Skip to main content

Advertisement

SpringerLink
Log in

Using Two Languages When Learning Mathematics

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

This article reviews two sets of research studies from outside of mathematics education to consider how they may be relevant to the study of bilingual mathematics learners using two languages. The first set of studies is psycholinguistics experiments comparing monolinguals and bilinguals using two languages during arithmetic computation (language switching). The second set of studies is sociolinguistic research on young bilinguals using two languages during conversations (code switching). I use an example of a mathematical discussion between bilingual students to illustrate how sociolinguistics can inform analyses of bilingual mathematical conversations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Adler, J.: 1998, “A language of teaching dilemmas: Unlocking the complex multilingual secondary mathematics classroom”, For the Learning of Mathematics 18(1), 24–33.

    Google Scholar 

  • Adler, J.: 2001, Teaching Mathematics in Multilingual Classrooms, Dordrecht, The Netherlands: Kluwer Academic Press.

    Google Scholar 

  • Auer, P.: 1984, Bilingual Conversation, Amsterdam: John Benjamins.

    Google Scholar 

  • Baetens Beardsmore, H.: 1986, “Definitions and typologies”, in Bilingualism: Basic Principles, Clevedon: Multilingual Matters, pp. 1–41.

  • Barton, B., Fairhall, U. and Trinick, T.: 1998, “Tikanga Reo Tatai: Issues in the development of a Maori mathematics register”, For the Learning of Mathematics 18(1), 3–9.

    Google Scholar 

  • Bialystok, E.: 2001, Bilingualism in Development: Language, Literacy and Cognition, Cambridge Cambridge University Press.

    Google Scholar 

  • Bialystok, E.: 1999, “Cognitive complexity and attentional control in the bilingual mind”, Child Development 70, 636–644.

    Article  Google Scholar 

  • Bialystok, E. and Majunder.: 1998, “The relationship between bilingualism and the development of cognitive processes in problem solving”, Applied Psycholinguistics 19, 69–85.

    Article  Google Scholar 

  • Cazden, C.: 1986, “Classroom discourse”, in M. C. Wittrock (ed.), Handbook of Research on Teaching, New York: Macmillan.

    Google Scholar 

  • Cazden, C.: 1993, “Vygotsky, Hymes, and Bakhtin: From word to utterance to voice”, in E. Forman, N. Minnick and C. A. Stone (eds.), Contexts for Learning: Sociocultural Dynamics in Children’s Development, NY: Oxford University Press, pp. 197–212.

    Google Scholar 

  • Cook, V.: 1997, “The consequences of bilingualism for cognitive processing”, in A. de Groot and J. Kroll (eds.), Tutorials in Bilingualism, Mahwah, NJ: Erlbaum, pp. 279–299.

    Google Scholar 

  • Cumming, A.: 1989, “Writing expertise and second language proficiency”, Language Learning 39, 89–141.

    Article  Google Scholar 

  • Cumming, A.: 1990, “Meta-linguistic and ideational thinking in second language composing”, Written Communication 7, 482–511.

    Google Scholar 

  • Cummins, J.: 1976, “The influence of bilingualism on cognitive growth”, Working Papers on Bilingualism 9, 1–43.

    Google Scholar 

  • Cummins, J.: 1979, “Cognitive/academic language proficiency, linguistic interdependence, the optimum age question, and some other matters”, Working Papers on Bilingualism 19, 197–205.

    Google Scholar 

  • Cummins, J.: 1994, “Semilingualism”, in Encyclopedia of Language and Linguistics (2nd edn). Oxford: Elsevier Science.

    Google Scholar 

  • Cummins, J.: 2000, Language, Power, and Pedagogy, Buffalo, NY: Multilingual Matters.

    Google Scholar 

  • De Avila, E. and Duncan, S.: 1981, “Bilingualism and the metaset”, in R. Dur$#x00E1;n (ed.), Latino Language and Communicative Behavior, Norwood, NJ: Ablex Publishing Corporation.

  • Finegan, E. and Besnier, N.: 1989, Language: Its Structure and Use, NY: Harcourt Brace Jovanovich.

    Google Scholar 

  • Garcia, E. and Gonzalez, R.: 1995, “Issues in systemic reform for culturally and linguistically diverse students”, Teachers College Record 96(3), 418–431.

    Google Scholar 

  • Gee, J.: 1996, Social Linguistics and Literacies: Ideology in Discourses (3rd edn). London, The Falmer Press.

    Google Scholar 

  • Gee, J.: 1999, “An Introduction to Discourse Analysis: Theory and Method, NY: Routledge.

    Google Scholar 

  • Grosjean, F.: 1999, “Individual bilingualism”, in B. Spolsky (ed.), Concise Encyclopedia of Educational Linguistics, London: Elsevier, pp. 284–290.

    Google Scholar 

  • Gumperz, J.: 1982, “Discourse Strategies”, New York: Cambridge University Press.

    Google Scholar 

  • Gutierrez, K., Baquedano-Lopez, P. and Alvarez, H.: 2001, “Literacy as hybridity: Moving beyond bilingualism in urban classrooms”, in M. de la Luz Reyes and J. Halcon (eds.), The Best for Our Children: Critical Perspectives on Literacy for Latino Students, New York: Teachers College Press, pp. 122–141.

    Google Scholar 

  • Hakuta, K. and Cancino, H.: 1977, “Trends in second-language-acquisition research”, Harvard Educational Review, 47(3), 294–316.

    Google Scholar 

  • Hakuta, K. and McLaughlin, B.: 1996, “Bilingualism and second language learning: Seven tensions that define research”, in D. Berliner and R.C. Calfe (eds.), Handbook of Educational Psychology, NY: Macmillan.

    Google Scholar 

  • Halliday, M. A. K.: 1978, “Sociolinguistic aspects of mathematical education”, in M. A. K. Halliday, The Social Interpretation of Language and Meaning, London: University Park Press, pp. 194–204.

    Google Scholar 

  • Khisty, L. L.: 1995, “Making inequality: Issues of language and meanings in mathematics teaching with Hispanic students”, in W. G. Secada, E. Fennema and L. B. Adajian (eds.), New Directions for Equity in Mathematics Education, New York: Cambridge University Press, pp. 279–297.

    Google Scholar 

  • Kolers, P.: 1968, “Bilingualism and information processing”, Scientific American 218, 78–86.

    Article  Google Scholar 

  • MacSwan, J.: 2000, “The threshold hypothesis, semilingualism, and other contributions to a deficit view of linguistic minorities”, Hispanic Journal of Behavioral Sciences 22(91), 3$#x2013;45.

    Google Scholar 

  • Magiste, E.: 1980, “Arithmetic calculations in monolinguals and bilinguals”, Psychological Research 42, 363–373.

    Article  Google Scholar 

  • Malakoff, M. and Hakuta, K.: 1991, “Translation skill and meta-linguistic awareness in bilinguals”, in E. Bialystok (ed.), Language Processing in Bilingual Children, Cambridge: Cambridge University Press, pp. 141–166.

    Google Scholar 

  • Marsh, L. and Maki, R.: 1976, “Efficiency of arithmetic operations in bilinguals as a function of language”, Memory and Cognition 4, 459–464.

    Google Scholar 

  • McLain, L. and Huang, J.: 1982, “Speed of simple arithmetic in bilinguals”, Memory and Cognition 10, 591–596.

    Google Scholar 

  • Mehan, H.: 1979, Learning Lessons: Social Organization in the Classroom, Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Moschkovich, J. N.: 1999, “Supporting the participation of English language learners in mathematical discussions”, For the Learning of Mathematics 19(1), 11–19.

    Google Scholar 

  • Moschkovich, J. N.: 2002, “A situated and sociocultural perspective on bilingual mathematics learners”, Mathematical Thinking and Learning, Special issue on Diversity, Equity, and Mathematical Learning, N. Nassir and P. Cobb (eds.), 4(2 and 3), 189–212.

    Article  Google Scholar 

  • Orellana, M., Reynolds, J., Dorner, L. and Meza, M.: 2003, ‘In other words: Translating or ”para-phrasing“ as family literacy practice in immigrant households‘, Reading Research Quarterly, 38 (1), 12–34.

    Google Scholar 

  • Paulston, C.: 1982, Swedish Research and Debate About Bilingualism, Skoloverstyrselsen: National Swedish Board of Education.

    Google Scholar 

  • Pfaff, C.: 1997, “Contacts and conflict: perspectives from code switching research”, in M. Putz (ed.) Language Choices: Conditions, Constraints and Consequences, Amsterdam: John Benjamins, pp. 342–360.

    Google Scholar 

  • Pimm, D.: 1987, Speaking Mathematically: Communication in Mathematics Classrooms, London: Routledge.

    Google Scholar 

  • Qi, D.S.: 1998, “An inquiry into language-switching in second language composing processes,” Canadian Modern Language Review 54(3), 413–435.

    Google Scholar 

  • Ramirez, A. and Milk, R.: 1986, “Notions of grammaticality among teachers of bilingual pupils”, TESOL Quarterly 20(3), 495–513.

    Article  Google Scholar 

  • Roberts, T.: 1998, “Mathematical registers in aboriginal languages”, For the Learning of Mathematics 18(1), 10–16.

    Google Scholar 

  • Sanchez, R.: 1994, Chicano Discourse: Socio-Historic Perspectives, Houston, TX: Arte Público Press.

    Google Scholar 

  • Setati, M.: 1998, “Code-switching and mathematical meaning in a senior primary class of second language learners”, For the Learning of Mathematics 18(1), 34–40.

    Google Scholar 

  • Setati, M. and Adler, J.: 2001, “Between languages and discourses: Code switching practices in primary classrooms in South Africa”, Educational Studies in Mathematics 43, 243–269.

    Article  Google Scholar 

  • Skutnabb-Kangas, T.: 1984, Bilingualism or Not: The Education of Minorities, Clevedon: Multilingual Matters.

    Google Scholar 

  • Tamamaki, K.: 1993, “Language dominance in bilinguals arithmetic operations according to their language use”, Language Learning 43(2), 239–262.

    Article  Google Scholar 

  • Torres, L.: 1997, Puerto Rican Discourse: A Sociolinguistic Study of a New York Suburb, Mahwah, NJ: LEA.

    Google Scholar 

  • Tse, L.: 2001, Who don’t they just learn English? Separating fact from fallacy in the U.S. language debate. NY, NY: Teachers College Press.

    Google Scholar 

  • Valdés-Fallis, G.: 1978, “Code switching and the classroom teacher”, Language in Education: Theory and Practice, Volume 4. Wellington, VA: Center for Applied Linguistics.

  • Valdés-Fallis, G.: 1979, “Social interaction and code switching patterns: A case study of Spanish/English alternation”, In G. D. Keller, R.V. Teichner, and S. Viera (eds.), Bilingualism in the Bicentennial and Beyond, Jamaica, NY: Bilingualism Press.

    Google Scholar 

  • Zentella, A. C.: 1997, Growing up Bilingual: Puerto Rican Children in New York, Malden, MA: Blackwell Publishers.

    Google Scholar 

  • Zentella, A.C.: 1981, “T$#x00E1; bien, You could answer me en cualquier idioma: Puerto Rican code switching in bilingual classrooms”, In R. Dur$#x00E1;n (ed.), Latino Language and Communicative Behavior, Norwood, NJ: Ablex Publishing Corporation, pp. 109–130.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Education Department, University of California, Santa 755 Cruz, 1156 High Street, Santa Cruz, CA, 95064, USA

    Judit Moschkovich

Authors
  1. Judit Moschkovich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Judit Moschkovich.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moschkovich, J. Using Two Languages When Learning Mathematics. Educ Stud Math 64, 121–144 (2007). https://doi.org/10.1007/s10649-005-9005-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-005-9005-1

Keywords

Search

Navigation