Fluency in mathematical language is essential for learning mathematics. Teachers must understand and use their diverse mathematical knowledge, including language and communication difficulties inherent to mathematics instruction. According to recent South African research, Grade 1 teachers are not equipped to utilise learners’ linguistic skills for efficient learning of mathematics.
This research investigates South African Grade 1 teachers’ mathematical language perceptions, experiences, and feelings. These Grade 1 teachers’ transcripts were analysed to discover their understanding of the language of mathematics.
Exploratory, descriptive, and contextual research designs were used in conjunction with an adapted interactive qualitative analysis technique. Focus group interviews, individual interviews, and lesson observations, together with a purposive sampling technique, were used to gather the data from both public and private primary schools.
The results showed that Grade 1 teachers view mathematics as a separate language with its own vocabulary and register. The findings highlighted the need to simplify the language of mathematics to enhance understanding.
This research concluded that language is essential to mathematics learning and that mathematics has its own register, which is acquired like any other additional language. To help isiXhosa learners understand mathematics in English, scaffolding strategies must be aligned with their linguistic demands.
This article provides important recommendations for teachers who need to recognise the reality that English is the lingua franca and ensure isiXhosa home languagespeaking learners receive the necessary support to acquire actual proficiency in the academic register of English for mathematical language learning.
One of the primary reasons for South African learners’ poor performance in mathematics is that the significant role of language in education is overlooked in curriculum and teachertraining courses, resulting in a lack of language awareness. As a result, inadequate teaching strategies lead to language difficulties in curriculum areas such as mathematics (Robertson & Graven
Robertson and Graven (
This article is derived from a full doctoral thesis. However, as the aim of this research was to explore, describe, and understand what Grade 1 teachers’ understandings of mathematical language are in a South African context, the researchers only report on one of the subresearch questions, namely: ‘What are Grade 1 teachers’ understandings of mathematical language in the context of South Africa?’ In answering this research question, we add to a body of knowledge from which recommendations for Grade 1 teachers and their understanding of mathematical language were developed, allowing them to provide the necessary mathematical language support to isiXhosa home languagespeaking learners receiving mathematics education in an English Grade 1 classroom.
The article begins with an introduction, followed by an explanation of the significance of the study, a literature review, and a theoretical framework. The research design and method are described, followed by the results and deliberation of the findings. The article concludes with a conclusion and recommendations.
Mulaudzi (
The mathematics register is a distinct manner of using language and communicating information (Lee
As can be seen, the complicated ‘register’ of mathematics is comparable to that of a language, and, as such, it needs similar languageacquisition skills. In line with this perspective, Robertson and Graven (
Mathematics is a discourse and a type of communication, which is more than just language (Sfard
‘A socially accepted association among ways of using language, other symbolic expressions, and artefacts of thinking, feeling, believing, valuing, and acting that can be used to identify oneself as a member of a socially meaningful group or social network, or signal [
According to this explanation, discourses involve more than the use of specialised terminology and spoken or written language. Communities, viewpoints, values, and beliefs all contribute to discourse in this regard (Ní Ríordáin et al.
The difficulty of functioning within English language registers is one of the most significant obstacles that ELLs experience while attempting to learn mathematics in an EnglishLoLT classroom (Robertson & Graven
As a new type of language that must be taught and mastered, mathematical registers provide a major challenge for ELLs (Setati
Furthermore, understanding mathematicsspecific vocabulary is required for learners to be proficient in mathematics (Moschkovich
Regarding mathematical teaching and learning, learners already have a vocabulary. Although some LoLT terms may be known to ELLs, they may have different connotations in the context of mathematics (Morgan et al.
The phenomenon of multilingualism can be observed in classrooms all around the world. However, only major regional or national languages are used in the majority of classrooms, often for pragmatic or political reasons (Gandara & Randall
Mulaudzi (
Both Vygotsky’s (
The mathematical proficiency model developed by Kilpatrick et al. (
conceptual understanding of the core knowledge of mathematics, learners, and pedagogical strategies required for teaching;
procedural fluency in carrying out basic instructional procedures;
strategic competence in planning effective instruction and solving problems that arise while teaching;
adaptive reasoning in rationalising a decision; and
a positive attitude (productive disposition) toward mathematics, teaching, learning, and improving mathematics practice.
The five strands of mathematical proficiency of Kilpatrick et al. (
A fundamental connection between Vygotsky’s (
The researchers conducted an interpretive qualitative case study using Northcutt and McCoy’s (
The researchers conducted this study in 2021 at public and independent primary schools in the Western Cape, Metro East Education District. The participating teachers ranged from newly qualified teachers to more experienced teachers teaching mathematics in EnglishLoLT Grade 1 classrooms. Although the LoLT of the classrooms is English, more than a quarter of the learners speak isiXhosa as their HL, of which 41% is the highest percentage of learners whose HL is not that of the classrooms’ LoLT. The teacherlearner ratio ranged between 1:29 and 1:37.
All Grade 1 teachers in the Western Cape constituted the study’s population. Using the technique of purposive sampling, the researchers selected four schools and 11 Grade 1 teachers (nine teachers representing three public primary schools and two teachers representing one independent primary school) as participants for this study (Creswell
The researchers acquired their data using an adapted IQA data collection method. In this sense, original IQA research often collects data using two techniques, such as unstructured, openended focus group interviews and semistructured individual interviews (Northcutt & McCoy
The data analysis process consists of three distinct steps.
Qualitative data analysis process.
The 11 participants of the unstructured, openended focus group interviews were involved in the first step of data analysis. During this interactive session, the participants of the focus group generated and recorded on index cards (inductive analysis) their perceptions, experiences, and feelings regarding the research statement (based on the subresearch question), namely: ‘Tell me what you think or feel or call to mind when I use the term “mathematical language”’. The brainstorming exercise was followed by a deductive analysis exercise in which the participants sorted and clustered the written cards into groups that represented the topics. The written ideas were accompanied by descriptive paragraphs that served as the framework for the interview.
The second step of the data analysis consisted of analysing the transcribed semistructured individual interviews using John Stuart Mill’s analytic comparison technique as an analytical tool to detect patterns among themes (Neuman
The researchers sought ethical approval from the Cape Peninsula University of Technology (CPUT) and the education authorities (Western Cape Education Department [WCED]) before beginning the investigation. The participants were given informed consent forms to sign and the researchers made it clear that their involvement was voluntary and that they could withdraw from the processes at any time. Participants remain anonymous and are simply identifiable by a number, for example Participant 1. Audio recordings and transcripts will be preserved in a secure safe for at least 5 years after the completion of this research.
The results of the two unstructured, openended focus group interviews, semistructured individual interviews, and classroom observations are described in the three sections that follow.
By employing Mill’s analytic comparison technique (Neuman
The theme ‘Mathematical language’ generated by Group 1’s openended focus group interview.
Group 1 – Openended focus group interview 


Cards consisting of a brainstorming activity of teachers’ perceptions, experiences, and feelings  Theme  Descriptive paragraph 
Simplifying mathematical terms (2×) Numbers and symbols (4×) Story sums? Concentration Numbers, patterns and relationships, patterns, Space and shape, measurement, data (2×) It is a language of its own (like music) (2×) Relatable terms first thereafter formal terms (2×) Relating concepts to learners’ own experiences Speak slowly 
Mathematical language  ‘Maths is a language of its own. It includes symbols, signs, numbers, patterns, space and shape, measurement, data handling etcetera. When introducing a new mathematical concept, speak slowly, clearly and use repetition as well as visual aids. Simplify words and relate it to their everyday lives so they can make meaning of it’. 
The theme ‘The language’ generated by Group 2’s openended focus group interview.
Group 2 – Openended focus group interview 


Cards consisting of a brainstorming activity of teachers’ perceptions, experiences, and feelings  Theme  Descriptive paragraph 
‘Buddy’ system We sing Xhosa counting songs to help them feel included + relevant LoLT is English: Learners • understand English although they can speak isiXhosa Comprehension of what is being asked and understanding concepts (3×) Simple understandable language Words that mainly relate to understanding of how to do maths (2×) Using body language or signs alongside a new term Overwhelmed with what is expected (2×) Difficult to comprehend for learners (who are more concrete or visual) Mathematical terminology (3×) Numbers Learning how to write or say and/or read number names Introduce vocabulary alongside a concrete example Using a problemsolving approach 
The language  ‘The language is all about understanding which may incorporate words, signs or symbols and rhythm. Start with (and revise) prior knowledge. Make use of body or sign language while introducing a concept with an everyday problem or experience. Introduce a symbol alongside a term. There must be a relationship between a visual concept and the verbal instruction. Pair up a nonEnglish speaker with an English speaker.’ 
The semistructured individual interviews were analysed to look for patterns. The researchers analysed the individual interview transcripts from the six participants individually to determine the following:
if the participant agreed with the interview framework’s theme (method of agreement),
if the participant disagreed with the interview framework’s theme (method of difference), and
if the participant elaborated on or modified the interview framework’s theme (method of difference).
As previously mentioned, the category ‘Mathematical language’ was developed by grouping the themes ‘Mathematical language’ and ‘The language’ derived from the two focus group interviews (see
‘It is a language of its own’ (Participant 1, Educator, 30 years).
‘It’s a language of its own; I mean, we’re teaching the children maths and then they see it as numbers’ (Participant 5, Educator, 28 years).
‘But as far as mathematical language is concerned, we basically have to start right at the beginning. So, no matter what language they’re speaking or just say predominant language, even the English children are learning it [
‘So, language is … when we teach maths in the Grade 1 classroom and not only for those learners that don’t speak English as their first language, but children don’t speak maths. Maths language is something you teach them whether they are English speakers or not first language English speakers, and that is how you build any maths concept for a child, and from there you build onto those concepts.’ (Participant 11, Educator, 30 years)
Le Cordeur and Tshuma (
Two of the participants agreed that mathematics has its own terminology, which is in line with the participants’ statements above. However, they stressed that mathematical terminology is difficult:
‘When I think of the language with regard to mathematical, or mathematics, the mathematical language, … then the first that … come to mind… is the mathematical terminology, … and the specific terminology we use when teaching a new concept … division of maths … part of mathematics [
‘I also think that it’s [mathematical language] about simplifying the terms because sometimes they get so overwhelmed. … You got to plus this and minus this, or if you even bring up the word divide, they’re like looking at you like, “what does that mean?”’ (Participant 3, Educator, 24 years)
According to Jourdain and Sharma (
In addition to the quotes provided by the participants thus far, they also acknowledged the significance of language to the understanding of mathematics. Mulaudzi (
‘… [
‘The learners do not necessarily understand the language itself [
‘The language [LoLT] and the concept goes hand in hand. If they don’t get the language, they’re not going to get the [
This demonstrates that language (both the LoLT and the language of mathematics) plays a role in fostering mathematical comprehension (Barwell et al.
In addition, a participant’s response validated Le Cordeur and Tshuma’s (
‘If I teach say Afrikaans, I would always put a visual with a word and we do a lot of repetition, so for mathematical language we would do the same. We would introduce a concept, we would give the concept a name, and then we would work around that concept and all the children are learning the same mathematical language.’ (Participant 9, Educator, 62 years)
Participant 9’s perspective above is consistent with Robertson and Graven’s (
In conclusion, the method of agreement reveals that all individual interviewees agreed that mathematics has its own language with its own vocabulary (i.e. mathematical terminology). In addition, they have agreed that language plays an essential role and must be simplified for mathematical understanding. The method of difference, on the other hand, showed that only one person thought that mathematical language could be learned in the same way as another language.
As one of the aims of this research study was to explore, describe, and understand what Grade 1 teachers’ understandings of mathematical language are in a South African context, the researchers could not obtain a full picture of the category ‘Mathematical language’ by just observing Grade 1 teachers teaching mathematics. Nevertheless, to a certain extent, the method of agreement revealed that the participants used visual representations for mathematical concepts, which form part of the language of mathematics. In this regard, all the teacher participants displayed mathematical information on a wall with all the mathematical terms together with pictures so that learners who speak isiXhosa could understand the mathematics vocabulary.
Moreover, the researchers found that Participants 1, 7, and 9 made the mathematics terms easier to understand by exposing learners to different words that meant the same thing. Participants 5 and 11 made the language easier when they introduced word sums, for example, by using simple, everyday English that was relevant to learners’ everyday lives. Participant 3 made the language easier to understand by giving learners the chance to revise terminology as a group before they did an individual activity about the same thing. The observations of these activities are displayed in
Activities observed during mathematics lessons related to the category ‘Mathematical language’.
Participant  Activities observed during participants’ mathematics lessons 

Participant 1  When the teacher introduced the activity of ‘bonds’ to the learners, she talked about tens and units, but also mentioned to the learners that units are also referred to as ones. 
Participant 7  Before the teacher embarked on an addition activity, she first asked the learners what addition is. The learners answered that ‘you plus’. The teacher acknowledged their answer and told the learners that addition also means you add or make something more. 
Participant 9  The teacher read the word sum to the learners: ‘If I have 8 sweets and eat 2 of them, and I eat another 3, how much do I have left?’ Before the learners were left to solve the problem, she first asked them what kind of sum it is. Then she asked them why they said it is a minus sum. She asked the learners to think about the sum and picture it in their heads. ‘If I eat 2 sweets, what happens? It gets less. If I eat three more sweets, it gets less.’ 
Participant 5  When the teacher taught story sums, she used learners’ names in the classroom and related the story to their everyday experiences – as the teacher said, for example, when she taught a sharing story sum, she would use real objects (e.g. real lollipops) to share among the learners, as everyone likes sweets. 
Participant 11  Instead of just asking learners which number is greater than 5, the teacher simplified the language and related it to their everyday life by asking: ‘If she has five sweets and they have three sweets, who has more?’ 
Participant 3  The teacher asked learners a few before and after questions (e.g. ‘What comes before 12?’; ‘What comes after 12?’) As soon as the teacher saw that everyone was on par with the terms before and after, she gave them an individual activity to complete in this regard. 
Participant 9 asserted that mathematics can be taught and learned in the same way as any other language can be. In this instance, the method of difference revealed that all the participants were using various language strategies (e.g. semiotic systems), which are also used in second or third language acquisition. For example, all the teachers employed visual representations to help learners learn the language and concepts of mathematics.
Through analysing the transcripts of the classroom observations for the category ‘Mathematical language’ and comparing them to the transcripts of the individual interviews, the method of agreement showed that all six participants agreed that mathematics is made up of different terminology. They also agreed that language is a key part of understanding mathematics, which is why the participants tried to make mathematical terms easier to understand. During the analysis of the individual interview transcripts, the method of difference showed that only Participant 9 mentioned that strategies for teaching mathematics in a second language could be used. In line with what Participant 9 said above, it was noticed that all the other interview participants used secondlanguage didactic strategies in their mathematics lessons without even realising it.
According to the data in
Subresearch question, research objective and deliberation on the findings.
Subresearch question  Research objective  Category: Mathematical language 


Theme  Findings  
‘What are Grade 1 teachers’ understandings of mathematical language in the context of South Africa?’  The researchers used a qualitative data collection method to establish what (explore) Grade 1 teachers’ understandings of mathematical language are in a South African context.  The language (of mathematics).  
According to Vygotsky (
As was previously stated, this research was conducted using the theoretical framework of Vygotsky’s (
Conclusion of the findings based on Vygotsky’s theory of learning and Kilpatrick et al.’s strands of ‘conceptual understanding’ of the mathematical proficiency model.
Development strand for mathematical proficiency  Recommendations for teachers 

Teachers must know that mathematics has its own register (mathematical terminology) and is learnt like any other second or third language (Le Cordeur & Tshuma IsiXhosaHL speaking learners first need to understand the English LoLT before they can make sense of mathematics itself (Mulaudzi 

Teachers need to acknowledge that mathematical terminology can be challenging for learners from other cultural or linguistic backgrounds (Ní Ríordáin et al. Teachers need to understand the significant role that language plays in learning mathematics, and, therefore, it is recommended that the language of mathematics needs to be simplified (scaffolded) for isiXhosa learners to support their mathematical understanding (Vygotsky Scaffolding strategies during mathematics discourse must be tailored to the isiXhosa learners’ individual language needs to promote mathematical proficiency in the English LoLT (CGCS Strong language and metalinguistic skills are necessary to communicate mathematically (Robertson & Graven 
LoLT, Language of learning and teaching.
The primary objective of this article was to report on Grade 1 teachers’ understandings of mathematical language in the South African context. This study found that teachers must recognise that mathematics has its own register and is learnt like any other second or third language (Le Cordeur & Tshuma
Due to the global COVID19 pandemic, many educational institutions were unwilling to take part in the research as the teachers already had ‘too much on their plates’. This study was limited to a small group of Grade 1 teachers in the Western Cape of South Africa and focused solely on Grade 1 teachers teaching mathematics to isiXhosa HLspeaking learners in EnglishLoLT classrooms. Therefore, this research study does not provide generalisable findings to the wider Grade 1 teacher population. Furthermore, one of the original data collection methods of the IQA systems method, which is facetoface individual interviews, was replaced with online interviews as the researchers had to limit any unnecessary facetoface interaction due to the COVID19 pandemic’s restrictions on social distancing at the time.
The researchers suggest that education programmes for preservice and inservice teachers be developed and implemented in accordance with the findings of this study and monitor the outcomes thereof so as to inform current mathematics practice. We also suggest that additional research be conducted to determine how the recommendations made in this study can support other teachers (the wider Grade 1 population). Furthermore, we suggest additional investigations into issues such as the terminology used in mathematics for African languages as well as the availability and accessibility of bilingual teaching materials that could assist learners with limited mathematical proficiency in the LoLT.
Prof. Janet Condy is acknowledged for proofreading the article and Prof. Candice Livingston for the language editing of this article.
The authors declare that they have no financial or personal relationships that may have inappropriately influenced them in writing this article.
C.L. served as the main supervisor and E.B. as cosupervisor for T.C.’s doctoral study. C.L. and E.B. gave input as coauthors of this article, while T.C. wrote the majority of the article.
The authors affirm that the supporting data for this study’s conclusions are included in this article.
The opinions and viewpoints presented in this article belong to the authors and do not accurately represent the official policy or stance of any agency with which the authors are affiliated.