Teaching Mathematics Using Two-Languages

Teaching Mathematics Using Two-Languages



University of Deakin, Geelong-Victoria

January, 2011



The use of English as the language of classroom instruction has become significant especially in the third-world countries such as Indonesia, Malaysia, and some African countries. Bilingual schools exist to cooperate the use of English and official language in the content classrooms, typically mathematics and science. According to Cummins, bilingual education is defined as “the used of two (or more) language of instruction at some point in a student’s school career” (cited in Crees & Blackledge, 2010:103).

The use of English as the medium of class instruction in mathematics classrooms, however, creates another barrier for students, besides mastering content subjects. It is undeniable that teaching mathematics in the bilingual classroom, when the language of learning and teaching (LOLT) is not the learners’ mother tongue, is a complex issue (Setati et al 2002).

The purpose of this essay is to discuss the advantages and disadvantages of the bilingual approach in the mathematics classroom in Indonesia, as well as to explain current issues regarding the use of two-languages, and  some useful suggestions for teachers in my school for the use of L1 (Bahasa Indonesia) in English-medium classrooms.


Bilingual education is one of CLIL (Content and Language Integrated Learning) models. CLIL is defined as “an educational approach in which various language-supportive methodologies are used which lead to a dual-focused form of instruction where attention is given both to the language and the content” (Coyle et al 2010:3).

Historically, the idea of combining content and language learning (CLIL) comes from countries such as the USA and Australia, where many immigrant people are forced to learn English as the second language, so that, they will be accepted in the society. In addition, it provides opportunities for them to pursue further education (Klippel 2003).

Recently, developing countries such as Indonesia are following their footsteps in the purpose of creating future generations that are competent and capable participating in the world competition. Therefore, some educational institutions are moving from traditional language teaching that use only the first language as the medium of instruction to content and language learning (Klippel 2003).

The climate of globalisation, in addition, has presented challenges for teaching and learning of additional languages, because English is presumed as the mainstream language of class instructions for accelerating technological, life style and socio-culture changes in the global community. Moreover, Baker argues that in the present days, “English is acknowledged as a significant and prestigious language that many people may be exposed to it in a particular domain” (2006:86). Specifically in Indonesia, although English has no official status, the intention to learn English and become proficient in English is increasing among young people. Therefore, CLIL is seen as an ideal mode of acquiring language proficiency of English without actually attending language class (Klippel 2003).

There are various models of CLIL introduced by researchers, particularly for secondary high school students, which is recognized as highly demanding for cognitive development, namely, dual-school education, bilingual education, interdisciplinary module approach, language-based projects, and specific-domain vocational CLIL (Coyle et al 2010).

Bilingual education is likely becoming very popular in Indonesia.  In the bilingual education approach, learners learn some particular subjects through CLIL with the intention of mastering both content and language proficiency. In this case, learners participate in ‘international streams’ and develop advanced CLIL language skills for specific subjects, such as mathematics and science, and often linked to national/international certification, or special status of assessment and recognition (Coyle et al 2010).

Therefore, it is not surprising to see bilingual education in Indonesia has been acknowledged as ‘the prestige education institution’ which has special assessment systems and certification. Indeed, this kind of achievement and accomplishment will provide many opportunities and benefits for learners in their future.

The CLIL model of bilingual education must have links to the conceptual framework that have four components; content, communication, cognition, and culture. The content component is the comprehension in new knowledge. The communication component has to do with interaction, progression in language using and learning. The cognition component means the engagement in learners’ intellectual development, their ability and capacity to think rationale and critically. The culture component expresses self awareness and appreciation of the culture where the language belongs (Coyle et al 2010).

There are several types of bilingual educations offered by Baker (2006) that are presumed to be the ‘strong’ form of bilingual education where bilingualism and biliteracy are part of the objectives. First, immersion, that caters for majority language students learning through the second language (bilingualism with initial emphasis on L2). Second, maintenance/heritage language, that have purposes to maintain home languages and culture (focuses on L1). Third, dual-language education is the sort of bilingual education with equal numbers of language minority and language majority students in the same classroom. Therefore, both languages are used for instructions.

Lastly, mainstream bilingualism, is the bilingual education in majority languages that joint two (more) languages in the classroom. In this case, there are significant numbers of natives or expatriates waiting to become bilingual (Baker 2006). This kind of bilingual education is very dominant in Asian, especially Indonesia that has the national language (Bahasa Indonesia) with a desire to introduce a second international language (English). The international language, in addition, is used as the medium of class instruction alongside the national language.


It seems to be true that learners who can practice proficiency of certain subjects and even mastery in two languages are likely to enjoy variety of choices and opportunities to enhance success in life. Adopting bilingual programs, however, is a definitely challenging and complex that cannot be simply taken with idealistic wishful (Davies 2005).

In the context of Indonesia, typically in Banda Aceh, the idea of bilingual education is often be incorporated into school policies without sufficient groundwork or perceptive of what is required to set up the system. The majority of bilingual schools in Aceh have poor quality of supportive resources. These schools, in addition, cannot simply implement an adjustment curriculum without adequate resources and properly trained teachers, which they do not have.

The example of bilingual education in Aceh province is Fatih Bilingual School which is the prior school to the existence of other private bilingual schools such as Lab School and some government schools that have bilingual classes attached as international stream classes. At Fatih Bilingual School, in the junior level, English is taught based on the learners’ acquisition of English. Additionally, some subjects such as mathematics and science are taught in English. As students’ proficiency of English is increasing, starting from secondary grade 1, they have more opportunities to sharpen their English skill from content classrooms, social interactions in the school context and extracurricular activities, despite high exposure of English.

Nevertheless, in practice, sometimes both teachers and students tend to encounter difficulties especially in classroom discourse. It emerges, because neither teacher nor students have adequate proficiency of English. Therefore, Bahasa Indonesia is used to ease the pupils as a transitional language of instruction.


The implementation of the bilingual approach in the content classroom has both positive and negative effects. Some researchers argue that the bilingual approach can be detrimental, but many more are on the opposite side. For those who are against dispute that the bilingual approach is not essential to be put in to the curriculum which would require a lot of time and funds to make the adjustment curriculum (Lim and Presmeg 2010).

In addition, Yunisrina states that in the classroom, the use of L1 has an inadequate capability that makes the instruction unintelligible (2009). Montague, likewise, declares that establishing bilingual programs need well-prepared of the fundamental components and resources, otherwise, it will not maintain the quality of bilingual school itself (1997).

In the context of bilingual schools in Indonesia, it is presumed to be the expensive school and only certain people can afford their children entering the school. Other than that, most teachers and students tend to speak using their mother tongue with their peers, even in the classroom and in the school environment, so they stick to their native language.

Regarding the students achievement, the majority of students encounter difficulties to learn mathematics in English. Those students who enjoy and master learning mathematics using Bahasa Indonesia, may lose their desire and motivation to learn in English.

Nevertheless, both students and teachers are in agreement of the importance of the bilingual approach in their school. There are many benefits of using Bahasa Indonesia in the English-medium classroom, especially in Indonesian schools. First of all, in the bilingual education where mathematics, three science subjects (biology, chemistry, and physic) and English are taught using English as the medium of instruction, L1 is used to enhance understanding of students who experience barriers to use L2 to express their ideas and views in L1 (Santoso 2006).

Subsequently, it is undeniable that teaching and learning mathematics using two languages have created challenges both for teachers and students. In the classroom when English is popularly used as the medium of class instructions, first language, on the other hand, provides an effective way of understanding the content deeply and quickly (Nation 2001).

Furthermore, Lim and Presmeg state that using students’ first language in the content classroom encourages students to practice target language (English) (2010), because in the classroom there always attempts from the students to get in use in English. In addition, they also argue that using two languages in teaching and learning in mathematics classrooms, bring additive effect on students’ cognitive ability that provides students to not only be competent in mathematics lesson, but also for both their languages proficiency (2010).

Moreover, the bilingual education also enables learners to apply a range of strategies to foster their understanding in English-medium classrooms, where students have chances to find alternatives of understanding of certain terminology by looking at a dictionary, asking the teacher and discussing with their peers using L1 (Santoso 2006).

Baker also states that bilingualism has certain thinking dimensions, particularly in “divergent thinking, creativity, early metalinguistic awareness and communicative sensitivity” (2006:164). In addition, there are possibility of many additional thinking skills on which there are no actual differences between bilingualism and monolinguals (Baker 2006)

From my point of view, the existence of the bilingual approach has brought positive aspects for education fields in Indonesia, but should be maintained for its quality and purpose. Adopting bilingual approach in one education institution, in addition, should be done by focussing to available resources and capabilities both teachers and students in English proficiency.



Language Competency of Teachers and Students


According to Cummins postulate “there exists a minimal level of linguistic competence, a threshold, that a student must attain to perform effectively on cognitively demanding academic task such as mathematical learning” (1981 cited in Lim and Presmeg 2010), which means that to learn mathematics effectively in the classroom, students should have certain levels of language proficiency. Therefore, it is undeniable that English acquisition of Students and teachers is the most important element in the English-medium classroom.

In the content classroom where English is used as the medium of instruction, often we see students talk with their peers using their mother tongue. In fact, in mathematics classrooms, students who are not fluent in English might not engage and tend to encounter difficulties in understanding subject materials. Moreover, often misunderstanding occurs during the lesson.

The bilingual school or classes in Aceh province have the minimum standard of threshold level of English proficiency in receiving and selecting the students. Consequently, many students are falling to attain cognitive and linguistic demanding either for mathematics or English. Likewise, the teachers that still struggle to teach mathematics in English.

On the other hand, some researchers argue that students become conversant in English because in mathematics lesson, “students are exploring, explaining, reflecting, reasoning, and communicating through language” (Ron 1999 cited in Kersant, Thompson, Petrova 2009:91). In a bilingual classroom, if students encounter difficulties during mathematics lesson, teacher intervention would be one alternative. The L1 can be used to scaffold students understanding, as well as to give opportunities for them to explore their ideas by talking and discussing it with their peers and the teacher.

In addition, according to cognitive research and language acquisition theory, initial mastery of L1 is presumed to be the best way for learners before they start learning content in English and proficient in English linguistics (Krashen & Biber, 1988; Krashen 1996; Willig, 1985 cited in Montague 1997). Marcer, likewise, state “…talk is understood as a social thinking tool…” (Mercer, 1995 cited in Setati & Adler 2000:246).  When a student can present his/her ideas in his/her mother tongue language, they bring a great deal of resources from their lives and habits, as well as increase potential repertoire practice for his/her peers and teacher in the classroom.

Indeed, Developmental Interdependence hypothesis by Cummins (1978, 2000a, 2000b) suggests that the second language acquisition of a child is relatively dependent on the language competency of his/her first language. The more proficient the first language, the easier it will be to develop the second language, and vice versa (cited in Baker 2006).

There are some strategies that can be used by teachers to assist learners understanding of mathematics in English medium classroom which I presume to be effective for secondary levels. For instance, introducing important vocabulary and terminology before learning the concept, connecting mathematics language to daily life, and constructing word walls and personal dictionary (Kersant, Thompson, Petrova 2009).

Bilingual Resources


In this section, I would like to briefly discuss some useful resources and suggestions that can be used by mathematics teachers in the bilingual education approach.



According to Yunisrina, code switching refers to “the alternate code for using two genetically unrelated languages; L1 and target language (L2), at word, phrase, and clause or sentences level in instructional context in a bilingual classroom” (2009:8). In the content classroom, most of the time teachers used code switching to explain, provide input, convey meaning and achieve teaching goal (Then & Ting 2009),  whereas students code-switch when talking to their peers and discussing certain topics.

Furthermore, in the context where English acquisition of students is lacking, code switching is an indispensable instrument used to transmit the knowledge by teachers (Then & Ting 2009).  For example, the teacher can use students’ first language to translate some terms or definition for students before writing them down or giving exercises in the target language. By doing this, students will obtain clear ideas and avoid misconceptions which may occur during teacher discourse (in English).

However, the use of code switching should be controlled and limited by the teacher, referring to the students’ language competency and stream. Typically for students, code switching should be seen as the scaffolding that can assists them in understanding the content subject as well as increasing their proficiency of English.

Teaching Material

Providing appropriate material is also the key component for success in bilingual education programs (Montague 1997). The textbook, in addition, provides valuable information and resources for students about the content.

The majority of bilingual schools in Indonesia use bilingual text-books that have both languages; Bahasa Indonesia and English attached, but do not rule out the existence of full-English textbooks. My school for example, use full-English textbooks for subject such as mathematics and science. Such a textbook, however, raises a lot of obstacles for teachers and students in the classroom.

From my experience using a full-English textbook, every time I have to translate and explain the definition and terminology in L1, which takes time away from teaching them the mathematical concepts. If I can choose, I would like to use a bilingual textbook where students can refer to it in case they find some difficulties regarding definition and terminology rather than depending much on me.

Teacher Training

Another important issue in the bilingual approach is the teacher training program. This issue emerges since the teachers have not been trained as bilingual teachers. In addition, they often are not qualified to teaching techniques such as a link with context, extensive use of para-linguistic cues, etc (Montague 1997).

In this case, the government and schools should give opportunities for teachers to participate in certain professional development programs and activities, typically for increasing English proficiency of teachers. Teaching in bilingual schools requires not only mastering the content and concept of mathematics, but also understanding the language of mathematics itself. Obviously, providing sufficient training for teachers will benefit a lot for the school that can increase the standard and quality of the school.


Supportive Material in classroom

Material support in the classroom and in the school environment should be provided in collaborative with teachers and students. In the classroom, for example, students can create word-wall about useful vocabulary, poster and newsletter about school even and history of mathematics, and attractive sign to enhance students enthusiastic in learning mathematics. During teaching and learning, the teacher can provide authentic material such as geometry shapes in teaching geometry. By doing this, students will get more exposure and become familiar with English.


The assessing learning system used in bilingual schools in Indonesia is referred to as the national curriculum. It is compulsory for students to sit for national examinations in the end of the primary, junior, and secondary years. In the school-based assessments, however, some bilingual schools/classes will provide assessment system in English language adjusting international standard.

In practice, sometimes, students find difficulties in understanding the question instructions and answering mathematics questions in English. In this case, teachers are required to give oral translation for the students which may not effective and efficient. On the other hand, such an assessment system will encourage learners to learn English which I assume as a positive reinforcement. Consequently, students will struggle and make a great endeavour to learn not only mathematics topics, but also instructions in English.

Indeed, evaluating the effectiveness of any teaching and learning experience is important (Groundwater-smith et al 2003). Therefore, any assessment and reporting in the school must be to improve and inform the performance of students in learning mathematics. Baker states that “assessment for bilingual students is beneficial when there is the observation in/outside classroom context by trained assessors who seek to empower the students rather than focusing more on testing, curriculum based-assessment, a cultural and linguistic awareness of bilinguals” (2006:367). Meaning that, in the bilingual school-based assessment, teachers can provide alternative assessment such as portfolio assessment, performance assessment, and project assessment.

In the portfolio assessment, which is based on the artefact of learning, teachers and students make judgments about learning according to a variety of evidence. For instance, the evidence of students’ learning records including their achievements and demonstrations (Groundwater-smith et al 2003).

Subsequently, the performance assessment is a sort of assessment that the teachers assess students’ work and comprehension in the classroom for specific topics in mathematics such as problem solving, group working, and discussion (Groundwater-smith et al 2003). The essential part of this assessment is the quality of teachers’ observations on the activities of the students in the classroom.

Lastly, project assessment where students can work either individual or together in a group to do a research and compile the information, report their ideas and findings on the writing journal, poster, or paper, and present them in the classroom (Groundwater-smith et al 2001). This kind of assessment will encourage high cognitive skills, as well as enhance language acquisition of students in writing and speaking.



The Bilingual approach in education has been recently recognised as one of the CLIL models that emphasises to the use of two languages in teaching and learning. The bilingual education can be highly beneficial in Indonesia especially if the program is well managed and prepared to improve the quality of language learning, typically English as the second language.

Apparently, the efforts of using English as the medium of class instruction should be supported with the first language (Bahasa Indonesia), in order to ensure students’ understanding about a mathematical concept. Likewise, giving opportunities for students to develop and share their ideas. This approach is also presumed to be highly demanding for the language acquisition of the students.

In the mathematics classroom, where the teacher and students share the same first language (Bahasa Indonesia), teacher can employ the first language in a way to accelerates second language (English) acquisition, because in mathematics, students explore, explain, reflect, reason, and communicate through language. Consequently, the students will obtain the full benefits of bilingualism.

Some issues that have been presented regarding the use of two languages, should be concerned and taken into account not only by teachers and students but also school apparatus, government, and community, likewise assessment of learning and bilingual resources such as teachers’ capabilities, supportive material, and code switching. Code switching in bilingual approach, in addition, plays an important role as a potential resource to achieve learning outcomes.

Indeed, the bilingual approach has become phenomenal as a popular model of education in Indonesia, but perhaps, the most important aspect is how the teacher encourages his/her students to maximise use of English not only in the classroom context, but also in their social interaction in the school environment. Consequently, the objective of the bilingual approach to create sustainability and consistency of teachers and students to use English as the medium of class instruction will be attainable.


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Coyle, D, Hood, P & Marsh, D 2010. CLIL: Content and Language Integrated Learning. Cambridge University Press. UK.

Creese, A., Blackledge, A 2010. Translanguaging in bilingual classroom: A Pedagogy for Learning and Teaching?. The Modern Journal, 94(1). Retrieved in December 23, 2010 from Wiley Online Library.

Davies, Rachel 2005. Bilingual education-often misunderstoon, always complicated. The Jakarta Post [online], July 16, 2005, viewed December 24, 2010 from http://www.thejakartapost.com/news/2005/07/16/bilingual-education-often-misunderstood-always-complicated.html.

Groundwater-Smith, S,. Ewing, R., Le Cornu, R 2003, Teaching challenges and dilemmas (eds). Nelson Australia Pty Limited, Sydney.

Groundwater-Smith, S., Brennan, M., McFadden, M. & Mitchell,J 2001, Secondary Schooling in a Changing Context, Harcourt, Sydney, pp. 207-28.

Kersaint, G., Thompson, D. R., & Petkova, M 2009. Strategies to help English language learners understand mathematics language. Teaching mathematics to English language learner (pp. 91 – 111). New York: Routledge.

Klippel, F 2003. New prospects or imminent danger?: The impact of English medium instruction on education in Germany, Prospect, 18(1), 68-81. Retrieved Seprember 28, 2010, from Publisher site database.

Lim, C.S., & Presmeg, N 2010, 13th August. Teaching mathematics in two languages: A teaching dilemma of Malaysian Chinese  primary school. International Journal of Science and Mathematics Education, Online First. Retrieved September 28, 2010, from SpringerLink database.

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Santoso, Teguh 2006. The benefits of bilingual education and its applications in Indonesia. Jurnal Pendidikan Penabur 5(6). Retrieved in 24 December 2010 from http://www.bpkpenabur.or.id/files/Hal.42-45%20The%20Benefits.pdf

Setati, M., & adler, J 2000. Between languages and discourses: Language practices in primary multilingual mathematics classrooms in South Africa. Educational Studies in Mathematics, 43, 243-269. Retrieved September 28, 2010, from http://www.mamokgethi.com/pdf/19pub.pdf.

Setati, M., Adler, J., Reed, Y., Bapoo, A 2002. Incomplete journey: Code-switching and other language practices in mathematics, science and english language classroom in South Africa. Language and Education, 16(2). Retrieved December 15, 2010 from Informaworld Database.

Then, David Chen-On & Thing, Su-Hie 2009. A preliminary study of teacher code-switching in secondary English and science in Malaysia. Teaching English as a second or foreign language 13(1). Retrieved December 12, 2010 from Education Research Complete database.

Yunisrina, Qismullah Yusuf 2009. A pragmatics analysis of a teacher’s code in a bilingual classroom. The Linguistics Journal 4 (2). Retrieved December 12, 2010 from EBSCO database.




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