Introduction
In South Africa (SA), inclusive education aims to support learners with special needs, mainly those with disabilities, as a response to apartheid's segregation policies (Chirowamhangu, 2024). However, the inclusivity of school subjects, especially in mathematics, is questionable, with dropout rates rising despite three decades of efforts to promote STEM subjects. In rural areas, access is complicated by curriculum choices, mathematics, mathematical literacy, and technical mathematics, that are based on past performance, advice, and institutional pressures to pass Grade 12.
This article advocates equity as a pathway to inclusion in mathematics education. We adopt an ideological rather than an interventionist approach to inclusion (Roos, 2023), meaning that critical and societal perspectives matter. We see these perspectives as involving decisions about mathematics, especially those shaped by teachers' practices, not only by education authorities. While a school governing body can decide whether high school students in Grade 10 (around 15–16 years old) are allowed to study mathematics in SA, the curriculum is prescribed and monitored, leaving teachers with limited influence. Equity in mathematics education in SA remains underexplored. Gutiérrez (2009), in the US, outlines a four-dimensional equity framework: access, achievement, identity, and power. Given its broad scope, we focus on access. Gutiérrez (2009) describes access as a combination of resources, pedagogical, relational, and structural factors that influence opportunities to participate in mathematics. We draw on the literature on three types of access: socioeconomic, technological, and epistemological. In Sub-Saharan Africa, the focus tends to be on learner disabilities, gender disparities, physical challenges of girl learners, and curriculum gaps, including indigenous knowledge systems (Zickafoose et al., 2024). We propose inclusion through the three-layer access framework. This study aligns with Gutiérrez’s (2012) view that the context of teaching and learning is important; mathematical thinking (MT) encompasses not only subject matter but also the methods and rationale behind instruction. The goal is for skills such as evaluation, prediction, generalisation, and abstraction to be transferable, understood, and applicable in both familiar and unfamiliar mathematical contexts (Celik, Furkan, 2020). Agbata et al. (2024) recommend that, to advance mathematics education in Africa, sustainable progress depends on creating better learning environments, ensuring greater accessibility of digital resources, encouraging cross-disciplinary collaboration, and connecting educational institutions with industry and policy partners, each of which talks to access.
Literature review
Access to higher education (HE) in SA is influenced by ongoing socioeconomic inequalities and the lasting effects of segregation and discrimination (Du Plessis, Mestry, 2019). Although post-apartheid reforms aimed to expand participation and address historic injustices, access-related barriers still exist. While research often focuses on university entry, these inequalities start much earlier in schooling. Despite the notable progress made by the post‑apartheid government in improving the quality of mathematics teaching and learning, access remains a significant issue (Du Plessis, Mestry, 2019). Many rural schools remain severely under‑resourced (Mojapelo, Durodolu, 2022). Such disparities influence learners’ exposure to curriculum, pedagogy, and technological tools long before they reach HE, reinforcing early cycles of advantage and disadvantage. Therefore, this literature review explores how three interconnected forms of access exist within school mathematics contexts, crucial for explaining the inequalities that later emerge in HE participation and success.
Socioeconomic access
We understand socioeconomic access, often termed physical access, as the financial and logistical conditions that enable or constrain participation (Child, Song, 2023). In HE, research shows that although enrolment among marginalised students has increased, financial constraints still affect their ability to succeed. Access to funding, affordable accommodation, and transportation remains uneven, creating pressures that affect students’ academic performance (Alyahyan, Düştegör, 2020). For example, in May 2026, the Higher Education and Training minister placed the National Student Financial Aid Scheme under administration following “prolonged governance failures, board resignations, and financial irregularities” (Lebaka, 2026). These media updates pressure students and carers relying on financial aid. Our work highlights the importance of considering not only the availability of financial resources but also the broader structural conditions that shape learners’ everyday educational experiences. Oyedemi and Mogana (2018) found that among 156 first‑year students schooled in rural SA, 82% had no access to computers or the internet, illustrating the extent to which poverty shapes educational opportunity.
Technological access
Technological access involves the availability and use of educational tools like calculators, computers, digital platforms, apps, and AI-enabled tools. In SA, access varies, including access to devices and the ability to use digital tools effectively to deepen understanding and practise MT beyond classroom instruction. In higher‑education research, technological access includes the capacity to engage meaningfully with online learning tools as part of routine academic practice (Samosamo, Divala, 2023). This framing is useful for clarifying the concept in school mathematics education. It cannot be reduced to owning a device or purchasing data. In many rural contexts, teachers may have laptops and even personal data yet lack reliable Wi-Fi or sufficient network coverage. While teachers may be keen to integrate technologies into teaching and learning, Maja et al.’s (2024) study, for example, shows that at five primary schools in the rural province of Limpopo in SA, the schools were unable to afford the cost of internet connectivity, which meant that even though there might be technologically savvy teachers, lack of connectivity hampered delving deeper into mathematical contexts. Signal instability in deeply rural areas means that connectivity itself becomes a structural barrier. Thus, access to technology is not simply about hardware or data availability; it is also about infrastructural conditions that enable, or constrain, meaningful digital participation in mathematics education.
Epistemological access
Epistemological access extends beyond the mere availability of textbooks and learning materials that ostensibly support knowledge production (Harland, Wald, 2018). Resources are necessary, but knowledge production assumes learners can access and engage meaningfully with the knowledge. In mathematics education, epistemological access relates to how learners understand what is offered and whether they can make sense of it, internalise it, and transform it into usable knowledge. Access to knowledge production involves more than irregular mathematical practice; it relies on teachers mediating knowledge coherently and meaningfully, and learners engaging independently with materials to deepen understanding. Epistemological access also requires applying knowledge in various contexts. Resources and teachers alone do not ensure true mathematical access without the capacity to interpret, internalise, and transfer knowledge. Mafugu’s (2023) study of 32 participating rural learners highlights social inhibitors to knowledge acquisition in mathematics. Their qualitative study shows that irregular mathematics practice was linked to competing household responsibilities, limited time, and diminished motivation, all of which reduced learners’ participation in meaningful mathematical activities. In Sub-Saharan Africa, the plethora of African languages necessitates translanguaging, which acknowledges diversity and removes language barriers to advance curricular achievement (Zickafoose et al., 2024). In SA, the language of teaching and learning is determined by a school’s governing body, although many teachers code-switch (change languages) when they teach to accommodate their learners’ home languages. Still, learner examinations are written and expected to be answered in the school’s language of instruction.
Theoretical framework: сultural-historical theory
Access to mathematics involves more than school entry or subject selection; it also entails mediated access to the development of higher psychological functions through participation in mathematical activity. From a cultural-historical perspective, learners do not engage with mathematics directly but through mediation by cultural tools and signs (language, symbols, diagrams, examples, calculators, and digital resources), by social interaction (teacher guidance and peer collaboration), and by institutional structures (curriculum pacing, assessment practices, streaming, and subject allocation) (Vygotsky, 1978; 1986). Access therefore includes not only entry into a subject but also access to the mediational means through which mathematical meaning-making becomes possible.
In Vygotskian terms, mathematics learning involves the development of higher psychological functions such as abstraction, voluntary attention, logical memory, conceptual reasoning, and self-regulation (Vygotsky, 1978; 1986). These capacities do not arise simply through enrolment in a mathematics classroom but through sustained participation in mediated social activity. When mediation is limited, through weak instructional support, restricted conceptual explanation, limited language scaffolding, inadequate technological resources, or fragmented curriculum coverage—the development of these functions may be constrained. This explains why physical presence in a classroom does not in itself constitute meaningful access to mathematical learning.
A distinction can therefore be made between formal access and mediated epistemological access. Formal access refers to enrolment in schooling and participation in mathematics as a subject. Mediated epistemological access refers to the conditions that enable the development of mathematical concepts and higher psychological functions through participation in teaching and learning activities. This distinction is particularly significant in rural South African contexts, where learners may be formally included in schooling and mathematics classes yet remain excluded from deep conceptual understanding and subsequent opportunities for HE participation.
Materials and methods
This study employs a qualitative, interpretivist paradigm to explore participants’ lived experiences through a purposeful lens. Using a purposive sampling strategy, the study’s design investigates a cohort of rural mathematics teachers who are attending the third or fourth course in a seven-course professional development sequence at a non-government institution. This methodological framework aligns with the interpretivist goal of understanding social phenomena from the perspectives of those involved, acknowledging that research design must be contextually grounded to produce meaningful insights (Mouton, 2001). By focusing on this specific group, the study aims to capture the complex, situated nature of these teachers' professional development within their unique institutional and geographic environment.
Seventy-six teachers agreed to participate in the study, providing consent electronically and by signing consent forms. Pseudonyms (Teacher1-Teacher76) were used to ensure anonymity in the article. All the participating teachers had completed at least three professional development courses delivered by a non-government organisation in SA. The professional development courses centred on MT. Data were collected from a survey consisting of four questions administered via a Google Form (available for 3 months) to mathematics teachers attending the professional development course from January to April 2025. Participating teachers were asked to describe and reflect on classroom experiences where constraints influenced their ability to teach for MT, adapt lessons, respond to learners’ understanding, and prepare learners for examinations. The teacher’s responses were thematically analysed to explore how three access types affected decisions and practices. They demonstrated how these access types limited inclusive participation in mathematics teaching and learning. A new theme, systemic access, also emerged.
Results
Socioeconomic access as material and temporal conditions
The data indicate that socioeconomic access significantly shapes the conditions under which participation in mathematics becomes possible. Teachers consistently described material constraints that extend beyond isolated shortages. These included limited access to textbooks and manipulatives, difficulties in reproducing or sharing resources, and limited prior exposure of learners to foundational mathematical concepts. These constraints are not merely logistical challenges; they structure who can meaningfully engage in mathematical activity. When learners lack access to adequate materials, relevant examples, or stable learning environments, inclusion is constrained before pedagogical strategies can be enacted.
A second dimension of socioeconomic access emerged in relation to time. Teachers described persistent pressure to cover CAPS (Curriculum and Assessment Policy Statements of the South Africa’s education system), to “teach large classes” (T5), to teach multiple grades, and to prepare learners for examination-driven assessment regimes, “you have to go back and teach basics, knowing very well that time is not on our side” (T10). Within these conditions, pedagogical time becomes compressed. “The ATP (prescribed Annual Teaching Plan) is quite long … time is limited”, states T9. Opportunities for exploration, conceptual discussion, remediation, and consolidation are reduced. Time, therefore, functions as a socioeconomic resource — unequally distributed and structurally regulated. In historically marginalised schools, limited temporal flexibility restricts teachers’ capacity to respond to learners’ developmental needs.
Technological access as expanded mediational possibilities
The results indicate that technological access operates as a significant, though often implicit, lever for inclusion in mathematics education. While teachers did not always frame their challenges explicitly as technological problems, their responses reveal multiple dimensions of constraint. Teachers described difficulties in efficiently sharing resources, reliance on traditional instructional approaches even when learners struggled, and limited access to adaptive tools to support differentiation. These accounts point to infrastructural limitations, including unstable or absent internet connectivity, limited access to interactive software, inadequate projection facilities, and the absence of mathematical visualisation platforms. T18 stated that “there was no computer lab or internet for learners to revise or watch video lessons” at their school. T56 reported that “learners did not have calculators”. These constraints limit the depth of mathematical participation.
Another dimension concerns pedagogical flexibility enabled by technology. Teachers reported needing to adapt lessons when learners struggled with abstract concepts such as fractions, functions, exponents, and geometry, but limited access to working devices constrained this. As T4 noted, lack of functioning computers and learner cellphones prevented resource sharing, forcing reliance on time-consuming chalkboard instruction. Tools such as dynamic geometry, graphing software, simulations, and AI-assisted differentiation can enhance epistemological access by enabling multiple representations, experimentation, and multilingual explanations. The results suggest that teachers are pedagogically responsive but constrained by limited technological resources. Importantly, technological access also emerged as a matter of teacher inclusion. The teachers in this study described constantly adapting lessons, frequently replanning, managing curriculum pressure, and carrying substantial cognitive overload. Yet many lacked access to sustained professional development in educational technology, AI-supported lesson planning tools, collaborative digital communities, or open educational repositories. In this sense, teachers themselves remain excluded from innovation in mathematics education. Technological access serves as a structural mechanism of inclusion for both teachers and learners, shaping who can fully participate in contemporary mathematical practices and who remains constrained by limited mediational means.
Epistemological access as participation in meaning-making
A third prominent result relates to epistemological access, or access to mathematical meaning-making. Teachers frequently reported that learners struggled to understand concepts such as algebra, functions, fractions, and geometry despite instruction, often relying on procedures without conceptual understanding. As T8 noted, limited opportunities for open-ended exploration and learners’ familiarity with rote learning constrained critical engagement. Teachers also observed difficulties in transferring knowledge across topics and applying concepts in unfamiliar contexts. These results point beyond content coverage to the depth and quality of learners’ mathematical engagement. Epistemological access involves more than the ability to execute procedures; it requires participation in explanation, justification, representation, and abstraction. The data reveal a persistent tension: while teachers expressed a clear desire to cultivate deep understanding, curriculum pacing pressures and assessment demands often compelled them to prioritise procedural coverage. As a result, opportunities for sustained conceptual engagement were frequently curtailed.
I wanted them to design a cylindrical object with a cone at the top… to solve the problem of the total surface area of combined objects. I couldn't do it because I thought it would be time-consuming. I ended up just giving them formulae to memorise. (T16)
Systemic access as autonomy of structural conditions
A fourth result relates to systemic access, understood as access to pedagogical autonomy within broader policy and curriculum structures. T38 affirmed that, in order to “reinforce knowledge and build confidence, this choice is a commitment [of a teacher] to foster inclusion”. Other teachers described an ongoing tension between curriculum compliance and pedagogical responsiveness. They cited constant CAPS temptations, pressure to meet deadlines, lesson adjustments for learner difficulties, and balancing exam prep with understanding. These highlight structural constraints affecting teachers' responses to learners' needs. Systemic access, in this sense, concerns the extent to which teachers have the institutional space to pause, revisit, extend, or redirect learning based on learners' current understanding. It reflects access to flexibility in pacing, sequencing, and assessment alignment. Where assessment remains rigid, pacing remains fixed, and curricula remain overloaded, teachers’ autonomy to enact responsive and conceptually oriented pedagogy is limited. T18 illuminates that:
I realised that moving forward to simultaneous equations would only make things worse. I was faced with a difficult decision: follow the pace of the curriculum or slow down to revisit the foundational concept. I chose to re-teach the key concepts in the next lesson using a different approach.
Discussion
Inclusion in mathematics education goes beyond access to content; it involves mediated developmental access, including tools and resources that help teachers develop learners' understanding. According to Vygotsky (1978), human development is significantly influenced by culturally produced tools and signs, including a shared language that is crucial for effective communication and deeper comprehension of mathematical concepts. This goes beyond teaching in a student's home language or translanguaging; it encompasses the use of a teaching and learning language that promotes conceptual development and MT — essential for internalising higher psychological functions such as interpreting, reasoning, and justifying (Vygotsky, 1986). It involves posing open-ended questions to learners to promote engagement with mathematics, not just each other, and trialling new ideas that are not necessarily prescribed by a curriculum.
A strictly content-based mathematics curriculum, governed by rigid timelines on when and how topics should be taught, hinders the development of critical thinking skills at a systemic level. While the lack of resources is a legitimate concern, especially in rural schools, focusing solely on this scarcity can be distracting. Often, resource constraints are an enduring reality, and excessive emphasis on them may divert attention from what truly matters: cultivating critical thinking in mathematics education. When teachers recognise, model, and engage with MT, they make the subject more visible, relevant, and transferable, promoting interest and engagement. Inclusion involves access to mediational means for participation. Many teachers cited time as a barrier, noting the need for opportunities to try new pedagogical approaches that could improve teaching and learning. What would teachers do with the time if they had it? The answer to this question is perhaps the biggest limitation in this study and requires further investigation.
Access to technology (e-textbooks, Quizlet, Google Classroom, simulations) provides dynamic representations, exploration, and immediate feedback. Without these, representations are static, hindering experimentation and teachers' ability to support deep understanding, and promoting traditional chalk-and-talk approaches to teaching and learning, perpetuating historical injustices on the African continent. Without effective mediated practices, learners struggle to engage in activities like explanation, justification, linking concepts, and disciplinary discourse, which are vital for internalising mathematical reasoning. Findings show that teachers see themselves as mediators limited by systemic barriers, which transform them from agents of inclusion into agents of exclusion despite their role as educators. In other words, teachers themselves limit learning.
Systemic access highlights that educational progress depends on mediation supported by institutional structures that enable scaffolded learning within the Zone of Proximal Development. The movement from interpsychological to intrapsychological understanding of mathematics is constrained by rigid educational systems (Vygotsky, 1978), not only in SA but across Sub-Saharan Africa. Limited systemic access raises questions about teachers’ autonomy to adapt instruction responsively. Inclusion in rural mathematics classrooms is therefore relational and multifaceted. From a Vygotskian perspective, axes of access are interdependent and collectively shape mathematical development. The development of higher psychological functions depends on time, responsiveness, and guided participation within the ZPD, yet rigid curriculum pacing and assessment pressures restrict teachers’ ability to pause, revisit, and scaffold learning, thereby constraining learners’ developmental trajectories. In historically marginalised contexts, inclusion requires creating conditions that support the emergence and stabilisation of higher psychological functions, expanding opportunities for conceptual development rather than merely redistributing resources.
Vygotsky’s (1978) distinction between lower and higher psychological functions offers a useful lens for understanding cognitive development in mathematics education. Mathematical reasoning, as a higher psychological function, does not develop through repeated exposure to procedures or rote learning, but through deliberate engagement with conceptual activity. In cultural-historical theory (Vygotsky, 1986), education is understood as the process through which learners move beyond everyday experience toward increasingly complex forms of reasoning and abstraction. From this perspective, inclusion is not simply about access to schooling, but about access to opportunities for conceptual development and inquiry.
The quality of educational mediation plays a crucial role in shaping the knowledge learners construct. Without dynamic visualisations and interactive simulations, abstraction is often limited to procedural mimicry, disconnected from the underlying mathematical logic. In classrooms without technological tools, opportunities to navigate seamlessly between concrete and abstract representations are significantly diminished. Dynamic visualisations and simulations, as well as immediate feedback mechanisms, can help learners connect symbolic expressions with conceptual meanings. Therefore, the nature of the knowledge constructed is influenced by the quality and availability of mediation. This understanding has significant implications for the process of internalisation. For Vygotsky, higher psychological functions initially manifest on the social plane before becoming internalised by individuals. If classroom experiences are characterised by fast pacing, procedural rehearsal and limited dialogue, the social conditions conducive to deep internalisation are weakened. Consequently, learners may replicate steps without developing voluntary, conceptual control over mathematical ideas. Inclusion must therefore extend beyond merely providing tasks; it necessitates creating mediated experiences that facilitate the gradual transformation of shared activities into individual understanding.
Conclusion
This article examines equity in mathematics education as central to inclusion. It adopts an ideological rather than deficit-based view of inclusion and explores structural and pedagogical factors that shape participation from teachers’ perspectives. Using Gutiérrez’s (2009) equity framework, focused on access, it investigates socioeconomic, technological, and epistemological barriers in rural South African schools. Findings show these forms of access are interconnected. Beyond the three forms identified in the literature, teachers highlight systemic access — institutional conditions such as curriculum pacing, assessment pressures, and limited pedagogical autonomy that shape their ability to revisit, scaffold, and support learning.
Using Vygotsky’s cultural-historical theory as an analytical lens, the findings suggest that equity requires mediated developmental access. Inclusion depends not only on access to content and pedagogy, but also on the material, technological, epistemological, and systemic conditions that enable meaningful engagement with mathematical ideas. As mathematical reasoning develops through culturally mediated tools, signs, and social practices, inclusion also requires access to the resources that support abstraction, reasoning, and higher psychological functioning. The findings further suggest that exclusion often stems from systemic constraints rather than teachers’ pedagogical choices alone. Structural pressures may position teachers as unintended agents of exclusion in both rural (and urban contexts). Teachers often operate within systemic constraints that limit their capacity to enact responsive and conceptually oriented teaching. Under such conditions, teachers may inadvertently become agents of exclusion, not by intention, but through the structural pressures that shape their practice. Future research should examine these constraints in urban schools and explore how achievement, identity, and power shape inclusion in mathematics education.
Limitations. The study is limited by its temporal scope. The data snapshot captures teachers’ experiences at a specific moment. Inclusion, access, and pedagogical change are ongoing processes. A longitudinal study could reveal how teachers’ practices evolve, respond to constraints, and whether support promotes more inclusive mathematics teaching.