowledgeable teachers in an authentic classroom setting. In this way, the sampling 

strategy enabled nuanced, contextually grounded data collection focused on a unit of analysis 

aligning with the research objectives (Yin, 2018). The insights garnered from this carefully 

selected sample illuminated the complexities of implementing formative assessment in real-

world practice. Convenience sampling was also employed in the study as the research site was 

where I am formally employed as a grade 5 teacher and the participants in this study are my 

colleagues. As a teacher in this school, using convenience sampling could be rationalised based 

on the practicality and efficiency it offered in data collection. Through convenience sampling, 

I was able to select participants based on their easy accessibility and availability, making it a 

quick and cost-effective method to gather data. In a school setting, where time and resources 

are often limited, convenience sampling was beneficial for conducting research that require 

timely data collection. 

1.9.3 Data collection strategies  

This study utilised semi-structured interviews as the primary data source to provide flexibility 

in capturing teachers’ perspectives while still guiding the topics of interest (Kvale & 

Brinkmann, 2009). Initial interviews gathered background information and assessed the 

teachers’ knowledge of formative assessment. Each interview was conducted face-to-face with 

individual participants and lasted for 45 minutes.  

Classroom observations complemented the interviews, generating real-time insights into 

formative assessment enactment. Over 9 weeks, each of the 3 teachers was observed for 3 

lessons with field notes taken during observation to document contextual details (Creswell & 

Poth, 2018). 

Combining teacher interviews with direct classroom observation of teachers' practices provided 

rich, multi-faceted data grounded in real settings. This enabled in-depth investigation of 

understandings translated into action over time while limiting reliance on self-reported data 

alone. The flexible conversational interviews coupled with observational data helped construct 

a vivid portrait of formative assessment integration. 



23 
 

In this study grounded analysis was applied to analyse data. The analysis process was 

influenced by the research questions and concepts derived from Black and Wiliam's (2009) 

theory of formative assessment. Additionally, the identification of themes was facilitated 

through inductive analysis, allowing patterns to emerge from the data. The practical guidance 

for qualitative data analysis was drawn from the work of Braun and Clarke (2006). 

1.10 Overview of the chapters  

The first chapter provides an overview of the study, delving into the nature of assessment and 

assessment reforms in South Africa. The background section emphasises the significance of 

formative assessment in the teaching and learning process. Moreover, the chapter articulates 

the problem statement and the rationale behind undertaking the study. It proceeds to outline the 

primary research questions and objectives guiding the research study. The significance and 

context of the study are also explored. Lastly, the chapter details the adopted research 

methodology. 

The second chapter presents the literature on feedback perceptions, practices and the theoretical 

framework employed in this study. It illustrates the literature on feedback both nationally and 

internationally.  

The third chapter explains the methodological positioning. It discusses the methodology, 

research design, sampling procedure used to choose participants for interviewing and the 

process by which the data was generated and analysed. In addition, it outlines a model for 

ensuring trustworthiness and ethical considerations. 

The fourth chapter presents the outcomes of the research study and emphasises the formative 

assessment feedback perceptions and practices of grade 4 mathematics teachers. 

The last chapter concludes and summarises the findings associated with formative assessment 

feedback practices and perceptions of grade 4 mathematics teachers. Lastly, it presents 

recommendations and provides directions for future research. 

 

 

 

 



24 
 

 

CHAPTER 2 

LITERATURE REVIEW 

 

2.1 Introduction  

The focus of this literature review was parallel to the aims of this study, namely, to examine 

teachers' knowledge and beliefs about formative assessment and how they translate these ideas 

into classroom practices in mathematics pedagogy. The literature review and theoretical 

framework for this study are grounded in Black and Wiliam's (2009) seminal work on 

formative assessment. Their theory posits that formative assessment, when integrated into 

classroom practice, can significantly enhance student learning outcomes. The five key 

strategies they propose - clarifying learning intentions, engineering effective discussions, 

providing feedback, activating students as instructional resources, and activating students as 

owners of their learning - serve as a guiding framework for analyzing formative assessment 

practices in mathematics classrooms. 

This chapter begins by exploring different types and purposes of assessment, with a specific 

focus on formative assessment. It then delves into the principles of formative assessment, 

drawing on Black and Wiliam's (2009) theory and other relevant literature. The review also 

examines South African assessment policies and their implications for classroom practice. 

Challenges in implementing formative assessment in mathematics education are discussed, 

starting with global issues, then narrowing to the African continent, and finally the South 

African context. The chapter concludes by elaborating on Black and Wiliam's theoretical 

framework and its application to mathematics pedagogy, linking the key principles to the 

study's research questions and objectives. 

2.2 Types and purpose of assessment in Mathematics 

A range of researchers have identified various assessment methods that can be effectively 

utilised in mathematics education.  

2.2.1 Informal assessment  

Andrade (2021) found that informal assessments seamlessly embedded into normal 

instructional activities can provide insight into student progress by checking understanding at 



25 
 

the moment. Informal assessment transpires through interactions between teachers and learners 

in class and involves continual informal checks embedded within normal teaching activities 

(Hodgson & Pyle, 2010; Spector et al., 2016). These assessments arise spontaneously based on 

student responses, questions, conversations and needs at the moment (Bell & Cowie, 2001; 

Ruiz-Primo & Furtak, 2007). For example, posing oral questions when content gets presented, 

eliciting explanations during activities, and observing practical work constitute informal 

assessments providing insight into evolving understanding (Cauley & McMillan, 2010; 

Eisenkraft, 2004 as cited in Ruiz-Primo, 2011). Rather than formal tests, everyday learning 

tasks become opportunities for informal evidence gathering through teacher observation, 

student work samples, peer discussions, or other means (Ruiz-Primo, 2011; Shirvani, 2009, 

Granberg et al., 2021; Martin et al., 2022). 

Such interactive assessment, happening “on the fly,” aims to quickly adjust instruction to foster 

learning, not merely audit it (Heritage, 2007; Tunstall & Gipps, 1996). Recent research reveals 

that teachers integrating more informal assessment through classroom dialogue, task analysis, 

and student self-assessment are better equipped to meet emerging learning needs (Cowie & 

Bell, 1999; Gamlem & Munthe, 2014). By continually checking student understanding, 

instructors can provide timely feedback, clear up misconceptions, tailor lessons, and improve 

outcomes (Boston, 2002; Clark, 2011). 

2.2.2 Diagnostic and Baseline assessment 

Complementing informal assessments are diagnostic and baseline assessments. As explained 

by Garrison and Ehringhaus (2007), diagnostic assessments are designed to precisely identify 

specific learning barriers or gaps that individual students or groups of students are 

experiencing. Pinpointing conceptual misunderstandings or skill deficiencies through 

diagnostic assessments allows teachers to provide appropriate targeted support, intervention 

strategies, and extra assistance, and make referrals to specialist help if required (NCTM, 2000). 

Garrison and Ehringhaus (2007) asserted that these assessments enable tailored remediation. 

On the other hand, baseline assessments often given at the very start of a course or unit can 

establish students' initial level of understanding of key concepts, skills, and background 

knowledge. This allows teachers to gain crucial insight into the incoming state of students' 

knowledge to inform instructional planning and differentiation of lessons to meet students at 

their current level (Black & Wiliam, 2009). 

 



26 
 

2.2.3 Summative assessment 

Formal assessments refer to planned evaluation activities, often administered periodically 

outside of usual instructional contexts to systematically document student learning (Garrison 

& Ehringhaus, 2007; Heritage, 2007). Also referred to as summative assessments, they aim to 

evaluate the overall achievement and progress students have made at the end of a defined 

instructional period, like the end of a grading term, semester, or school year (Harlen, 2007).  

These formal assessments play a vital role by providing summative assessments of cumulative 

mastery and achievement using tools like chapter tests, unit examinations, benchmarks, or state 

standardised tests (Black & Wiliam, 2004; Stiggins, 2005). Quantitative data on skills and 

knowledge acquisition equip teachers to assign grades, monitor gaps, and gauge progress 

towards content standards (Cauley & McMillan, 2010; Popham, 2008). However, Cauley and 

McMillan (2010) argued that these assessments should draw together multiple sources of 

information, not rely on a single examination event.  

2.2.4 Formative assessment 

Interestingly, formal assessments can also be formative. Formal formative assessment 

constitutes purposeful assessment activities designed to systematically gather information and 

provide feedback (Clark, 2011; Spector et al., 2016). Formal assessments aim to enhance 

outcomes by diagnosing learner needs, gauging readiness, targeting remediation, and 

informing placement or programming (Bennett, 2011; Shermis & DiVesta, 2011). Effective 

implementation requires: 1) strategic information gathering using deliberate methods, 2) 

analysis and interpretation based on goals, and 3) modification of instruction, curriculum or 

systems based on resulting data and insights (Mandinach & Gummer, 2016; Marsh, 2007). 

Also called "planned formative assessment," these structured assessment protocols can be 

organised at the start or end of a teaching unit (Bell & Cowie, 2001; Ruiz-Primo & Furtak, 

2007). Baseline assessments identify incoming knowledge, while end-of-unit checks evaluate 

learning progress (Heritage, 2007; Hodgson & Pyle, 2010). Formal assessments yield tangible 

documentation of understanding that complements ongoing informal checks (Garrison & 

Ehringhaus, 2007; Shepard et al., 2018). For example, a curriculum-based assessment sample 

can be focused on skills to systematically track growth across an academic year (Stecker et al., 

2005). Strategic integration of both formal and informal assessments provides comprehensive 

insights into enhancing teaching and learning (Bennett, 2011; Black & Wiliam, 1998). 



27 
 

The National Council of Teachers of Mathematics (NCTM, 1995) advocated using a balance 

of multiple methods, both informal, formative checks of understanding during instruction and 

formal tests assessing summative achievement in order to gain a comprehensive, holistic view 

of student learning. Cizek (2010) explained integrating informal and formal checks for 

understanding throughout lessons allows teachers to continually tailor instruction, feedback, 

and support based on emerging student needs. This empowers assessment to enhance, not 

merely measure, learning. 

Assessments in mathematics should reflect contemporary learning principles focused on active 

enquiry, problem-solving, and discussion (Boaler, 2016). Wiliam (2017) concurred that 

mathematics assessments should require demonstration and application of knowledge, not just 

factual recall measured through selected response items. Open-ended performance tasks, 

projects requiring extended mathematical thinking, and investigations situated in real-world 

contexts enable more meaningful assessment of mathematical proficiency according to 

Shepard (2000). Earl (2013) advised that teachers should make informed decisions to 

strategically select assessment types and methods that are purposefully aligned to specific 

instructional goals and information needs. Yet for Black and Wiliam (2009), formative 

assessment, woven seamlessly into ongoing teaching and learning, provides the most crucial 

ongoing feedback to actively adjust instruction, identify needs, and improve student learning 

outcomes. Rather than an audit, a formative assessment constitutes an assessment for learning, 

not just of learning (Earl, 2013).  

2.3 South African National Assessment Policies 

The dismantling of apartheid precipitated radical re-envisioning of education policies in South 

Africa towards redress and democratic ideals. Curriculum 2005 (C2005) thus engendered a 

monumental departure from the past by officially eradicating all prior racially-differentiated 

curricula and establishing continuous assessment as a defining orientation (Chisholm, 2000). 

Assessment was framed as integrated classroom activities for unlocking participation through 

project-based learning rather than standardised high-stakes testing which had severely 

disadvantaged black learners historically. 

However, extensive critiques emerged about ambiguities and inadequate guidance given the 

multiplicity of new outcomes spanning eight learning areas and the weaker-resourced 

conditions of the majority. Jansen (1998) critically examined the gulf between the idealised 

policy formulations of C2005 and implementation realities, arguing its “conceptual and 



28 
 

linguistic complexity” coupled with “constant changes and policy pivots” fostered immense 

teacher confusion, resistance and ultimate rejection (p.3). Similarly, Botha (2002) highlighted 

implementing dramatically widened assessment areas without reductions in content coverage 

or teaching time overburdened teachers and undermined curriculum delivery. 

Attempts to address overreach through the streamlined National Curriculum Statements (NCS) 

in 2002 and CAPS in 2012 still sustained the core emphasis on formative assessment but aimed 

to clarify prescribed methods and assessment criteria. Standardised testing would supplement 

but not replace school-based judgement using flexible criteria (Umalusi, 2014). However, 

debates persisted on whether tighter specifications better enabled meaningful integration 

amidst conditions of scarce assessment capabilities and training support. Complex policy 

trajectories ultimately left an uneven legacy of assessment reform. 

Assessment policies have consistently maintained that learner assessment must be rooted in 

daily teaching and learning activities. As the National Education Department detailed CAPS 

expectations, “Assessment should be both informal (Assessment for Learning) and formal 

(Assessment of Learning)” (DBE 2011, p. 5). This mandated integration of continuous 

assessment via investigations, simulations, discussions and projects to leverage “frequent 

feedback” (RNCS 2003, p. 110). The Teacher’s Guide for the Development of Learning 

Programmes aligned summative testing with flexible ongoing records of achievement 

including observations, questioning, self-review exercises and rubric-based peer critiques of 

investigations (DBE, 2011b). In Mathematics, Yackel (1992, p.138) reveals that "formative 

assessment includes project classrooms; mathematics guidelines which consist of discussion of 

problems". In this situation, the educator poses a problem to the class and allows learners to 

work in pairs to solve problems posed on worksheets. The whole class discussion and educators 

should allow learners to explain the solution/methods they have developed during small group 

work. 

Besides the National Curriculum and Assessment Policy Statements (CAPS), implemented by 

the South African Department of Basic Education (DBE, 2011), South African private schools 

are subject to a variety of policies and frameworks influencing assessment for learning 

practices. Some private schools opt for the Independent Examinations Board (IEB), an 

autonomous assessment body (IEB, 2021). Schools registered with the IEB adhere to its 

independent assessment policies. The Independent Schools Association of Southern Africa 

(ISASA), an association of independent schools, offers member schools guidelines and best 



29 
 

practices concerning assessment, with a focus on formative assessment (ISASA, 2018). 

Furthermore, individual private schools may formulate their own assessment policies aligning 

with national and international frameworks, addressing aspects like formative assessment, 

grading, and reporting (Taylor et al., 2013). Additionally, accreditation bodies like the Council 

for Quality Assurance in General and Further Education and Training (Umalusi) establish 

standards and guidelines for assessment practices in both public and private schools (Umalusi, 

2020). 

Guidelines have sustained movement towards continuous assessment and formative models 

allowing tracking of skills development despite ongoing debates regarding consistency and 

links to certifying examinations (Kanjee & Moloi, 2014). Jansen (2019) argued for reducing 

narrow audit assessments and utilising collective practical tasks and qualitative feedback 

cycles, building assessment capital. Umalusi (2014) also argued that improving enabling 

conditions for these classroom-based approaches remains vital for the meaningful development 

of capacities. Equity and adequacy of systemic implementation persist as a policy challenge. 

2.4 Principles of formative assessment 

Formative assessment refers to the ongoing process of gathering evidence about student 

learning during instruction in order to provide feedback to improve learning (Black & Wiliam, 

2009). It stands in contrast to summative assessment, which evaluates learning at the end of a 

unit or grading period. According to Black and Wiliam (1998), formative assessment 

encompasses "all those activities undertaken by teachers, and/or by their students, which 

provide information to be used as feedback to modify the teaching and learning activities in 

which they are engaged" (p.10). This means that formative assessment is centred on activities 

woven into the learning process, not separate tests. Both teachers and students engage in 

assessment as part of instruction. Feedback provides usable data to guide improvement. Hence 

the information from formative assessment is intended to adapt teaching and learning as it 

happens. It allows adjustment of instruction and student work at the moment based on evidence 

revealed. 

Seminal work on formative assessment emerged from Black and Wiliam whose 1998 literature 

review highlighted substantial learning gains achieved by implementing formative practices. 

They defined key elements of formative assessment, including: 1) eliciting evidence of learning 

to determine where students are, 2) providing feedback to move learning forward, 3) student 

self-assessment and monitoring, and 4) adjusting teaching based on assessment data (Black & 



30 
 

Wiliam, 2009). John Hattie and Helen Timperley (2007) added by examining the feedback 

aspect of formative assessment. They asserted that effective feedback must address three 

questions: 1) where am I going? (goal), 2) how am I going? (progress), and 3) where to next? 

(improvement strategy). Answer the first before the second, and both before the third, they 

argued. This feedback model provides a framework for constructive information. Educators 

should use ongoing assessment feedback all the time in their mathematics classes to make 

judgements about how learners are coping; whether they understand, whether there is a need 

to recap, and so on. Brookhart, Moss and Long (2010) characterised feedback as the "linchpin" 

binding the formative assessment process components into an integrated system. Effective 

feedback translates assessment interpretation directly into pathways for progress (Black & 

Wiliam, 1998a; Hattie & Timperley, 2007; Shute, 2008, Huisman et al., 2020; Kaur et al., 

2021).  

Other key theorists like Royce Sadler (1989) stressed that assessment is formative when 

students comprehend assessment criteria and accurate self-monitoring. Wiliam (2011) 

specified five key strategies: clarifying learning intentions, engineering effective discussions 

and tasks, providing feedback that moves learners forward, activating students as instructional 

resources for each other, and activating students as owners of their learning. These theories 

outline core, interconnected principles of effective formative assessment centred on feedback 

loops between students, teachers, and peers. 

Recent work has further elaborated on key principles of formative assessment. Moss et al. 

(2022) synthesised five core formative assessment practices: eliciting evidence of student 

thinking, analysing that evidence, providing descriptive feedback, supporting student self- and 

peer-assessment abilities, and using evidence to adjust instruction. They emphasised the 

centrality of responsiveness - teachers must be able to flexibly respond by adapting lessons 

based on the evidence gathered about student needs through formative assessment. 

Additionally, Recino and Beck (2023) advocated for ensuring formative assessment activities 

embody principles of equity, cultural responsiveness, and inclusive design. They argued that 

formative assessment tasks and feedback processes should draw on and validate students' 

diverse funds of knowledge, lived experiences and cultural backgrounds. This allows formative 

assessment to be an affirming, identity-safe experience leveraging all students' strengths. 



31 
 

2.5 Impact of formative assessment on learning 

The new goal in mathematics assessment emphasises reasoning skills, communication and the 

development of critical attitudes which are called "higher order thinking skills" (Brodie, 2000). 

Stiggins (2005) argues that formative assessment is essential because it provides teachers with 

continuous, up-to-date data on the skill levels, learning needs, and perspectives of individual 

students. For example, formative assessments like short quizzes, observation of in-class work, 

questioning, and homework checks allow teachers to pinpoint exactly which students are 

struggling with particular concepts. This is far more insightful than relying solely on 

summative assessments like examinations or final projects conducted at the end of a module 

or term. With formative data, teachers can identify learning gaps while there is still time to 

address them. 

Building on this, Tomlinson (2014) highlights that the individualised data gathered from 

formative assessments should enable differentiated and personalised instruction tailored to 

learners' needs. Thus, if a formative assessment shows a subset of students struggling with a 

key mathematical concept, the teacher can provide targeted support like re-teaching, additional 

examples, or learning resources specifically focused on the area of difficulty. Similarly, 

formative assessment might reveal advanced students who have swiftly grasped the core 

concepts and are ready for more challenging work. The teacher can then provide this group 

with enrichment materials, extension tasks, or opportunities to broaden and apply their new 

knowledge. In this way, formative evaluation facilitates a responsive, student-centred mode of 

instruction. 

Similarly Black and Wiliam, (2009) assert that, unlike periodic summative tests which only 

evaluate learning after instruction is complete, formative assessment is an ongoing process 

interwoven with learning that gives teachers real-time insight into exactly where each student 

is in their understanding, of what gaps or misconceptions they have, and what material they are 

struggling with or have already mastered. Strategies like questioning students to elicit their 

thinking, facilitating rich discussions, carefully observing students working, and analysing 

their in-progress work samples provide a rich source of data on learners' developing needs and 

capacities. Hence formative assessment promotes more meaningful, substantive interactions 

between teachers-students and peers through rich discussion, dialogue, questioning, and 

collaborative analysis of work centred on elaborating thinking and deepening mutual 

understanding (Black & Wiliam, 2009; Shepard, 2005). These formative assessment discourses 

help build collaborative classroom communities and cognitive scaffolds to advance learning. 



32 
 

Brookhart (2007) highlights the importance of teachers providing customised feedback loops 

to learners based on insights from formative assessments. For example, constructive feedback 

can prompt reflection on progress areas for improvement, give pointed guidance on the next 

steps, and motivate ongoing effort. As opposed to standardised feedback, differentiated 

feedback is tailored to individuals' revealed strengths, weaknesses, and learning approaches 

based on assessment data (Brookhart, 2010). Targeted feedback loops also facilitate monitoring 

both skill acquisition and wider learner attributes like self-efficacy and engagement (Hattie & 

Timperley, 2007). Teachers can provide differentiated feedback to prompt learner reflection, 

give guidance for growth, and motivate continued effort based on revealed needs (Brookhart, 

2007). Ongoing formative assessment data also facilitates flexible adaptation of pace, content 

complexity, materials, and lesson structure to meet emerging learning needs and maximise each 

student's advancement from their current skill level (Heritage, 2007). 

Wiliam (2011) conducted a study examining how mathematics teachers use formative 

assessment data to differentiate teaching. He found that by carefully analysing evidence from 

strategies like exit tickets, discussions, and student work samples, teachers were able to 

pinpoint areas where advanced learners could be challenged with expanded content while 

struggling students needed additional targeted support. For advanced students, teachers gave 

enrichment problems, offered chances to explain concepts to peers, and facilitated 

investigations going deeper into mathematical theory. For students needing more assistance, 

teachers retaught content using alternative explanations, provided extra scaffolding like 

manipulatives and models, and gave additional feedback with more concrete next steps. Wiliam 

(2011) concluded that mathematics teachers could effectively differentiate on both ends of the 

spectrum based on gaps revealed through routine formative assessments. 

Similarly, Ruiz-Primo and Furtak (2007) studied how middle school science teachers used 

formative discussions and work sample analysis to adapt support for struggling students. They 

found teachers were able to identify common misunderstandings and tailor feedback 

accordingly. For example, teachers noticed through lab report drafts that many students shared 

misconceptions about energy transfer. In response, they modified instruction to address this 

gap, giving targeted feedback to prompt student reflection and self-correction. The study 

showed using formative assessment evidence, science teachers could pinpoint conceptual 

difficulties and provide customised feedback and instructional revisions to meet revealed 

needs. 



33 
 

Formative assessment also cultivates students' own self-assessment capacities, goal-setting 

abilities, and metacognitive skills by actively engaging them in monitoring their learning 

progress (Andrade & Brookhart, 2020). Formative assessment classroom routines allow 

students to continually assess their own understanding against learning goals and success 

criteria made transparent by the teacher (Clark, 2012). For example, Wiliam (2011) examined 

how teachers can effectively build students' skills in self-evaluation of their work, a key facet 

of self-regulated learning. Self-regulation involves an interplay between commitment, control, 

and confidence. It addresses how students monitor, direct, and regulate actions towards the 

learning goal (Hattie & Timperely, 2007). He found that using rubrics, checklists, and 

exemplars as tools for peer and self-review of work in progress helped students learn to 

critically analyse their own performance. In Wiliam's study, middle school science teachers 

introduced students to collaboratively developed rubrics outlining criteria for success on an 

investigation project. They modelled analysing sample projects using the rubric, highlighting 

areas where the samples showed mastery and needed improvement. Students were then guided 

to use the rubric to assess their own and peers' draft work, citing evidence from the rubric to 

justify evaluations during peer review discussions. Teachers also provided checklists of key 

elements students should include in their final reports. Students used these to monitor their own 

progress in revising drafts. Teachers periodically reviewed a sample checklist to give feedback 

on its use. Additionally, teachers presented exemplars of high-quality past projects. Students 

analysed features that made these exemplary by comparing them to their own work. Teachers 

facilitated discussions encouraging students to identify their own areas of strength and areas 

needing improvement relative to the exemplars. 

Across these strategies, Wiliam (2011) found that students developed stronger skills in 

analytical self-evaluation, an ability Zimmerman (2008) links to improved self-regulation 

using concrete tools like rubrics, checklists, and exemplars for self-assessment gave students a 

clearer standard for evaluative reasoning and metacognitive monitoring. Teachers reported 

improved ability to identify areas for growth independently. This study demonstrated how 

purposefully engaging students in structured peer and self-review activities with tools like 

rubrics and models facilitates careful analytical evaluation of their own work. This builds vital 

skills in monitoring performance relative to standards that support lifelong learning. 

 Teachers also guide students in setting specific personal learning goals based on this self-

assessment data, planning the next steps for improvement. Andrade, Du, and Wang (2008) 

demonstrated that student goal setting strengthened engagement and outcomes. Having clear 



34 
 

goals enhances self-efficacy. Generating their own goals and strategising steps to reach them 

facilitates metacognitive monitoring of incremental progress, an ability Andrade and Brookhart 

(2020) find critical yet often underdeveloped without explicit training. Teaching students to 

continually chart growth towards goals through sustained formative assessment activities 

powerfully builds independent metacognitive regulation rather than relying on teacher 

monitoring alone (Zimmerman, 2002). 

Clark’s (2012) study found that having students regularly analyse their own thinking and work 

explicitly during mathematics problem solving developed their metacognitive awareness and 

ability to recognise where they needed to slow down and self-correct. Clark's (2012) study 

focused specifically on whether guiding students through intentional and structured self-

analysis of their thinking and problem-solving processes during mathematics lessons could 

cultivate their metacognitive skills over time. The intervention was based on existing research 

showing self-assessment and strategic monitoring of one's own learning are key facets of 

metacognition that can be actively developed rather than fixed traits (Veenman et al., 2006). 

The study followed 150 grade 4 learners in s five classes in two schools. Teachers were trained 

in facilitation techniques to regularly prompt student self-analysis through prediction of 

performance, documented self-questioning during problem-solving, personal strategy/error 

analysis, and self-evaluation versus set goals. These reflective prompts were embedded across 

units over one academic year. Quantitative analysis found the intervention group demonstrated 

significantly higher growth in metacognitive ability than the control group who received 

regular mathematics instruction without explicit skill reflection. The frequency of conscious 

monitoring of one's strategy use, recall of facts, and self-correction increased substantially. 

Qualitative reports from teachers observed students actively recognising areas of over-

confidence, knowledge gaps, and procedural mistakes that previously evaded their awareness. 

Students exhibited tangible behaviour shifts - slowing down when tackling complex problems, 

consciously checking work against models, and re-evaluating and adjusting ineffective 

strategies. Clark (2012) concluded that when reflection on the processes and outputs of learning 

is structured into regular teaching practice, students can develop heightened metacognitive 

awareness and skills that enable them to better regulate their own mathematical problem-

solving independently. The implications support embedding consistent self-analysis in subject 

learning to cultivate lifelong metacognitive learners. 



35 
 

Hence formative assessment is imperative at primary school level as mathematics encompasses 

developing foundational knowledge and skills across core domains, including numbers, 

operations, algebra, geometry, measurement, data analysis, and mathematical problem-solving. 

Primary mathematics centres on moving from informal concrete experiences towards 

representing and manipulating mathematical concepts more abstractly. This includes the use of 

symbols and tools. Primary mathematics also emphasises identifying and applying patterns as 

well as developing logical thinking abilities (DBE, 2011a). Teaching focuses on basic 

numeracy, arithmetic fluency, familiarity with space and shapes, interpreting data, and 

mathematical awareness applicable to daily life. 

Compared to secondary mathematics, primary level mathematics concentrates more on 

tangible demonstrations, manipulatives, visual models and practical connections to help 

scaffold understanding. As Matteson (2006) discusses, primary mathematics pedagogy 

strategically bridges active exploration to abstract problems through stages of enactive, iconic 

and symbolic representation. Assessment should similarly focus more on observable skills like 

counting principles, spatial reasoning, measurement, and basic operations than advanced 

symbolic manipulation through a product approach. Building foundational conceptual 

understanding, flexible thinking and problem-solving skills remain vital to enable future 

mathematical success. 

A recent meta-analysis by Zhai et al. (2023) synthesised findings from 92 studies between 

2010-2022 examining the effects of formative assessment on mathematics achievement across 

primary and secondary grades. Their analysis revealed an overall positive and statistically 

significant impact, with effects increasing at higher grade levels. Importantly, they found 

effects were stronger when formative assessment involved explicit training for students in self-

regulated learning strategies like goal setting, metacognitive monitoring, and self-evaluation. 

This highlights the value of positioning students as active agents engaged in the formative 

process. 

Additionally, a mixed-methods study by Lee and Bryant (2022) traced how embedding 

formative assessments focused on conceptual discussions enabled substantial learning gains 

compared to procedural skill practice alone. Students demonstrated greater flexibility in 

mathematical reasoning and the ability to generalise across concepts when instruction centred 

on formative tasks probing conceptual understanding through discourse. The researchers argue 



36 
 

that such formative approaches counter tendencies towards rote procedural instruction in 

mathematics. 

2.6 Teaching, Learning and Assessment in Primary Mathematics 

Assessment is regarded as an "essential issue" in mathematics education, requiring "careful 

consideration" by educators (Silver, 1992). Some mathematics teachers define assessment 

merely as an administrative process to track progress (Hove & Hlastshwayo, 2015). However, 

others argue assessment in the teaching of mathematics should function as a "tool for 

supporting students’ learning," not just measurement (Bell & Cowie, 2001; McMillan, 1997). 

Indeed, the NCTM (2000) asserts that assessment should "inform and guide teachers" and 

enhance learning, "not merely be done to students" (p. 3). This conception frames assessment 

as central to the learning process itself in mathematics education (Kilpatrick, 1993). 

Quality assessment should "elicit, assess and respond to mathematical understanding and 

problem-solving," not just test content knowledge (Oduro, 2015, p. 89). The NCTM (2014) 

advocates assessment that serves to monitor progress, modify instruction, evaluate 

achievement, and assess programme efficacy. Moreover, assessment should "furnish useful 

information to both teachers and students," supporting the learning of valued mathematics 

(NCTM, 2000, p.2). 

In South Africa, mathematics is a compulsory learning area in primary schools and learners in 

grade 4 must achieve a 40% pass (level 3) to progress to the next grade. Educators are expected 

to use the learners’ formative assessment to determine a learner's level of achievement since 

the Department of Education bases grade 4's progression primarily on what they have achieved 

through the year (continuous assessment).  

At primary school level, mathematics encompasses developing foundational knowledge and 

skills across core domains, including numbers, operations, algebra, geometry, measurement, 

data analysis, and mathematical problem-solving. Primary mathematics centres on moving 

from informal concrete experiences towards representing and manipulating mathematical 

concepts more abstractly. This includes the use of symbols and tools. Primary mathematics 

also emphasises identifying and applying patterns as well as developing logical thinking 

abilities (DBE, 2011a). Instruction focuses on basic numeracy, arithmetic fluency, familiarity 

with space and shapes, interpreting data, and mathematical awareness applicable to daily life. 

This means that mathematics should be “real” (Davis 1995, p.55) and deal with finding 

problems, conceptualising problems, considering someone's else alleged solution and asking if 



37 
 

they are any gaps in the reasoning process, recognising ambiguities and solving them and other 

matters of that sort. Yackel (1992) extends this idea by stating that mathematics educators 

should also motivate learners by asking learners questions and asking them to explain their 

solution methods to each other and then the educators use the information to "scaffold" them. 

This holds the potential for making feedback more formative in a way that the matched teachers 

espoused intentions. 

Compared to secondary mathematics, primary level mathematics concentrates more on 

tangible demonstrations, manipulatives, visual models and practical connections to help 

scaffold understanding. As Matteson (2006) discusses, primary mathematics pedagogy 

strategically bridges active exploration to abstract problems through stages of enactive, iconic 

and symbolic representation. Assessment similarly should focus more on observable skills like 

counting principles, spatial reasoning, measurement, and basic operations than advanced 

symbolic manipulation. However, building foundational conceptual understanding, flexible 

thinking and problem-solving skills remains vital to enable future mathematical success. For 

mathematics, the CAPS document prescribed four formal assessment tasks for each grade – 

tests, examinations, and projects. The policy also delineated the specific weighting and forms 

to be utilised for recording and tracking learner’s progress in relation to subject topics and skills 

(Kanjee & Moloi, 2014). Assessment in CAPS expects teachers to employ a variety of 

assessment strategies beyond traditional tests and explicitly document these assessment results. 

Pedagogical principles for teaching primary mathematics emphasise active, multimodal 

learning experiences to construct knowledge and make mathematics meaningful (Uğurel & 

Bukova Güzel, 2006). Discussion of mathematical ideas and processes is also critical for 

developing thinking and communication abilities (Bruce et al., 2007). Making cross-curricular 

connections through data analysis activities or geometric art projects enables application. 

Differentiation using tiered assignments and scaffolds is vital to support learners at varying 

levels. 

Assessment in primary mathematics aims to gauge development in conceptual understanding 

of core content, procedural fluency, mathematical reasoning, and problem-solving skills 

(Clarke et al., 2003). Teachers employ informal but frequent formative assessments through 

observation, oral questioning, analysis of classwork and homework, and completion of short 

tasks. These timely checks provide insight into learners’ progress and gaps requiring 

intervention. Simple written tests assessing skills and concepts may supplement more robust 



38 
 

project-based assessments allowing synthesis and demonstration of learning (Earl, 2003). 

Assessments require cognitively appropriate tasks and multiple representations allowing 

learners to show skills beyond tests. Tracking growth within the developmental scope of 

primary mathematics necessitates varied formats giving holistic insight (Shepard, 2000). 

However, while research advocates for robust assessments facilitating learning, debatably, 

little is documented regarding educators' actual knowledge and practices in implementing 

assessments, particularly formative assessments in the teaching of mathematics. As training 

programmes model best practices, studying teacher educators' use of formative assessment is 

vital. 

Recent years have seen a growing emphasis on integrating computational thinking into primary 

mathematics teaching (Chalmers et al., 2022; NCTM, 2022). Computational thinking skills like 

decomposing problems, recognising patterns, and using abstraction and algorithmic thinking 

are seen as foundational to developing proficiency with mathematical reasoning and problem-

solving. As such, curricula and assessment frameworks are expanding to incorporate tasks and 

rubrics targeting these abilities from an early age. 

Chiu et al. (2022) conducted one of the first large-scale studies examining primary teachers' 

formative assessment practices around computational thinking skills. Using classroom 

observations and teacher surveys across 288 classrooms, they found that while most teachers 

felt able to assess student computational thinking conceptually, they struggled to assess 

students' procedural skills in areas like developing algorithms. The study highlighted 

assessment literacy needs in this emerging domain. 

2.7 Assessment challenges in Mathematics education 

Assessing student learning in mathematics has long posed challenges for educators (NCTM, 

1995; Shepard, 2000). The limitations of traditional standardised mathematics tests in 

measuring critical competencies are a widely established issue facing mathematics educators. 

As Shepard (2000) underscored in her research, high-stakes assessments utilising exclusively 

multiple-choice and short-answer questions fail to assess mathematical reasoning, problem 

formulation, communication, making connections, and other standards set forth by the National 

Council of Teachers of Mathematics NCTM (1995) as central goals for pedagogy. The 

predominant use of selected and constructed response items allows efficient testing of 

computational skills and factual knowledge but falls short in assessing students’ deeper 



39 
 

conceptual understanding or complex problem-solving abilities (Webb, 1993; Clarke et al., 

2003). 

Similarly, Schoenfeld (2002) described widespread mathematics assessments as “both 

intellectually shallow and seriously out of line with the recommendations of discipline-based 

researchers” (p. 13). Schoenfeld's research in the Second Handbook of Research on 

Mathematics Teaching and Learning offered an impassioned critique of the disconnect between 

mathematics education research and standardised testing practices. He underscored that large-

scale assessments used across states and national monitoring efforts like the National 

Assessment of Educational Progress (NAEP) or The Trends in International Mathematics and 

Science Study (TIMSS) rely overwhelmingly on multiple-choice and short-answer items 

focused on recall of facts and execution of procedures. This stands in complete opposition to 

repeated calls from leading disciplinary organizations (National Council of Teachers of 

Mathematics, Mathematical A