Closing the Gap in Early Mathematics: Domain and Cognitive Insights from TIMSS 2023 in South Africa and Singapore

Research questions

Literature review: Comparative analysis of South African and Singaporean grade 5 mathematics achievement

Benchmarking with TIMSS 2023

The Trends in International Mathematics and Science Study (TIMSS) serves as an international benchmark to evaluate the mathematical learner achievement of both primary and secondary school learners. Singapore was consistently ranked as the top achiever, with learners assessed at Grade 4 achieving an overall average of 615 points, while South Africa, assessed at Grade 5, scored 362 points. This means that Singaporean learners who are on average a year younger still outperform South African learners by more than 250 points (von Davier et al., 2024). The magnitude of this achievement gap underscores the need to analyse not just overall scores but also performances across content domains (numbers, measurements, geometry, and data) and cognitive domains (knowing, applying, and reasoning) to understand how curricula and teaching practices shape outcomes.

Curriculum alignment and content domains

Singapore’s mathematical curriculum is internationally recognised for its coherence and spiral structure, which involves systematically revisiting concepts at increasing levels of complexity. In TIMSS 2023, Singapore scored 613 in numbers, 619 in measurement and geometry, and 616 in data, while South Africa scored 362, 353, and 362, respectively. Maqoqa (2024) and Tachie (2020) reported that the largest achievement gap is in measurement and geometry (266 points), an area long identified as a “blind spot” in South African classrooms. These gaps suggest that South African learners struggle with reasoning and geometric domains, while Singaporean learners benefit from early exposure to concrete manipulatives, reasoning, and visual models that build conceptual skills and knowledge.

Cognitive demands: Knowing, applying, and reasoning

TIMSS distinguishes between three cognitive domains: knowing, applying, and reasoning. Singapore’s Grade 4 learners achieved 624 in knowing, 615 in applying, and 609 in reasoning, whereas South Africa’s Grade 5 learners scored 357, 366, and 363. This result reveals a profound weakness in knowing (–267 points compared to Singapore), which reflects learners’ difficulties with knowing domains. South African learners performed slightly better in the applying domain (366) relative to their average, suggesting that when knowledge is available, learners can engage in routine applications. The reasoning domain, on the other hand, shows a persistent weakness. This means that South African learners are not being prepared for non-routine, multi-step problem-solving tasks, which is a strong point of the Singaporean system.

Instructional and structural factors

Several systemic factors reinforce these disparities. According to Meier and West (2020), South Africa’s classrooms often suffer from overcrowding, with class sizes averaging over 50 learners, which hinders formative feedback and personalised support. Teacher content and pedagogical knowledge remain uneven, particularly in geometry and measurement (Bhagwonparsadh & Pule, 2024; Taylor, 2021). In contrast, Singapore invests heavily in sustained teacher development, smaller class sizes, and instructional leadership, creating a conducive learning environment where consistent teaching and learning take place. Furthermore, although South Africa’s curriculum aims for comprehensive coverage, it has faced criticism for being “overloaded” and not allowing adequate time for the mastery of fundamental skills (Milne & Mhlolo, 2021). By contrast, Singapore’s Concrete–Pictorial–Abstract (CPA) approach deliberately scaffolds learning so that conceptual understanding precedes abstraction, enabling a positive learner achievement in higher-order reasoning (Leong et al., 2015; Lutfi & Dasari, 2024).

Curriculum–Cognitive alignment in International research

International evidence further illustrates how disparities between curriculum objectives and classroom practices shape academic learner achievement. Yılmaz et al. (2021) found that, while mathematics curricula emphasised reasoning, textbook activities leaned more toward application, creating a mismatch between intended and taught cognitive emphases. Similarly, Bulut and Taşpınar-şener (2023) reported that the application domain is most frequently prioritised in the secondary mathematics curriculum, disregarding the ECE curriculum, whereas the emphasis placed on knowledge and reasoning differs across grade levels. In primary schools, Pertiwi and Wahidin (2020) showed that fourth-grade assessments are dominated by number-related content, with far less attention given to geometry or data activities. These results reflect TIMSS’s framework, where knowing entails factual recall and procedural fluency, applying involves transferring knowledge to structured contexts, and reasoning requires non-routine problem-solving and critical thinking (Peduk & Ateş, 2019). Importantly, the study also found that content domains exert a more positive effect on mathematics learner achievement than cognitive domains.

This body of research provides an explanatory lens for South Africa’s TIMSS 2023 mathematics learner achievement. The relative strengths of South African Grade 5 learners in the application domain, alongside persistent weaknesses in knowledge and reasoning, reflect the misalignment noted by several studies internationally, where instruction and textbooks emphasise routine application but fail to develop the basic knowledge and reasoning capacity required for learner progression. In contrast, Singapore’s balanced curriculum and pedagogy demonstrate how alignment across content and cognitive domains fosters sustained learner achievement.

TIMSS: A diagnostic instrument

TIMSS offers a diagnostic lens to evaluate the effectiveness of the current curriculum and teaching practices, rather than viewing the legacies of apartheid inequalities as the main reason for the ongoing poor achievement in mathematics among learners. The comparative analysis with Singapore illustrates that South Africa’s curriculum is aligned superficially in content but misaligned in cognitive expectations, particularly at the levels of knowing and reasoning. This mismatch leaves learners underprepared for both academic progression and broader applications of mathematics in their everyday lives. The fact that Singapore’s Grade 4 learners significantly outperform South Africa’s Grade 5 learners further shows that the gap in mathematics achievement among learners is not simply attributable to learner age or exposure but to differences in curriculum coherence, cognitive scaffolding, and teacher training and development.

The TIMSS 2023 results highlight not just the scale of South Africa’s underperformance but also its domain-specific and cognitive weaknesses. While Singapore demonstrates how curriculum coherence and sustained teacher training and development can support an understanding of teaching and learning across content and cognitive domains, South Africa’s challenges are rooted in weak foundations, gaps in geometry and measurement, and systemic barriers in teacher training, development, and the classroom environment. Addressing these challenges requires targeted curriculum reforms in ECE, early-grade numeracy, curriculum streamlining, and teacher professional development, with a particular emphasis on geometry, critical thinking (reasoning), and basic knowledge. Context-sensitive adaptations, rather than comprehensive importation of Singapore’s model, offer a pathway for South Africa to strengthen learner trajectories in mathematics.

Conceptual framework

This study was guided by the TIMSS conceptual model, which distinguishes between mathematical content domains (numbers, measurement, geometry, and data) and cognitive domains (knowing, applying, and reasoning) (Mullis et al., 2020). These dual dimensions provide a diagnostic lens for understanding not only what mathematics learners are expected to know but also how they engage with mathematical activities in the classroom. Therefore, the researcher can investigate South Africa’s historically poor mathematics learner achievement by identifying specific weaknesses in basic knowledge (knowing), conceptual understanding (applying), and higher-order reasoning.

To explain these disparities, the study draws on curriculum alignment theory, which emphasises coherence between curricular intentions, classroom practices, and assessment demands (Porter, 2002). High-performing education systems such as Singapore demonstrate strong alignment through a spiral curriculum that revisits concepts at increasing levels of complexity supported by the Concrete–Pictorial–Abstract (CPA) approach that scaffolds learning from concrete manipulatives to abstract reasoning (Leong et al., 2015; Lutfi & Dasari, 2024). In contrast, research in South Africa highlights curriculum overload, insufficient time for mastery of basic domains, and persistent weaknesses in geometry and spatial reasoning, exacerbated by gaps in teacher content knowledge (Maqoqa, 2024; Taylor, 2021).

Situating South Africa’s Grade 5 TIMSS 2023 results against Singapore’s Grade 4 performance thus allows for a comparative curriculum lens that identifies both where South African learners struggle most and how Singapore’s curriculum scaffolds progression from knowledge to application and reasoning. To guide this analysis, the study therefore adopted an integrative conceptual framework that combines the Comparative Lens (South Africa versus Singapore, considered at macro, meso, and micro levels) with the TIMSS Curriculum Model (distinguishing intended, implemented, and attained curricula, as well as content and cognitive domains) (Alemu et al., 2021; Mullis et al., 2020) and Curriculum Theory Dimensions (alignment, spiral progression, CPA scaffolding as described by Lutfi and Dasari (2024), and Grundy’s (1992) product–process–praxis–context typology). Together, these components ensure that the framework is both diagnostic, by mapping learner strengths and weaknesses, and explanatory, by linking performance to curriculum and pedagogy, while also generating practical insights for educational reform. Figure 1 illustrates this integrative conceptual framework, showing how the comparative, curricular, and theoretical dimensions interact to guide the study’s analysis.

Figure 1. Adapted conceptual framework combining the comparative lens, TIMSS curriculum model, and curriculum theory dimensions guiding the study.

Building on this conceptual framework, the study’s methodology was designed to operationalise these dimensions through an analysis of the TIMSS 2023 data. The TIMSS curriculum model provided the basis for investigating both content and cognitive domains, while the comparative lens allowed for benchmarking South African Grade 5 learners against Singaporean Grade 4 learners. Curriculum theory informed the interpretive aspect of the analysis by connecting observed performance trends to overarching concerns of curriculum alignment, learner advancement, and pedagogical practices. The following section outlines the research design, participants, data collection, analytical strategy, and ethical considerations employed in this study.

Research design

This study employed a quantitative secondary data analysis design, using data from the Trends in International Mathematics and Science Study (TIMSS) 2023. This design is particularly appropriate for investigating the mathematics achievement of South African Grade 5 learners across content and cognitive domains for several reasons. First, TIMSS provides a large, internationally standardised dataset that is both rigorous in design and nationally representative, making it suitable for examining learners’ performance patterns with a high degree of reliability. Second, secondary analysis enables the use of TIMSS’s robust psychometric procedures, including item response theory and plausible values, which strengthen the validity of inferences about learners’ achievement. Third, the TIMSS framework allows for meaningful international benchmarking, making it possible to situate South Africa’s performance in relation to high-performing education systems such as Singapore. Guided by the TIMSS assessment framework, the analysis focused on three content domains (numbers, measurement, geometry, and data) and three cognitive domains (knowing, applying, and reasoning). This two-fold focus not only enabled a diagnostic assessment of learners’ strengths and weaknesses within the South African context but also provided comparative insights to inform curriculum and policy reform globally.

Participants

The South African Grade 5 sample for TIMSS 2023 consisted of approximately 10,424 learners drawn from 285 schools (Department of Basic Education, 2024), while Singapore sampled 6530 Grade 4 learners from 181 schools (von Davier et al., 2024). The International Association for the Evaluation of Educational Achievement (IEA), in collaboration with Statistics Canada, utilised a two-stage stratified cluster sampling methodology to guarantee nationally representative estimates (Siegel & Foy, 2024). In the first stage, schools were selected with probabilities proportional to their size, and in the second stage, intact Grade 5 classes were sampled. The stratification variables included the school sector (public or private), the language of instruction, the geographic region, socioeconomic indicators, the degree of urbanisation, and prior academic achievements (Ibid.). This rigorous design ensured that the results accurately reflect the diversity of the South African education system and provide robust population-level estimates of learner performance.

Data collection and analysis

Learners completed mathematics assessments together with contextual background questionnaires. The TIMSS mathematics achievement is measured on a scale with a standard deviation of 100 and an international centre point of 500, which makes it possible to make valid comparisons between countries. According to Reynolds (2024), the mathematics assessment comprised 183 items distributed across the three content domains (numbers: 94 items; measurement and geometry: 49 items; data: 40 items) and three cognitive domains (knowing: 58 items; applying: 85 items; reasoning: 40 items). Each student took one test booklet, and the results were estimated using item response theory and reported as plausible values (von Davier, 2019). This design ensures reliable population-level estimates while reducing respondent burden.

The analysis concentrated on South Africa’s Grade 5 results, using Singapore’s Grade 4 outcomes as a benchmark to emphasise comparative mathematics learner achievement. Weighted descriptive statistics were computed according to IEA guidelines for handling complex sampling. These weights take into account the hierarchical structure of TIMSS, which makes sure that the estimates are not biassed at the national level (Siegel & Foy, 2024). Differences in performance across domains were tested for statistical significance at p < 0.01. In addition, effect sizes (Cohen’s d) were calculated to assess the practical significance of observed gaps between content and cognitive domains and between South Africa and Singapore. This combination of statistical significance and effect size estimation provided a more profound understanding of performance trends.

Ethical considerations

This study is based on secondary analysis of TIMSS 2023 restricted-use datasets provided by the IEA. The data contain no personal identifiers and were collected under strict international ethical protocols during the original administration. Because this research involved secondary analysis of anonymised data, no institutional ethics approval was required. There was no formal request to use the dataset from the IEA since the data is available in the public domain, and all analyses adhered to its guidelines for responsible data use.

Content domain achievement

Table 1 reports the mean scores for South African Grade 5 learners and Singaporean Grade 4 learners across the three TIMSS mathematics content domains. The results reveal consistently lower learner achievement for South Africa across all three areas, with the largest gap evident in measurement and geometry. This persistent weakness in spatial reasoning reflects long-standing challenges in South African classrooms and emphasises the need for targeted curricula and pedagogical reforms in this domain that are context-sensitive.

All three domains reveal large effect sizes (d > 2.5), signifying profound disparities. The most pronounced gap lies in Measurement and Geometry (d = 2.66), confirming that South African learners face persistent difficulties in spatial reasoning and geometric concepts.

Cognitive domain achievement

Table 2 presents performance across the TIMSS cognitive domains. The results show that South African learners are much less knowledgeable than their Singaporean peers in all three areas. The biggest difference is in the knowing domain. This result points to fragile foundations in knowing domain, which limit learners’ ability to advance toward higher-order reasoning activities. Although performance in the applying domain is relatively positive, it remains well below international benchmarks, suggesting that gains in procedural applications are insufficient without deeper conceptual mastery.

The knowing domain shows the largest gap (d = 2.67), underscoring fragile foundations in factual knowledge and procedural fluency. South African learners’ relatively positive achievement in applying (366) suggests that when basic knowledge is accessible, learners can engage with routine procedures. However, the consistent deficits across domains indicate that foundational gaps constrain progression to reasoning tasks, where Singaporean learners excel.

Item-level illustrations

To illustrate the cognitive demands underlying these results, examples from released TIMSS items are useful. In the knowing domain (numbers), more than 90% of Singaporean learners were able to recall multiplication facts correctly, while fewer than 40% of South African learners were able to do the same. This shows that there are big gaps in basic fact fluency. In the applying domain (data), routine tasks such as interpreting a simple bar chart were accessible to many South African learners, suggesting some competence with structured and familiar problems. However, in the reasoning domain (geometry), where items demanded multi-step reasoning with angles, most Singaporean learners responded correctly compared to fewer than 20% of South African learners, reflecting limited exposure to non-routine problem-solving beyond procedural recall. Collectively, these examples highlight how curriculum exposure and classroom instructional practices shape learners’ preparedness to engage with domain-specific cognitive demands.

Visualising the gaps

Figure 2 illustrates the comparative performance of South African Grade 5 and Singaporean Grade 4 learners across the three TIMSS content domains. The visualisation confirms the consistently lower achievement of South African learners, with the largest gap observed in measurement and geometry. This finding supports the tabulated results and highlights the ongoing challenges that South African learners encounter in spatial reasoning and geometric concepts. By presenting the disparities graphically, Figure 2 highlights the structural nature of these weaknesses and the extent to which curriculum design and instructional practices shape domain-specific performance.

Figure 2. Comparative performance of South African Grade 5 and Singaporean Grade 4 learners across TIMSS content domains (Numbers, Measurement & Geometry, and Data).

Figure 3 presents the comparative performance of South African Grade 5 and Singaporean Grade 4 learners across the TIMSS cognitive domains. The figure makes clear that the widest disparity lies in the knowing domain, where South African learners demonstrate severe deficits in foundational knowledge and procedural fluency. While relative performance in applying appears slightly positive, it remains far below international benchmarks, limiting progress to more complex reasoning. These results show how gaps in basic knowledge can lead to fewer chances for higher-order thinking. On the other hand, Singapore’s curriculum scaffolding helps all three cognitive domains grow in a balanced way.

Figure 3. Comparative performance of South African Grade 5 and Singaporean Grade 4 learners across TIMSS cognitive domains (Knowing, Applying, and Reasoning).

Summary of results

The results of the analysis highlight three critical insights into South African learners’ mathematics achievement. First, geometry and spatial reasoning continue to represent the weakest domain, pointing to enduring structural gaps in both curriculum design and teacher preparation. Second, the severity of deficits in foundational knowledge, reflected in the knowing domain, restricts learners from progressing toward higher-order reasoning tasks. Third, although learners demonstrate relatively positive learner achievement in the applying domain, this potential remains constrained by the absence of solid basic skills and limited opportunities for reasoning skills, which prevents the development of sustained mathematical learner achievement. Collectively, these results suggest that South Africa’s performance challenges are not incidental but rather systematic, domain-specific, and deeply embedded in pedagogical practices. In contrast, the comparison with Singapore emphasises the value of curriculum coherence and deliberate cognitive scaffolding for supporting learners’ steady progression across domains.

Differentiation from previous research

Most South African studies using TIMSS data focus on Grade 9, highlighting long-term inequalities and secondary-level deficits. This study’s focus on Grade 5 performance adds novel evidence at the stage when foundational mathematical concepts are consolidated and future trajectories are set. By disaggregating results across content and cognitive domains, it reveals early learning disparities that aggregate reports often obscure. The comparative lens with Singapore enhances interpretive depth by demonstrating how curriculum alignment, pedagogical scaffolding, and teacher preparation in high-performing systems cultivate balanced cognitive development. Thus, this paper contributes grade-specific, comparative evidence that complements rather than duplicates existing analyses, offering practical insights for foundational-phase teacher education and classroom reform.

Policy and practice implications

The TIMSS 2023 results demonstrate that socioeconomic and systemic inequalities, which directly manifest in classroom practice, entrench South Africa’s mathematics challenges (Taylor, 2019). Learners in Quintile 1–3 schools, serving the poorest communities, often face overcrowded classrooms, resource scarcity, and underqualified teachers. These conditions constrain formative assessment, differentiated instruction, and sustained skill development. Although pro-poor funding policies provide some redress, resources remain inadequate to counter entrenched disparities. Drawing comparative insights from Singapore while contextualising them for South Africa, this study proposes three interrelated pillars of reform, anchored in teachers’ daily practice.

Pillar 1: Strengthening foundations through diagnostic teaching

Persistent deficits in the knowing domain indicate that many learners progress without mastering number facts, place value, and basic operations. Policy should prioritise early diagnostic assessments in Grades 1–3 to identify learning gaps before they widen. Schools, particularly in low-SES contexts, could implement structured catch-up programmes modelled on Singapore’s Learning Support Programme, adapted for multilingual and resource-limited settings. Professional development in formative assessment and error analysis will enable teachers to translate diagnostic data into responsive teaching. Dedicated funding for remedial support staff, small-group tutors, and low-cost learning materials would operationalise this pillar at the school level.

Pillar 2: Enhancing geometry and spatial reasoning through pedagogical innovation

Measurement and geometry remain the weakest domains, highlighting persistent gaps in spatial reasoning. Professional learning programmes should therefore emphasise visual, experiential, and problem-based approaches to geometry. In resource-constrained schools, teachers can employ locally available materials, outdoor activities, and hand-drawn representations to cultivate geometric understanding. Over time, they can be complemented by affordable digital visualisation tools. Embedding spatial reasoning modules in pre-service and in-service teacher training will institutionalise these practices across the system.

Pillar 3: Leveraging learners’ strength in applying to cultivate reasoning

The relatively stronger The relatively stronger performance in the Applying category provides an opportunity to foster deeper reasoning. Curriculum reform should integrate contextually relevant problem-solving tasks drawn from everyday experiences, such as budgeting or community-based measurement activities, to enhance engagement and conceptual transfer. Teachers should be supported to design inquiry-based lessons that promote explanation, justification, and collaboration. District-level mentoring and professional learning communities can help disseminate and sustain these pedagogical innovations.

System-level coherence: Linking policy, curriculum, and classroom practice

The effectiveness of these pillars depends on systemic coherence from early childhood education through the intermediate phase. Singapore’s ongoing progress shows that real change happens when policy goals, teacher training, classroom practice, and assessment design all work together. Accordingly, South Africa’s Department of Basic Education must integrate curriculum reform with continuous professional development, accountability structures, and resource provision. Reducing class sizes, ensuring consistent access to learning materials, and strengthening school-based mentoring will translate curriculum goals into meaningful learning. Ultimately, bridging policy and practice requires recognising teachers as the primary agents of change. When professional learning, curriculum design, and resourcing converge around clear pedagogical objectives, early mathematics education can evolve from procedural instruction toward conceptual understanding, advancing equitable foundational learning in line with Sustainable Development Goal 4 (SDG-4): Quality Education.