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Evelyn Njurai
Kiriri Womens University of Science and Technology
This paper discusses how trilingual undergraduate students of mathematics in Kenya explored mathematical meaning using languages at their disposal as resources. The languages were Language of Learning and Teaching (LoLT) and their home languages. They were however, faced with a dilemma which was either language related or not. The discussion draws on the notion of language of teaching dilemmas. The data was drawn from a wider study which explored language practices of trilingual undergraduate students of mathematics. The focus was on first year students undertaking mathematics in their programs. Findings show that, while the students viewed code switching as a practice and opportunity that facilitated exploration of mathematical meaning, time was wasted and there was the potential of misinterpreting tasks. In contrast, when a task is not understood in the LoLT, one wastes time and would better switch to home language at the earliest opportunity. An attempt to deal with the dilemmas presented a complex situation. The findings contribute to the field of mathematics education in trilingual contexts and further research is suggested. .
INTRODUCTION
In most parts of the world and particularly in Africa, teaching and learning takes place in a language that is not the students home language. However, in the process of learning, students may use other languages in their repertoire as resources to explore meaning of mathematical tasks and in fact, in mathematical language and more particularly in mathematical discourse. The exploration is not necessarily a straight forward matter and students may experience dilemmas. In the growing field of mathematics education in context of language diversity, there is need to explore the possible dilemmas and how students deal with them.
A dilemma of code switching among trilingual mathematics students in Kenya is here discussed. In particular, students exploration of mathematical meaning, and how and why they faced a dilemma of code switching. While previously, the notion of dilemma of code switching has been discussed in teaching contexts, the purpose of this paper is to explore the language and non-language dilemma of code switching among undergraduate students as they individually engaged with mathematics tasks. In particular, the tension between acquisition of mathematical meaning and the challenges it presents.
The paper, therefore, responds to the questions;
Why do undergraduate students of mathematics switch to translate mathematics tasks?
When do undergraduate students of mathematics switch to translate mathematics tasks?
What are the language and non-language dilemmas the students face when they code switch?
How do they deal with the dilemmas?
Exploring mathematical meaning and the language dilemma in teaching and learning process
Students' home languages have been explored and discussed in details as important resources for teaching and learning especially as a means to improve bi/multilingual students' participation and performance in mathematics (Setati, 1998; Setati & Adler, 2000). In fact, research on the language practice of code switching, between the Language of Learning and Teaching (LoLT) and students home language have been widely documented.
Code switching and Language proficiency
Code switching may be verbal (Baker, 1993) or non-verbal(Moschkovich, 2005) and can involve a word, a phrase, a segment of a sentence, a sentence or several sentences. The non-verbal strategy during solitary and/or mental arithmetic computation advanced by Moschkovich involves switching between languages when thinking through computations. This paper focuses on the non-verbal strategy when students individually engage in thinking and working on mathematics task.
Code switching is necessary when learners have limited proficiency in the LoLT; this is because limited proficiency in LoLT may prevent them from expressing their mathematics ideas in the LoLT and more particularly in mathematical language. Despite the fact that some students perform well in the LoLT, they also face interpretation challenges in mathematics,(Clarkson, 2006; Njurai, 2015). In such instances, it is observed that some students draw on their home languages to solve such problems. Code switching by students with limited proficiency in LoLT and those proficient in it presents an opportunity to find out how students explore mathematical meaning in tasks presented in LoLT. Code switching has however not been straight forward and dilemmas have been experienced.
The Dilemma of Code Switching
The language of teaching dilemmas developed by Adler (1998) provides an explanatory and analytical tool in multilingual mathematics education. Adler addresses three key dilemmas among them the dilemma of code-switching.The dilemma describes and explains mathematics teachers knowledge of their practice in multilingual mathematics classrooms of South Africa. In this dilemma of code switching, Adler explores tensions between developing spoken mathematical English, where English is the LoLT, visa vie ensuring mathematical meaning. Embedded in this dilemma is the need to access mathematical concepts and at the same time access to English language, the language of power, furthermore, access to language of mathematics and mathematics discourse (Adler, 1998). The teachers were faced with a dilemma; to switch or not to switch. The dilemma was at once personal, practical and contextual.
Based on the language of teaching dilemma, researchers in mathematics education have explored and discussed the dilemma of code switching in multilingual mathematics classrooms from the teachers perspective in diverse language contexts which includeMalaysia, Malawi as well as South Africa (Barwell, Chapsam, Nkambulem, & Phakeng, 2016;Chitera, 2010; Lim & Presmeg, 2010; Setati & Adler, 2000). A question that begs response then is whether students who practice code switching experience the dilemma.
I find this notion of dilemma of code switching illuminating to describe and explain dilemmas experienced by trilingual undergraduate students of mathematics in Kenya when engaging with mathematics at an individual level.
The trilingual context
The Language of Learning and Teaching (LoLT) at university in Kenya is informed by the Language in Education Policy (LiEP). The policy states that during the first three years of their schooling, students in public schools are taught through the medium of the home language that is predominant in the school environment. The learners are introduced to learning their home languages as well as English and Kiswahili as subjects. The learners can then be described as trilingual learners. A trilingual person is one proficient in three languages and whose proficiency in the languages is not necessarily equal(Hoffmann, 2001). The speaker uses the three languages either separately or by switching between any two in ways that are determined by his/her communication needs. It is noteworthy that neither Kiswahili nor English are first or home languages for the majority of students. English is the official language while Kiswahili is the national language and co-official language (Republic of Kenya (RoK), 2010). While the three language formula is not implemented uniformly throughout the country in these early years, it recognises the value and importance of home languages while it progressively inducts learning in English only from the fourth year. At university, the LoLT is English for all non-language subjects. Even with the constitutional provision that both English and Kiswahili be used as official languages, the position of English as the LoLT is still dominant. It is the accepted language of teaching though it may not necessarily be the language of learning or thinking.
Research Method
This paper draws from a wider study which explored language practices of trilingual undergraduate students of mathematics in Kenya and which adopted a qualitative inquiry process, specifically a case study approach (Njurai, 2015). It was conducted in one public university in Kenya with a focus on first-year undergraduate of engineering students taking mathematics in their programmes. Data were collected using three instruments students questionnaire, and clinical and reflective interviews.
The transcripts of reflective interviews, in which semi structured questions were used, are key in this paper in providing details of the code switching practices and the associated dilemmas. It is in them that the students talked about mathematics (Adler, 1998)explaining the different languages and language practices that were not apparent during the clinical interviews. The transcripts also provided data on how and why the participants used each language while processing the task, in speech in writing or other non-verbal means. The focus was on students who indicated that they code switched to translate part or whole task and expressed that in so doing they faced a dilemma.
The participants
The participating students were high performers in both mathematics and English. These were S10, S14 and S12, all taking a Bachelors degree in Civil Engineering. Their home languages were Kikamba, Dholuo and Luluhya respectively and were aged between 19 and 21 years. A common thread was that the students needed to understand the mathematics task and saw the need to use their home languages to facilitate the understanding and interpretation. In their utterances, two students S10 and S14 indicated that they experienced the dilemma of to switch or not while the third student S12 offered a different view on the same.
Data Analysis and Findings
In working on the particular task, S10 used English throughout his written and spoken explanation of the task expectation, interpretation and solution process withthe researcher. In his reflections, he revealed that he used Kikamba to interpret the whole task, because it was the more familiar language.
S10: Yeah, yeah, yeah. First, after seeing the question, in all my studies, I try to interpret in Kikamba, which Im more conversant with. I read in English then I interpret it in Kikamba, which I can understand more than English.
R: Are there particular parts or it is the whole question that . {S10 interjected}
S10: The whole question.
R: How do you put it in Kikamba?
S10: I do it in Kikamba then I transfer to the paper in English.
R: Is it {translation} something that you can write?
S10: No, no, no.
Yeah, Im more conversant with Kikamba more than any other language.
This extract reveals that S10 not only translated the present task but that he did this with all other tasks. His reason was that he was more familiar with Kikamba than with English. He interpreted the task to Kikamba in his mind but neither verbalised nor wrote it down in this language. It was interesting that when requested to write the interpretation in his home language, S10 gave an emphatic no, despite arguing that he was more fluent in this language than in any other. While this explanation may seem to contradict his use of Kikamba, in a way it demonstrates that conversational proficiency in a language is not commensurate with written proficiency. His home language was significant for understanding and interpreting the task.
His dilemma of code switching between English and Kikamba is explicit in the following extract.
S10: After seeing the question, first the question was very tricky, so I had to read it, reread it so that I can understand it more. Then in my translating to Kikamba and then to English, I think it wasted a lot of time.
R: Wasted time?
S10: Yeah
R: You have said it helps you to understand it better?
S10: It helps but it wastes a lot of time.
R: What would be the option?
S10: If it is possible, I can try to practice to interpret the question in English which I use to write in paper.
He finds the process of translating back and forth as a process that wastes his time. To avoid time wastage, S12 observes that he needs to practice interpreting in English. This would call for him to be more familiar with English than he currently is. Therefore, his dilemma is to switch to interpret and understand the task hence taking more time or remain in the LoLT probably not get the required meaning while working in a shorter time of period.
In the task that was at hand, S14 used English only in his communication with the researcher. However, his reflections indicated that he translated part of the task into Dholuo. In this extract, S14 had reworked the task after an incorrect first attempt.
S14: I involved it {Dholuo} at the stages where I was not able to interpret in terms of English.
S14: In part (b) I had to involve, I was a bit confused in terms of these people {450} and the number of seats here. I had to involve Dholuo and Kiswahili so that I interpret that each chair was supposed to accommodate an individual. So depending on the equation that I got in part (b), I had to equate to the number of people so that I could solve it.
R: How did it go like? If you can write.
S14: Ka ji 450 obedo to gi wuoyo kombe, kombe ma odong' onego bed ni ting'o ji 150. [If 450 are seated and they rearrange the chairs, the remaining chairs should accommodate 150 people] {He then read out the translation}. I set out the equation for the remaining chairs... {inaudible}.
S14 had difficulties in the interpretation of the task in the second part and this caused some confusion. He needed to link the solution arrived at earlier to the requirements of the second part. In order to do so, S14 translated part of it into Dholuo and arrived at the solution. From S14s account, it is clear that Dholuo was used as a linguistic resource when he faced interpretation challenges in English.
S14 considered knowledge and use of a language in mathematics as important and that if one code switches, they must be careful to get the right interpretation.
S14: I think it [language] is a very important factor when it comes to mathematics. We have to comprehend the question and if you do the wrong interpretation especially when somebody switches from English and then brings another language lets say mother tongue or Kiswahili, it may bring a different interpretation apart from what was expected. So language is very important especially English is very important for mostly performing in mathematics.
R: Yes but it contradicts what you have already done; interpreting and translating to home language and you were able to succeed in that question
S14: So what I can say when you now switch to other languages apart from English then it consumes a lot of time. If you understand English better, you can understand the question and then do it within the expected time.
S14 brings out two issues here: the possibility of misinterpretation and use of more time in translating. As observed by Setati (1998), mathematics registers may not be developed in all African languages as it is developed in the LoLT (commonly English or French in Africa). Therefore, the translation may not yield the expected interpretation. S14 notes that English is important for his working and performance in mathematics. This could simply not be the ordinary English but also mathematical English.
S14 also notes that a lot of time is used when code switching. Like S10, he suggests that if one is able to interpret the task in English, then one would be able to work on the task in the expected time period.
The need for more time by S10 and S14 resonates with the findings of Lim & Presmeg (2010) that, when code switching happens, then more time than is stipulated is required to translate both ways from LoLT to home language and back to LoLT.
A contrasting finding emerged with the analysis of data of S12. He explained that code switching is not a time wasting process but one that would save time. While his home language is Luluhya, he translated parts of the task into Kiswahili, the national language of Kenya and a language he commonly uses. He translated what he referred to as the general parts of the task into Kiswahili and the specifics he worked in English. The general parts appear to be the parts involving ordinary language and knowledge while the specifics involve mathematical language. In the latter, he was involved in making assumptions for the unknowns. In fact, in the following extract like S14 he says that English is key in understanding mathematics, but code switching to a more familiar language has its advantage of saving on time;
S12: For you to be able understand the concept in mathematics, you have to be good in some other languages, but for this case, English is the key, then there are other languages which can help you to understand mathematics. You know in mathematics we are tested on time and so many other things. So if you will not understand the concept may be in English or it will take you so long to understand, then you are killing your time. The best thing you can do is understand it maybe in another language so that you can minimize on that time waste for you to be able to handle the question.
S12 suggests that code switching to a language that one is familiar with is a prerequisite to understanding mathematical tasks. He suggests that if one does not understand a task in the LoLT, they can switch to their home languages; it is both easier that way and also saves on time.
Discussion
The use of home languages does not seem to interfere or hinder expected meaning, in fact the languages are resources that provide opportunities for engaging with mathematical discourse. For all the students S10, S14 and S12, code switching facilitated understanding of the task; either partially or in whole. Their home languages were resources necessary in understanding and interpreting the task. S10 translated the whole task, S14 parts of the task while S12 translated the general parts but not those involving mathematical language. However, S10 and S14 sighted dilemmas at individual levels to switch or not to switch and waste time, and to lead into a possibility of misinterpretation. In contrast, S12 opines that by code switching one would save time by efficiently understanding the task in the language they are more familiar with.
It is evident from the findings above that while the students were proficient in LoLT, they needed to explore meaning in their other languages because of confusion, habitual practices and where the task involved general information (not mathematics specific). They needed their home languages to explore and access mathematical meaning of the task. This is in line with the finding by Clarkson (2006) that students who are proficient in LoLT also code switch to their home languages to explore mathematical meaning.
From the discussion, the notion of dilemma is apparent to learners who practice code switching as it is for teachers. The dilemmas are personal and interpersonal, and practical. The contribution of this study in the field of mathematics education and language diversity is that there are dilemmas that are language related (misinterpretation) or non-language (time wastage). Furthermore, in a classroom situation, misinterpretation may be corrected by the teacher, when students engage with tasks at individual levels, their interpretation in other languages is final and the misinterpretation are not corrected. The findings add to the on-going discussion on dilemmas faced in multilingual classrooms.Further research is recommended on dilemmas that students may be faced with and ways of dealing with them.
Conclusions
The dilemmas of code switching and exploring mathematical meaning in home languages takes significance in the context of curriculum reform in Kenya that is currently being piloted. Students varying use of code switching and associated dilemmas suggests that language in-education policy needs to engage more seriously and explicitly with what bi/tri/multilingual practices like code-switching can and do mean in the day to day realities of trilingual students engagement with mathematics.
References
Adler, J. (1998). A Language of teaching dilemmas: Unlocking the complex multilingual secondary mathematics classroom. For Learning Mathematics, 18, 24-33.
Baker, C. (1993). Foundations of bilingual education and bilingualism. Clevedon, Avon: Multilingual Matters.
Barwell, R., Chapsam, L., Nkambulem, T., & Phakeng, M. (2016). Tensions in teaching mathematics in context of language diversity. In e. a. Barwell R, Mathematics Education and Language Diversity (pp. 175-192). Nwe ICMI Study-Series, Springer.
Chitera, N. (2010). Code-Switching in a college mathematics classroom. International Journal of Multilingualism, 6(4), 426-442.
Clarkson, P. (2006). Australian Vietnamese students learning mathematics; High ability bilinguals and their use if their languages. Educational Studies in Mathematics, 64, 191-215.
Hoffmann, C. (2001). Towards description of trilingual competence. International Journal of Bilingualism, 6(1), 1-17.
Lim, C., & Presmeg, N. (2010). Teaching mathematics in two languages; A teaching dilemma of Malaysian-Chinese primary schools. International Journal of Science and Mathematics Education, 137-161.
Moschkovich, J. (2005). Using two languages when learning mathematics. Educational Studies in Mathematics, 64, 121-144.
Njurai, E. (2015). Language practices of trilingual undergraduate students engaging with mathematics in Kenya. Pretoria: Unpublished PhD Thesis.
Republic of Kenya (RoK). (2010). Constitution of Kenya. Nairobi: Government Press.
Setati, M. (1998). Code-switching in a senior primary class of second-language mathematics learners. For Learning Mathematics, 18, 34-40.
Setati, M., & Adler, J. (2000). Between languages and discourse: language practices in primary multilingual mathematics classrooms In South Africa. Educational Studies in Mathematics, 43, 243-269.
While I have reported elsewhere that S14 switched between any two of his three languages, the current discussion engages in his switch to Dholuo where he faced dilemma of code switch.
Njurai
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