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In South Africa, the debate on the Language of Teaching and Learning of mathematics in Grade R has been underway. Amid the robust debate on the teaching of mathematics in home language, the students have no voice. This paper explored the language that Grade R students use to navigate mathematics space to achieve the policy’s envisaged outcomes. The theoretical premise for the study is based on Vygotsky’s theory of social constructivism. The qualitative approach guided by the case study design of Grade R 8 students were employed in the study. It is anticipated that this paper provides valuable insights into the understanding of the Grade R students’ acquisition of mathematical language and contributes to the increased awareness in the field of Grade R mathematics teaching to achieve active learning. The findings revealed that (i) students failed to establish that the number of objects does change with the changed arrangement of the same number of objects and (ii) students were able to understand questions asked in their home language, yet their responses were in English.
*Address all correspondence to: schiphambo@wsu.ac.za
1. Introduction
In South Africa, schooling system ranges from Grade R to 12. Grade R is the reception year. This is part of the Department of Basic Education’s National Curriculum. It is aimed to give children a firm foundation in preparation for grade one (it is preprimary phase). Grade R is not mandatory; however, the child who skips it is more disadvantaged than the one who goes through it.
Language plays a major role in the teaching and active learning of mathematics to any grade. Many students find it difficult to excel due to the language of instruction, which acts as a barrier to their learning. Several studies [1, 2] acknowledge that English proficiency heralds mathematics proficiency, particularly when English is the medium of instruction. As English second language (ESL) students struggle to understand mathematics concepts that are being taught the English first language (EFL) speakers feel more comfortable because they understand the medium of instruction. Research confirms that ESL performs low in mathematics compared to their counterparts EFL speakers [3]. Numerous research studies in language acquisition and mathematical learning have developed along mostly discrete trajectories, for example, studies examining the links between linguistic and mathematical literacy [4], the functions of language in the math classroom [5] established the framework defining the four stages of mathematical learning: Receiving, Replicating, Negotiating meaning and Producing. However, few studies have investigated the language that Grade R students use to navigate the mathematics space to achieve the envisaged outcomes of the policy. The two questions that still need to be answered in this study are the following:
Which language do Grade R students use to achieve the envisaged outcomes in the policy?
How do Grade R students navigate the language space in the lesson?
Research shows that home language is important and it is acquired during early childhood, commonly before the age of three [6], it is at this stage that the child’s development and acquisition of mathematical concepts is critical. Learning a language is not just a simple thing that happens effortlessly. Research argues that learning the first language is one of the unexplainable daily mysteries surrounding us [7]. Many people think that children put no effort to learn the language, but the truth is that there are several stages that a child must go through to learn a language. If learning mother tongue language is that difficult what more adding a foreign language to the child’s mind? Across multiple contexts, research on the language of instruction reveals that where native language is used for mathematics learning, teaching and assessment, native speakers of the language of instruction achieve higher scores than the non-native language speakers [8, 9, 10].
In [11] behaviourist theory argues that the acquisition of language can be observed. Skinner believed that children are born with a blank slate of mind or tabula rasa. Children acquire the first language by responding to stimuli given to them and they respond through conditioned reinforcement. The innatist theorists including [12] believed that children have a blueprint for language acquisition called Language Acquisition Device (LAD). The LAD is responsible for swift mastery of the language, and this makes it possible even if a child is exposed to the abstract language. The innatist theorists refute Skinner’s theory [13] theory also supports the innatist theorists’ claims indirectly though, by arguing that the conversations that children engaged in constitute the origins of both language and thought, where thought is fundamentally internalised speech and speech develops in social interaction.
Even though many people advocate for the use of Home Language (HL) as the only medium of instruction, research heightens the importance of learning a second language as well. It is argued that bilinguals have more advantage in performance than monolinguals [14, 15, 16]. Second language acquisition increased working memory, and this enables second language learners to achieve higher in mathematics because maths achievements are influenced by the enhanced working memory [17, 18]. The acquisition of the second language is associated with the increase in the density of the grey matter in the brain, which enhances performance [19]. Piroozan et al. [20] study in Iran found out that the children who acquired a second language outperformed in mathematics tests their counterparts who were monolingual and knew their mother tongue only.
2. The South African curriculum and assessment policy statements
In South Africa, the Department of Education introduced the National Curriculum and Assessment Policy (CAPS) for the subjects listed in the National Curriculum Statement for Grade R-12. The CAPS was designed to shed more light on teachers on what and how they should teach students. According to [21] the National Curriculum Statements Grade R-12 envisaged producing students who can:
identify and solve problems and make decisions using critical and creative thinking;
work effectively as individuals and with others as members of a team;
organise and manage themselves and their activities responsibly and effectively;
collect, analyse, organise and critically evaluate information;
communicate effectively using visual, symbolic and/or language skills in various modes;
use science and technology effectively and critically showing responsibility towards the environment and the health of others; and
demonstrate an understanding of the world as a set of related systems by recognising that problem-solving contexts do not exist in isolation (p. 5).
To achieve the intended outcomes, the designed activities are expected to be minds-on and hands-on to develop diverse mathematical skills in students. Asmal [21] emphasises that the designed activities must not be ‘keep busy’ activities but must focus on meaningful mathematics content. The Grade R curriculum is designed in a way that the time a student exits Grade R is fluent in number sense and the four basic operations. The aim is to ensure that students are competent and confident with numbers and calculations [21].
For the deliverance of mathematics content meaningfully, the Language of Learning and Teaching (LoLT) plays a vital role, with this understanding, the DBE made a provision through [22], which is discussed in the section below.
3. The South African language in education policy on education
In this section, we present the LiEP and how it tends to drive education. In South Africa, during the Apartheid regime, access to education was not equal for all, especially black people were offered low-quality education, for example limited resources, overcrowded classrooms, insufficient infrastructure and ill-equipped teachers [23]. To redress such racial inequality in education, the department of education developed LiEP which stipulates the aims of education as:
to promote full participation in society and the economy through equitable and meaningful access to education;
to pursue the language policy most supportive of general conceptual growth amongst students, and hence to establish additive multilingualism as an approach to language in education;
to promote and develop all the official languages;
to support the teaching and learning of all other languages required by students or used by communities in South Africa, including languages used for religious purposes, languages which are important for international trade and communication and South African Sign Language, as well as Alternative and Augmentative Communication;
to counter disadvantages resulting from different kinds of mismatches between home languages and languages of learning and teaching;
to develop programmes for the redress of previously disadvantaged languages.
The [22] advocates for all languages to be considered equal and for students to learn in the language that they are comfortable with. Research argues that even though the government advocates for the use of mother tongue, if there is no support, students can still suffer because every medium of instruction needs adequate support to attain the intended outcomes [24].
The next section discusses mathematics as a language and how it must be presented to the students for easy access.
Even though there is LoLT, mathematics is a language that has its own syntax and symbols. Asmal et al. [21, 25] describe mathematics as a language that uses symbols, terminology and notations for describing numerical, geometric and graphical relationships to communicate information. To provide students with multiple opportunities to learn worthwhile mathematics, mathematics teachers need to understand the specialised language of mathematics learning and teaching [26]. For the students to pass mathematics, they must first understand basic concepts which are the building blocks of this subject. It is from those basic concepts that the bigger mathematical ideas emerge.
In the true sense of the matter, many African countries have been considering the language of the colonisers as more superior to their own native languages, such connotations are misconceptions because early mathematical concepts are easily understood at a young age when learnt in their mother tongue. The literature argues that forcing students to learn mathematics in the second language poses a threat to their ability to ‘thrive’ mathematically and, subsequently, undermines their interaction with the wider mathematics community [24, 27]. For years the government has been pushing children to learn mathematics in the ESL, but without adequately supporting them with resources to develop the required mathematical competencies [24]. Any language of learning and teaching needs adequate support for the students to access the information without any setbacks.
Language allows the possibility to link from one concept to another, it is from the link that the meaning of concepts is derived, if the language is weak, the ability to learn is negatively affected [28].
Likewise, [4] argues that language performs at least three critical roles in the classrooms:
It is the medium of instruction. It is the main mode of communication.
Students’ understanding and processing of ideas are through language.
We establish students’ misconceptions and assess understanding by listening to their oral communication and by reading their mathematical works.
Failure to put much attention to the language issues simply means failing the society. The medium of instruction must be accessible to the students without putting much effort. Students individually have their own ways of learning mathematics. Each person is unique, and this is what teachers must take into consideration when designing learning activities. The section below horns on ways Grade R students learn mathematics.
Research highlights that the first 1000 days of child are critical to the child’s future, that is where the child’s foundation for healthy behaviour and learning is determined [29]. This implies that once the foundation of learning mathematics concepts is not well-grounded, the whole school life of the child is doomed. In support of this, [30] emphasised that the foundation for lifelong learning concepts, skills and attitudes is acquired during the early years. It further explains that even the development of emotional intelligence namely, confidence, curiosity, purposefulness, self-control, connectedness, capacity to communicate and cooperativeness is acquired during the early years. Feza [31] highlights the numerical abilities of young children prior Grade R possess that exceed the Grade R curriculum expectations supporting literature on the attainment of numerosity before formal learning.
The learning and teaching aspect in Grade R should focus on the holistic development of the child [21]. The teaching aspect should aim to develop the child’s emerging numeracy through activities that develop cognitive (problem-solving, logical thinking and reasoning), mathematical language, perceptual-motor, emotional and social aspects. According to [21] the aspect highlighted in this paragraph can be learnt and developed through:
Stories, songs, rhymes, finger games and water play, educational toys including board games, construction and exploration activities (mass, time, capacity, measurement, etc.), imaginative play, outdoor play and ‘playground games’. Many kinds of games and play could include aspects of numeracy, for example measuring during cooking or counting during shopping (p. 14).
‘Play’ is undermined as one of the ways which children learn, yet it is essential to the development and strengthening of the child’s creativity, imagination, dexterity, cognitive, social, physical, healthy brain and emotional well-being [32, 33]. The studies by [34] have shown that for young students from low-income backgrounds, their numerical knowledge can be promoted by playing a simple number board game. Furthermore, [35] explored cultural games’ contribution to early years of mathematics, discovering their strength in developing number sense and sequencing. Barnard and Braund [36] argue that Grade R teachers continue to allow free play with no purpose although literature advocates for meaningful play. With intervention, this practice can improve towards meaningful goal-oriented play [24, 37]. This implies that Grade R teachers must be creative to instil the culture of learning through play in their centres of learning.
When children play, it means they are in contact with the environment. For mathematics to make meaning to the students, the teaching approach must be more immersed in context-based problems [38] that are meaningful and applicable to their background experiences [39]. Background experiences are important because when children learn to count, the newly acquired symbolic representations of numbers are made to fit onto pre-existing non-symbolic representations [40]. It is worth noting that Grade R come to school with the knowledge of informal numeracy, which needs to be expanded, enriched and developed through appropriately designed learning activities [41]. Learning and teaching that does not include play, rob students of their potential to learn. Games or songs need to be well planned that as they play or sing, mathematics concepts are acquired and developed.
Research highlights that a child learns mathematics informally in home environment; much of their learning is social in nature [42]; for example, it takes place with parents during time of meals, chores and shopping through one-to-one correspondence. The home environment is rich with numerical information [43]. Mathematics teachers must know that when planning for class activities, they plan for students who have some mathematical ideas from home. Home experiences must be taken as the framework upon which formal mathematics can be built.
To have minds-on and hands-on activities as envisaged by the DBE means Grade R teachers must be dedicated and creative in their preparations. As the mediator of learning the teachers must be proactive in everything to ensure that all students are catered for despite their differences. From what is presented, it can be emphasised that schools need well-trained qualified Grade R teachers who are creative enough in teaching mathematics.
This study is situated in a social and cultural context, and the sociocultural perspective provides a wider lens of how both the teacher and the school provide opportunities for students to learn mathematics. It also provides an opportunity to explore how students navigate through the language to access the intended mathematical content knowledge. The theoretical premise for the study is based on [13] theory of social constructivism. Ref. [13] argues that learning occurs when an individual internalises a social experience through interacting with a peer or an adult. In Vygotsky’s cultural-historical theory, play is an essential part of early childhood. Vygotsky believed that play promotes cognitive, social, and emotional development in children. In mathematics education, students are expected to construct their own mathematical knowledge from previous experiences as they interact with peer or adult.
The study employed a qualitative approach guided by the case study design. The study’s sample comprised eight Grade R students of mixed gender purposefully selected from the five primary schools in the Queenstown district of South Africa. Students in these schools belong to the same cultural group and speak the same home language. The data was collected using the video camera, and the video clips were then viewed to elucidate how Grade R students navigate the language space in the lesson. The data was coded and analysed thematically and reported in themes.
7.1 Instruments
The data was collected from the video clips which were captured in different schools when students were being engaged in different mathematical activities, for example, to identify the number of items per group as shown in Figure 1 below, in Figure 2 students were to identify numbers arranged in mixed order and to match the number of items on the right-hand side with the correct numerical value on the left-hand side. The questions were asked in learners’ HL (IsiXhosa) one of the South African native languages.
Figure 1.
(a) and (b) The two groups of five bottle-tops arranged in a different order.
Figure 2.
Identification and matching activity.
Activity 1.
Researcher: Jonga ezi zam zisemfanekisweni iziciko (Look at my bottle-tops in the pictures).
Question 1: Researcher: Zeziphi ezininzi? (Which ones are many?)
Question 3: Researcher: Xa uzidibanisa zonke zingaphi? (When you add them all, how many are there?)
After this activity students were further engaged in Activity 2 below, which sought to examine their language and numerical proficiency.
Activity 2.
Before the students were to match the number of items on the right-hand side with the correct numerical value on the left-hand side, they were asked to identify the numbers on the left-hand side arranged in mixed order.
Researcher: Khawutshatise inani ngalinye nomfanekiso walo? Sebenzisa icrayoni. (Match each number with its picture. Use a crayon).
All the instruments used to collect data for the study were ethically cleared by the Central University of Technology.
The permission to collect data from the schools was sought and granted by the Queenstown district education office. Subsequently, the school principals of the schools in the project permitted the researchers to collect data without any hindrances.
Considering the age of the participants, the consent forms were distributed and signed by the parents of all the participants involved in the research project.
Participants’ parents were assured of the anonymity that no real names of the participants were to be used when reporting the outcomes of the research project. The following codes were used: School 1: Student 1 (S1S1), School 1: Student 2 (S1S2), School 2: Student 1 (S2S1), School 2: Student 2 (S2S2), School 3: Student 1 (S3S1), School 3: Student 2 (S3S2), School 4: Student 1 (S4S1), School 4: Student 2 (S4S2), School 5: Student 1 (S5S1), School 5: Student 2 (S5S2).
When students were asked to compare the two categories of bottle-tops and identify the group that has many bottle-tops. Students’ responses varied as shown in Table 1.
Student
Question 1: Zeziphi ezininzi? (Which ones are many?) Responses
How students responded to questions 1 to 3 of Activity 1.
Table 1 shows how each of the eight students responded to the three questions of Activity 1. S1S1, S1S2, S2S1, S2S2 and S5S1 identified the number of bottle-tops in Figure 1b as greater than those in Figure 1a while S3S1, S4S1 and S4S2 considered the bottle-tops in Figure 1a to be more than those in Figure 1b. Responding to the second question, all other students counted the bottle-tops in English except S1S2 who counted in HL, but not in an orderly manner, the last number mentioned was ‘shumi’ (ten).
Responding to Question 3, S1S1 and S5S1 said that bottle-tops in Figure 1a and b combined together are ‘ten’ while S1S2 said that ‘shumi’ (ten). S2S2 and S4S2 responded that the bottle-tops combined are 11. S1S1 and S5S1 said that the total number of bottle-tops is five (5). S3S1 did not give any response to the question.
Table 2 illustrates how each of the students named the listed numbers. Of all the students in the sample, only S4S1 and S4S2 managed to identify the given numbers correctly. S2S1 managed to identify all other numbers except one which was identified as six. The responses given by S1S1 were in IsiXhosa (Home language, HL); even though HL was used, the students could not get the question correct. S2S2 could not be able to identify the given number correctly. S1S2 and S5S1 both students were not able to identify the first four listed numbers while the fifth number was identified by S5S1 as five, yet it is four and S1S2 gave no response to that.
Student
3
1
5
2
4
S1S1
Linye
Mbini
Sixhengxe
Sibhozo
Ntandathu
S1S2
No response
No response
No response
No response
No response
S2S1
Three
Six
Five
Two
Four
S2S2
Four
Six
Seven
Eight
Nine
S3S1
Four
Two
Six
Seven
No response
S4S1
Three
One
Five
Two
Four
S4S2
Three
One
Five
Two
Four
S5S1
No response
No response
No response
No response
Five
Table 2.
How the students identified and named the given numbers (3, 1, 5, 2 & 4).
The next question required students to match the number of items on the right-hand side with the correct numerical value on the left-hand side as shown in Figure 2. Table 3 below illustrates how each of the students responded to the question.
Table 3.
How students matched the group of items to the numerical value.
The data presented in Table 3 above illustrate students’ responses to the matching item question. S2S1, S4S1 and S4S2 managed to match the given number of items to the correct responding numerical values.
Another group of three students, S2S2, S3S1 and S5S1 matched five items to a numerical value of 4. S3S1 provided unique responses as follows: matched two and three items to numerical values of five and two, respectively. No match was given to numerical values of three and one; one and four items.
S2S2 matched three and four items to a numerical value of five and no match was made for the numerical value of three. S5S1 matched four and one items to the numerical value of one while three items and a numerical value of three were not matched to anything.
Another unique response was given by S1S1 who straight matched the number of items on the right-hand side to the numerical values on the left-hand side as explained; three, one, five, two and four items were matched to the numerical value of five, two, three, four and one, respectively.
The last student S1S2 when asked to match the items to the corresponding items could not match any.
The findings are discussed in this section. The discussion is based on how each of the students responded to the questions and what that means to the research community as far as learning and teaching early childhood mathematics is concerned.
The findings reveal that some of the students are comfortable with the use of HL to learn mathematics, i.e., S1S1 proved that by counting in HL as shown in Table 1. Even though the student was not accurate in the counting, but it showed the student had a bit of an understanding of the mathematical terms in HL, such ideas just need to be supported. This finding is consistent with [24] assertions that the principal use of HL represents an immeasurable fund of knowledge and an essential cognitive resource for mathematical sense-making for ESL speakers [24].
The ability to match the items to the given numerical values shows students’ proficiency in counting. The researchers asked the students in HL, but S2S1, S4S1 and S4S2 responded in English and got the question correct, this reveals that some students are bilingual. From the findings of this study, it is also revealed that most students use both languages (English and HL, IsiXhosa) to navigate the learning concepts. This leads to suggest that students must be supported in being proficient in HL which can be used as a resource to learn the second language. Literature reveals that bilinguals benefit from advanced inhibitory control skills compared to monolinguals [14, 15, 16] as a result they perform better in mathematics than their counterparts (monolinguals).
For students like S1S1, S1S2, S2S2, S3S1 and S5S1 who had problems in matching the items to the correct numerical values, such problems emanate from a misunderstanding of mathematical language. It is argued that communicating mathematically requires an in-depth comprehension of the mathematical language and the multiple illustrations employed in communicating mathematical concepts [5].
Some of the students, for example, S1S1, S2S1, S4S2 and S5S1 when counting the bottle-tops in Figure 1a and b counted in English, listening carefully to their counting, skipped some of the numbers which is an indication that they are not yet conversant counting in English. Literature highlights that students in the advanced stage of language native-language acquisition can easily extend vocabulary, and good comprehension of the second language [5]. This implies that students need to be thoroughly developed in HL to have access to the Second Language (SL). Researchers argue that HL must be viewed as ‘resources’ if it needs to benefit the bi- or multilingual education system [9, 10].
The researcher used HL in all the questions, but surprisingly most of the students responded to the questions in English, for example, the counting of the items. Out of eight students involved in the study, one used HL to name the given numerical values, and the rest responded in English. For such instances, there is a need to support bilingual abilities because learning a second language assists in the growth of the density of grey matter in the left inferior parietal cortex of the brain, which leads to an improvement in performance. Research highlights that the acquisition of the second language at a young age, the denser the grey matter gets which is an advantage to the students [19].
11. Conclusion
The findings of this study led to the following conclusions:
Students failed to establish that the number of objects does change with the changed arrangement of the same number of objects.
We have established that in Grade R students were able to understand questions asked in HL, yet their responses to the questions were in the second language (English).
12. Recommendations
Based on the findings of this study, we recommend the following:
Students must be engaged more in the use of visuals and manipulatives to enhance their mathematical skills, for example, visualisation and counting skills.
Grade R students must be supported to be bilinguals because they have shown elements of understanding both languages. The first preference should be given to the mother tongue because it can be used as a resource to access mathematics concepts in the second language.
13. Limitations
These research findings cannot be generalised but can be transferrable to other contexts to strengthen the findings. It is advisable that other researchers should interpret the findings with caution as they are based on the data collected from the same cultural group that speaks the same home language. The replication of the same research with a different cultural group may yield different findings.
14. Suggested areas for further studies
We suggest that further studies can be conducted on:
The language that Grade R teachers mostly use for teaching mathematics.
Grade R teachers’ competence in the teaching of mathematics using home language.
How Grade R students of other cultural groups learn mathematics.
Acknowledgments
The authors would like to thank all the students who participated in the study to make it a success.
Declaration of interest
No potential conflict of interest was reported by the authors.
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Written By
Shakespear M. Chiphambo and Nosisi N. Feza
Submitted: 15 April 2022Reviewed: 17 May 2022Published: 06 July 2022
Open access peer-reviewed chapter
