6 Findings
6.2 Language Use in Written Mathematical Explanations
Firstly, we discuss findings in relation to the question,What variation in language use is evident when teachers and students write mathematical explanations?Close to 90% of all teachers and students responded to all questions and gave explanations
Table1Therelationshipbetweenteacherandstudenthomelanguage:Grades3and4.(Gr3n=1506;Gr4n=1352) TeacherHL EnglishIsiXhosaIsiZuluSepediSesothoSetswanaXitsonga Learner HL/GradeGrade3 (%)Grade4 (%)Grade3 (%)Grade4 (%)Grade3 (%)Grade4 (%)Grade3 (%)Grade4 (%)Grade3 (%)Grade4 (%)Grade3 (%)Grade4 (%)Grade3 (%)Grade4 (%) Afrikaans00000000000000 English00001100000000 IsiNdebele00002102000000 IsiSwati00002100000000 IsiXhosa22005300121100 IsiZulu44234521042173513 Sepedi01001100003400 Sesotho10005200022200 Setswana310300001071010 Tshivenda00100100000000 Xitsonga00002100110010 Arabic00000000000000 Shona00000000000001 Total10836633206522162234
Fig. 2 Examples of mixed language used in explanations
for their answers. The language use analysis, carried out on all responses and expla- nations, was thus carried out on a large dataset which had been rigorously prepared and cleaned. In multilingual classes, there are many different languages that teachers and students may call on as a resource when answering mathematical questions.
These may be the same as or different from the LoLT of the classroom. Knowledge of mathematical content is extremely important (the goal of mathematics teaching is mathematics learning), but the purpose of this study was to give the students (and teachers) an opportunity to speak about mathematics by giving reasons for how they worked out their answers. The explanations they wrote were used to gain insight into their language use when writing mathematics. Teachers and students used both verbal language and mathematical symbols in their explanations and they also used pure and mixed language to say what they wanted to say. Examples of explanations are shown below, selected to show a range of possibilities according to the codes of mixed and pure language use. Figure2gives two examples of mixed language use in student explanations.
In the first example in Fig. 2, IsiZulu is used as the main language in a mix with English, which is used to write the number word. In the second example a mix of Setswana and English occurs in a similar way. This was one of the most common forms of language mixing found in student explanations. This is a classic
‘mix’ which teachers wish was allowed (seen in the responses to the open-ended questions which are discussed later in the findings), evidence of heteroglossia in practice, officially disallowed by CAPS policy. There are officials who attempt to stamp out such mixing, in favour of pure language use conforming to a monoglossic language ideology (Sapire,2018). There were other variations in language mixing:
some students used both English and Setswana/IsiZulu in their explanations but in full sentences. For example, they might explain Question 1 in IsiZulu and Question 3 in English. Some students wrote their full explanations in two languages without mixing languages—for a particular question they gave an explanation in both English and Setswana. Figure3gives two examples of pure language use in mathematical explanations.
In the two different examples shown in Fig.3, only one language is used in the explanation, which was the code for pure language use. The first example is from a Grade 3 response, with Setswana used for the explanation and the second one is an English explanation, given by a Grade 4 student.
Figure4shows the spread of language use in the explanations given by teachers
Fig. 3 Examples of pure language used in explanations
Fig. 4 Language of expression in teacher and student explanations
and students. Three categories of language use are identified in the figure: pure, mixed and symbolic.
The findings show that for both teachers and students pure language use was most common when giving explanations. Figure4 clearly shows that most of the explanations were given in a pure language. In that category, English was most highly represented for both teachers (83%) and students (Grade 3—38% and Grade 4—53%) even though English was not the home language of the majority of the participants.
This is evidence that, in spite of the multilingual context, the monolingual LoLT system enforced by CAPS policy pervades and strongly influences language use. The percentages for student explanations in all sub-categories other than English were higher than the percentages for teachers. The use of IsiZulu and English together was coded as EngZulu and the use of Setswana and English together was coded as TswaEng. There are interesting differences in these categories between Grade 3 and
Table 2 Teachers’ language use preferences with reasons (n=62)
Theme Percentage
I use mostly English (it is the common student language or it is the LoLT) 85
I code-switch to support students’ understanding 52
English is better for the teaching of mathematics (terminology advantage). 30
I use mostly IsiZulu/Setswana (it is the LoLT) 26
IsiZulu/Setswana is better—it is the home language and better understood by students
24 English should be used because of the policy switch to English in Grade 4 17 Teaching maths in IsiZulu/Setswana is difficult (terminology disadvantage) 9
Grade 4 students. Grade 3 students used more indigenous languages than Grade 4s.
Language mixing was not common, but was higher in the Grade 4 groups than in the Grade 3 groups. Symbolic language (broader use of the mathematics register) was also not common and was used more by Grade 4s which can be explained since Grade 4s would have greater knowledge of the mathematics register.
Aligned with the finding in relation to more pure language use in explanations can be seen in Table2, that most of the teachers favour one language when they teach and that this language is determined by the LoLT.
The CAPS policy thus appears to be influencing teachers’ language use and creating a system that favours multiple monolingualism rather than multilingualism.
A high percentage of teachers (85%) expressed a preference for English as the LoLT.
This could be seen as policy compliance, since from Grade 4 onwards, English is the LoLT in all schools in spite of it not being the home language of the majority of students. Despite the general tendency towards the use of pure language, 52% of teachers indicated that they used code-switching to support student understanding showing that while their expressed preference is evidence of a heteroglossic ideology, the enactment of this is monoglossic. 30% of teachers mentioned the terminology
‘advantage’ of English while 9% spoke of the terminology ‘disadvantage’ of the indigenous languages. Number names are worth noting here as they are mentioned by many teachers, who say things like,It is difficult to write number names in IsiZulu or Sesotho. This leads into the next section of the chapter which looks more closely at the mathematics register.