Prinsloo and Zondi (2020) found that concepts expressed in one language do not always have direct equivalents in another. This means that translating mathematical ideas across languages can result in subtle shifts in meaning, highlighting the need for careful linguistic versioning rather than relying solely on direct translation. In some cases, a specific concept is known in the target language, but the target language has no word for it, or the concept itself may be unknown in the target language, which implies that the language will also not have a word for such a concept. Table 1 illustrates the isiZulu equivalents of the mathematical terms share, part, whole, equivalence and inverse operations.

While the provision of African language equivalents for mathematics terms is a positive step towards MTBBE, it is noteworthy that the list of terms does not include complex Mathematics terminology. The effective use of these equivalents in isiZulu-medium mathematics classrooms for meaning-making is crucial. While Table 1 illustrates that equivalents of the basic terms exist, the equivalents for terms such as ‘share’ that can be used in both fractional and division concepts need to be considered in the development of more precise African language mathematics dictionaries. Furthermore, equivalents for isiZulu mathematical terms that refer to even more precise concepts such as sharing by distributing one by one need to be developed.

Versioning has emerged as a critical concept within recent discussions of MTBBE, particularly as policymakers and scholars recognise that African languages must be developed in ways that support the teaching of specialised academic domains. Mother Tongue-based Bilingual Education does not simply advocate teaching in African languages but calls for the deliberate creation of discipline-appropriate linguistic forms that preserve the conceptual integrity of school knowledge (August-Mowers 2025). In mathematics, where technical precision is essential for conceptual development, this distinction becomes especially important. Versioning refers to the intentional design of mathematical expressions in African languages that convey the specific meanings required by the discipline. It recognises that mathematical ideas are not always directly transferable from one language to another without conceptual loss. In contrast, translation often relies on familiar everyday meanings that may not align with the underlying structure of mathematical concepts. This tension between translation and versioning is central to understanding how learners access mathematical meaning in isiZulu-medium classrooms.

Translation assumes that languages map neatly onto one another and that equivalent words can be substituted without shifting conceptual meaning. This assumption is problematic in multilingual mathematics classrooms, where every day linguistic expressions frequently carry interpretations that differ from their intended academic meanings. Studies in African languages have shown that terms used for comparison, quantity or division as a mathematical concept hold multiple everyday meanings that are not mathematically precise (Essien 2018; Mostert & Roberts 2022). In the case of fractions, classroom discourse often draws on terms associated with sharing or distributing objects, because these expressions are culturally familiar and accessible for young learners. However, these linguistic choices may lead learners to conceptualise fractions through the logic of fair division rather than through the mathematical idea of partitioning a whole into equal parts. Without intentional versioning, teachers may inadvertently reinforce interpretations that diverge from curriculum aims, resulting in conceptual distortions. This demonstrates why translation alone cannot support epistemic access in mathematics.

Versioning acknowledges that mathematical concepts may require re-expression in ways that restructure linguistic forms to preserve disciplinary meaning. Rather than importing everyday meanings from the home language, versioning involves shaping new or revised linguistic forms that reflect the conceptual relationships needed for mathematical reasoning. This approach aligns with theories of language as a resource, which argue that linguistic practices must be intentionally designed to enable deep learning rather than simply reflecting conversational norms (Essien et al. 2023). In MTBBE, versioning therefore becomes a process of building the academic literacy of African languages so that learners can encounter mathematical concepts on their own linguistic terms. This development is essential because African languages were historically excluded from formal domains of scientific and mathematical discourse, creating gaps in their academic lexicons (Leeuw 2025). By engaging in versioning, educators contribute to the long-term project of linguistic development and epistemic justice. The concept thus operates not only as a pedagogical strategy, but also as a transformative practice within multilingual education.

In the absence of versioning, critical mathematical ideas become flattened or reinterpreted through everyday schemas that do not support conceptual progression. For example, when learners only learn fractions through sharing activities, they may later struggle to understand fraction symbols, how the top and bottom numbers work together and what the whole or unit represents. Research on early mathematics learning indicates that such misconceptions can persist over time, influencing performance in upper primary grades and beyond (Fritz et al. 2021). These misunderstandings are not simply the product of ineffective teaching but arise from the linguistic framing through which mathematical ideas are introduced. Mother Tongue-based Bilingual Education advocates argue that effective bilingual education requires intentional linguistic design so that learners can develop both conceptual understanding and the academic language needed to express it (August-Mowers 2025). Without this intentionality, the benefits of teaching in the home language are compromised because everyday language is not adapted to meet the cognitive demands of mathematics. This reinforces the argument that versioning is central to achieving the goals of MTBBE.

This article employed a qualitative design that combined the principles of LS with multimodal discourse analysis to investigate how language mediates the teaching and learning of fractions in early-grade isiZulu mathematics classrooms. Lesson Study is a collaborative professional development model in which teachers jointly plan a research lesson, teach it in a live classroom and observe how learners respond to the instructional approach (Perry & Lewis 2009; Xu & Pedder 2014). Lesson Study is particularly well suited to studies of mathematical meaning-making because it foregrounds the iterative refinement of teaching, the close observation of pedagogical decisions and the collective interrogation of learners’ sense-making processes. Subject advisers were intentionally selected because of their curriculum leadership role within the South African education system, where they support curriculum implementation, teacher development and instructional leadership across large clusters of schools (Department of Arts and Culture [DAC] 2013; Mbanjwa 2014; Sithole & Tachie 2024). In many districts, a single subject adviser is responsible for supporting between 50 and 150 schools, each with multiple Foundation Phase mathematics teachers. Using subject advisers within the LS process therefore allowed the article to examine instructional discourse that has the potential to influence teaching practices across a broader network of classrooms beyond a single school context. During the research lessons, the subject advisers assumed the role of classroom teachers and taught the lessons directly to Grade 3 learners. Although the lessons were presented by subject advisers rather than classroom teachers, the instructional interactions occurred within real Grade 3 classroom settings with learners engaging in authentic mathematical discussion and problem-solving activities. The article therefore does not position the lessons as representative of all everyday classroom practice, but rather as analytically valuable examples of how mathematically focused instructional discourse is constructed within isiZulu-medium fraction teaching. The LS structure further supported this by creating carefully planned lessons designed to surface learners’ mathematical reasoning and classroom interaction.

The article does not claim to provide direct evidence of learners’ internal cognitive processes. Rather, the focus of analysis is on how mathematical meaning was constructed through instructional discourse during classroom interaction. The primary unit of analysis was therefore the isiZulu linguistic patterns, explanations, comparisons and mathematical terms used within subject adviser (serving as a teacher)–learner and learner–learner interactions during the fraction lessons. To analyse these interactions, the study adopted a qualitative multimodal discourse analytic approach, drawing on social semiotic understandings of classroom communication. Multimodality recognises that mathematical meaning is conveyed not only through spoken language, but also through gestures, representation, material artefacts and other resources that interact simultaneously (Kress 2009; Royce 2002). According to Royce (2002), verbal and visual modes work intersemiotically to project meaning, each providing complementary dimensions of mathematical understanding. Sommer and Bembnista (2024) argue that qualitative research must extend beyond text to consider the multimodal combinations, speech, gesture, diagrams and inscriptions that co-produce meaning in instructional contexts. Given that fraction instruction frequently involves pointing, partitioning, modelling and using manipulatives, multimodal analysis enabled a fine-grained examination of how meaning was constructed across multiple semiotic channels. The intended contribution of the article is therefore primarily directed towards mathematics education researchers, teacher educators, subject advisers and policymakers working within MTBBE contexts, particularly those concerned with the development of mathematically precise African-language instructional discourse in the early grades.

This article is based on a study conducted in two Grade 3 mathematics classrooms located in two public primary schools situated in township communities within the City of Tshwane Metropolitan Municipality in the Gauteng province of South Africa. Both schools are classified as quintile three schools, reflecting their placement within lower-resourced public schooling contexts. In both schools, isiZulu is the Language of Learning, Teaching and Assessment (LoLTA) in the Foundation Phase. The classrooms reflect typical South African multiple-monolingual environments (Sapire & Essien 2021), in which isiZulu is widely used for both everyday communication and formal instruction, despite the presence of learners who speak different African home languages within the same classroom. This linguistic configuration is common in township schools, where one dominant African language is used institutionally, while multilingual repertoires are drawn on informally by learners and teachers. The learner participants consisted of Grade 3 learners, aged between 8 years and 9 years old, drawn from two intact classes. Each class comprised approximately 30–40 learners, reflecting typical Foundation Phase class sizes within the participating schools. Learners participated as intact class groups, enabling the observation of mathematical engagement and learning processes within authentic classroom contexts, rather than through isolated or experimental groupings.

The study population comprised two Foundation Phase mathematics subject advisers (serving as teachers) and two Grade 3 mathematics classes. Both subject advisers were female, isiZulu home-language speakers, with more than 5 years of experience in their roles as Foundation Phase mathematics subject advisers and more than 10 years of teaching the Foundation Phase. Their professional responsibilities included curriculum support, teacher development and monitoring of mathematics teaching and learning in primary schools, positioning them as key informants in relation to curriculum implementation and pedagogical practices. Thus, mathematics teacher language practices in this article refer to the mathematics subject adviser language practices as they designed and taught the research lesson on comparing fractions through real-life sharing scenarios, in lieu of teachers. The mathematics subject advisers also selected and prepared the teaching resources used to present it, including visual models and manipulatives. It is important to remind the reader that the subject adviser served as a teacher in this article.

The sampling strategy was purposive and guided by four inclusion criteria. Firstly, the lessons had to be taught in an African language, specifically isiZulu, to align with the study’s focus on linguistic mediation. Secondly, participating classrooms had to represent typical South African multilingual contexts. Thirdly, the grade level needed to match the developmental point at which formal introduction of fractions occurs. Fourthly, isiZulu was selected because it is the most widely spoken home language in South Africa; recent census reports show that isiZulu speakers increased from 22.8% in 1996 to 24.4% in 2022, reaffirming its national dominance (Statistics South Africa 2025).

The lessons analysed in this article formed part of a broader international research collaboration focused on strengthening Grade 3 learners’ understanding of fractions through LS. The international research team collaborated directly with the South African research team throughout the planning, implementation, observation and data collection processes. Both the South African and international researchers participated in the classroom observations and collection of lesson data. Ethical clearance was obtained through the relevant institutional processes by both research teams, and all members of the South African and international teams were formally included within the ethics applications and approval procedures. The original international problem posed to learners was: Whenever I have friends round for a tea party, I insist they share the brownies equally. On Monday I had a tea party. I invited a group of friends and bought some brownies for them which they shared equally. On Tuesday I have another tea party and I invite more friends than I had on Monday but have the same amount of brownies as I did on Monday. How does the amount of brownies each friend gets on Tuesday compare to Monday? On Wednesday I have another tea party. I invite the same number of friends as I did on Monday but buy more brownies than I did on Monday. How does the amount of brownies each friend gets on Wednesday compare to Monday?

Since this scenario was unfamiliar to many South African learners, the mathematics subject advisers adapted the task to create a more culturally meaningful version. The contextualised problem presented during teaching was: Zanele loves to share slices of bread with her friends. On Friday she bought a loaf of bread and shared the slices equally with some friends. On Saturday she bought the same size loaf as on Friday but shared them equally with more friends than she did on Friday. How does the number of slices of bread each friend gets on Saturday compare to Friday? On Sunday she invites the same number of friends as on Friday but buys more slices of bread to share equally with this group than she did on Friday. How does the number of slices of bread each friend gets on Sunday compare to Friday?

This adapted version maintains the mathematical structure of the original task while embedding it in a familiar food item and cultural practice, which research shows can enhance learners’ mathematics meaning-making for African language-speaking learners (Essien 2018).

Data were collected during the LS research lessons and consisted of full video recordings of the subject advisers teaching the contextualised fraction lesson. The subject advisers’ involvement in task adaptation, lesson design and presentation in this article is directly linked to their everyday practice of guiding teachers in curriculum implementation, including lesson design and presentation. Video was used because it enables repeated viewing and careful analysis of gesture, gaze, manipulation of objects and other semiotic features that influence mathematical reasoning (Sommer & Bembnista 2024). Capturing these multimodal features made it possible to examine how verbal and visual modes interacted to convey mathematical meaning. Each recording was transcribed verbatim in isiZulu and English, with annotations describing gestures and actions such as pointing to the board, demonstrating equal sharing or moving manipulatives. The dual language transcripts also strengthened reliability by allowing the research team to validate meaning across isiZulu and English. For the purposes of analysis, the primary data source was the annotated transcripts, although the videos were consulted to verify multimodal details and ensure interpretive accuracy.

The analysis followed a combination of thematic analysis and multimodal discourse analysis. Thematic analysis involved iterative coding to identify recurring linguistic and pedagogical patterns in the lessons. Multimodal discourse analysis examined how spoken language, gesture, material resources and visual representations worked together to shape learners’ interpretations (Kress 2009; Royce 2002).

The coding process was conducted as follows: Both transcripts were translated from isiZulu to English. After producing the transcripts, the researchers developed a coding rubric. Throughout both transcripts, the researchers examined words and ideas related to sharing and fractions. Two spreadsheets were then designed, with the main categories being concept, line number and quotation from the transcript. Subsequently, sharing and fractions were assigned specific categories as the analysis of the transcripts progressed. Each time a quotation matched a category, a mark was assigned. In a few instances, a quotation encompassed more than one idea, and each relevant category was assigned a mark. The purpose of allocating these marks was to subsequently determine the predominant ideas within each transcript under each sharing and fractions category.

The analysis of sharing discourse includes categories such as the aim of the lesson (context for sharing fractions), translation-based sharing language, knowledge of sharing, sharing equally, sharing as equivalence, questions about sharing, sharing as an action, sharing as a statement and comparing when sharing, each reflecting different pedagogical and linguistic perspectives on fractional intent. The discourse on fractions incorporates categories such as the introduction to fractions as comparison, fractions related to the idea of a whole, fractions related to half, fractions related to wholes and halves, fewer people equals more parts, more people equals less parts, fewer idea not linked to fractions, a lot and more, few and less, relationship between a lot and few and more and less, relationships between quantities, quarters and translation-based fraction language, each reflecting varied conceptual and linguistic approaches to fractional intent. Reliability was enhanced by using dual language transcripts to cross-check interpretation. This alignment across isiZulu and English helped ensure that linguistic nuance was preserved and that analytical claims were grounded in accurate representation of teacher and learner talk.

Ethical clearance to conduct this study was obtained from the University of the Witwatersrand Human Research Ethics Committee (Non-Medical) (Protocol no. H24/11/31). The lessons formed part of a broader international research collaboration, and both the South African and international research teams were formally included in the ethical clearance and approval processes. Permission to conduct the study was also granted by the Gauteng Department of Basic Education and by the principals and teachers of the participating schools. Parental consent and learner assent were secured prior to data collection. Both the South African and international research teams participated in the classroom observations and data collection processes. To minimise risk to learners, the video camera was positioned to focus primarily on the subject advisers rather than the learners. Data sharing between the collaborating research teams occurred only within the scope of the approved ethical agreements, with all shared data anonymised and used solely for research purposes related to the project. All data were stored securely in accordance with institutional ethical guidelines.

Table 3 shows that sharing equally was central to both lessons, confirming that both lessons used sharing contexts to introduce fraction concepts rather than focusing only on procedural division (DBE 2011; Hallett et al. 2010). However, the table also reveals important differences in how teachers linguistically structured sharing within classroom discourse. For L2, sharing equally was closely connected to questioning patterns, comparative language and action-oriented explanations, suggesting that the teacher repeatedly used discourse to foreground changing relationships within sharing situations.

This pattern is evident in teacher prompts such as: ‘When there are more people sharing, do they get more or less bread?’ (L2). While the action of sharing remained visible, the questioning structure and comparative language positioned sharing as a relationship between quantities rather than simply an act of fairness. In contrast, L1 also foregrounded equal sharing, but the discourse more frequently framed sharing as a condition of sameness to be achieved. For example, the teacher focused on ensuring that ‘everyone gets the same’ (L1), which emphasised fairness and equivalence within the sharing process. In contrast, L1 also foregrounded equal sharing, but the discourse more frequently framed sharing as a condition of sameness to be achieved. For example, the teacher focused on ensuring that ‘everyone gets the same’ (L1), emphasising fairness and equivalence in the sharing process. The comparison between the two lessons therefore demonstrates that teachers constructed sharing differently through discourse patterns related to questioning, comparison, fairness and action-oriented explanations (Essien et al. 2023; Moschkovich 2015).

One of the clearest distinctions between the two lessons emerges in Table 4, which shows differences in how teachers used comparative magnitude language such as few, more and less within fraction discussions (Fritz et al. 2021; Gabriel et al. 2013). In L2, the teacher repeatedly linked these comparative terms through questioning structures and relational explanations, foregrounding the relationship between the number of people and the size of shares during sharing activities. The discourse consistently connected changing quantities to changing outcomes within the sharing context.

This pattern is evident in teacher prompts such as ‘Are there few people or many people?’ followed by ‘So do they get more or less bread?’ (L2). Through these paired comparisons, the teacher explicitly verbalised relationships between quantities and sharing outcomes. In contrast, while L1 also contained references to more or less, the discourse tended to be more descriptive and less relationally linked. For example, statements such as ‘They have more’ (L1) described outcomes without consistently connecting them to the number of people sharing. The comparison between the two lessons therefore illustrates how teachers used comparative language differently to structure fraction concepts during sharing discussions (Barwell 2018; Mostert & Roberts 2022).

The importance of inverse relationships in fraction discussions is evident in Table 4, which shows differences in how teachers linguistically constructed the relationship between the number of people sharing and the size of the shares. While both lessons referred to the idea that more people receive smaller shares, L2 more consistently embedded this idea within comparative and relational discourse patterns. The teacher repeatedly connected quantity relationships through explicit comparative language, questioning structures and relational explanations during sharing activities, reflecting research that highlights the importance of relational reasoning in fraction learning (Gabriel et al. 2013).

This pattern is illustrated in the statement, ‘Because there are few people, each one gets more’ (L2), where the inverse relationship between the number of people and the size of the share is directly verbalised. Throughout the lesson, the teacher repeatedly linked few, more and less within explanations of sharing situations. Such discourse aligns with Barwell’s (2018) view that mathematical meaning is shaped through relationships between language and classroom discourse practices. In contrast, L1 tended to imply inverse relationships indirectly, as in ‘Now they are many, so it is different’ (L1). Although mathematically relevant, the discourse relied more on implied comparison than explicit relational language. This distinction reflects Mostert and Roberts’ (2022) argument that comparative terms in multilingual mathematics classrooms may remain descriptively everyday unless intentionally structured mathematically. The comparison between the lessons therefore demonstrates how teachers used different discourse patterns to linguistically construct inverse relationships during fraction instruction.

Table 4 shows that both lessons constructed fractions through whole-part relationships within sharing contexts, confirming a shared instructional focus on fractions as parts of a whole. In L1, the teacher explicitly referred to the whole and repeatedly linked wholes and halves during explanations of sharing situations. The discourse foregrounded equal parts, fairness and the relationship between the whole and divided shares, reflecting CAPS expectations that learners develop an understanding of fractions through equal partitioning and identifiable wholes (DBE 2011).

In contrast, L2 integrated references to the whole within broader comparative and relational discourse patterns. Even when the whole was not directly named, it remained implicit within explanations of changing sharing relationships, as seen in the statement, ‘The bread is the same, but there are more people’ (L2). Here, the teacher linguistically maintained the whole as constant while foregrounding changes in the number of sharers and the size of shares. This type of relational explanation aligns with research by Hallett et al. (2010), which argues that learners’ fraction understanding develops when they engage with relationships between quantities rather than isolated fraction labels. L2 also occasionally introduced additional fraction terminology such as quarters within comparative sharing discussions. Furthermore, Moschkovich (2015) argues that mathematical meaning emerges through discourse practices that connect language, context and mathematical relationships. The comparison between the lessons therefore demonstrates how teachers differently used whole-part language and comparative discourse to construct fraction concepts during sharing-based mathematics lessons.

Language as a resource theory emphasises that learners’ full linguistic repertoires such as their home languages, everyday language and translation practices, all contribute to learners’ meaning-making. By activating learners’ prior knowledge at the beginning of the lesson, the teachers provide opportunities for learners to recall cultural sharing practices such as family meals. This validated the learners’ prior knowledge while connecting the sharing practice to classroom concepts.

The study findings indicate that observed teachers positioned sharing as central to the mathematical discussions conducted in class. This position is aligned to the language as a resource theory, which frames sharing not only as a mathematical or social concept, but also as a linguistic one. In both lessons, equal sharing was highlighted as an important mathematical idea. Through expressions such as ‘shera ulanganise wonke umuntu’ [share equally among all] (L1), learners were able to express the concept of sharing in their isiZulu language, reinforcing inclusivity and deeper comprehension of the concept. The language as a resource theory supports using comparative expressions across languages to show that different ways of saying the same concept, such as ‘shera’ (isiZulu versioning of ‘share’), reinforce the mathematical idea. Furthermore, the expression provided learners with an opportunity to describe ‘everyone gets the same’ in isiZulu before associating this to the mathematical concept of division.

Translations and everyday language use as observed in the lessons highlight the use of learners’ home languages to explain the concept of sharing in daily life. The translation ‘… ma bebaningi bathola isinkwa esincane’ [when many learners share a loaf of bread, each learner gets fewer slices] (L1) bridges abstract mathematics vocabulary with familiar, lived experiences. Such bridging is aligned to the language as a resource theory. Both lessons used comparative language such as ‘kuningi’ [more], ‘kuncane’ [less] or ‘kuyalingana’ [equal] as illustrated in Figure 2, a group activity conducted in the observed lessons. Figure 2 presents a sample task on sharing 12 pieces of paper among 6, 3, 2 or 12 friends.

The use of comparative language complies with language as a resource’s construct of strengthening both linguistic awareness and mathematical reasoning.

Taken together, Table 3 and Table 4 demonstrate how teachers’ discourse and linguistic patterns constructed fraction concepts differently during sharing-based mathematics lessons in isiZulu-medium Grade 3 classrooms. The analysis shows that the construction of mathematical meaning was shaped not only by the sharing task itself, but by how teachers used language to foreground relationships between quantities, people and parts of a whole. In L2, comparative terms such as few, more and less were repeatedly connected through questioning structures and relational explanations, illustrating how everyday language can function as a mathematical resource when explicitly linked to fraction relationships. This supports MTBBE research advocating for versioning rather than direct translation, where everyday language is intentionally shaped to communicate mathematical meaning (August-Mowers 2025; Setati 2005). Such findings also align with Barwell’s (2018) argument that mathematical meaning emerges through relationships between language, discourse and classroom interaction.

In contrast, L1 more frequently relied on fairness discourse, equivalence language and descriptive explanations of sharing. While these linguistic patterns supported equal sharing, the relational connections between quantities were often less explicitly verbalised. This distinction reflects Mostert and Roberts’ (2022) argument that comparative terms in multilingual mathematics classrooms may remain at the level of everyday description unless intentionally structured mathematically. Furthermore, Moschkovich (2015) emphasises that multilingual mathematical discourse becomes meaningful when teachers intentionally connect everyday language with mathematical relationships and representations.

The discussion has shown that teachers used different discourse patterns to construct fraction concepts during sharing discussions. L1 mainly foregrounded fairness, wholes, halves and equal parts, while L2 more strongly relied on comparative language, inverse relationships and questioning patterns to explain how changes in the number of people affected the size of shares. These findings align with Gabriel et al. (2013), who argue that learners’ fraction understanding depends on coordinating relationships between quantities, as well as Hallett et al. (2010), who emphasise the importance of relational reasoning in early fraction instruction. The findings also support Planas and Setati-Phakeng’s (2014) view of language as a resource in multilingual mathematics classrooms, where discourse practices shape access to mathematical meaning. Overall, the article highlights the central role of comparative and relational language in the linguistic construction of fraction concepts within multilingual mathematics classrooms.