Learning Mathematics in a Second Language: Language Positive and Language Neutral Classrooms

Research focused on learning mathematics in a 2nd language is generally located in individual 2nd-language contexts. In this ethnographic study, I investigated mathematics learning in 4 different second-language contexts: a mainstream classroom, a sheltered classroom for Indigenous students, a welcome class for new immigrants, and a French-immersion classroom. The study was framed by a view of learning as socialization and the Bakhtinian notion of centripetal and centrifugal language forces. I present 7 socialization events that were particularly salient in 1 or more of the classrooms. For each socialization event, I identify various socialization practices. Based on a comparison of socialization practices in the 4 classrooms, I propose a distinction between language positive and language neutral mathematics classrooms. In language positive mathematics classrooms, students’ socialization into mathematics and language includes explicit attention to different aspects of language use in mathematics. In language neutral mathematics classrooms, the role of language in mathematics tends to be implicit.

Footnotes

The data collection for this research was funded by the Social Science and Humanities Research Council of Canada Grant No. 410-2008-0544. I am sincerely grateful to the teachers and students who participated in the study and from whom I learned a great deal. I thank Adil Dsousa, Carrie Learned, Jennifer Chew Leung, Maya Shrestra, Maha Sinno, and Élysée Cadet for their assistance with different aspects of the project.

Contributor Notes

Richard Barwell, Faculty of Education, University of Ottawa, 145 J-J-Lussier, Ottawa, Ontario, Canada; richard.barwell@uottawa.ca

(Corresponding author is Barwell richard.barwell@uottawa.ca)
Journal for Research in Mathematics Education
  • 1.

    AbediJ. (2009). Validity of assessments for English language learning students in a national/international context. Estudios sobre Educación16167183.

    • Search Google Scholar
    • Export Citation
  • 2.

    AbediJ. & LordC. (2001). The language factor in mathematics tests. Applied Measurement in Education14(3) 219234. doi:10.1207/s15324818ame1403_2

    • Search Google Scholar
    • Export Citation
  • 3.

    AdlerJ. (2001). Teaching mathematics in multilingual classrooms. Dordrecht, The Netherlands: Kluwer Academic Press. doi:10.1007/0-306-47229-5

    • Search Google Scholar
    • Export Citation
  • 4.

    BakhtinM. M. (1981). The dialogic imagination: Four essays ( M. Holquist Ed.; C. Emerson & M. Holquist Trans.). Austin: University of Texas Press.

    • Search Google Scholar
    • Export Citation
  • 5.

    Bakhtin M. M. (1986). Speech genres and other late essays ( C. Emerson & M. Holquist Eds.; V. W. McGee Trans.). Austin: University of Texas Press.

    • Search Google Scholar
    • Export Citation
  • 6.

    BarwellR. (2005a). Integrating language and content: Issues from the mathematics classroom. Linguistics and Education16(2) 205218. doi:10.1016/j.linged.2006.01.002

    • Search Google Scholar
    • Export Citation
  • 7.

    BarwellR. (2005b). Working on arithmetic word problems when English is an additional language. British Educational Research Journal31(3) 329348. doi:10.1080/01411920500082177

    • Search Google Scholar
    • Export Citation
  • 8.

    BarwellR. (2012). Heteroglossia in multilingual mathematics classrooms. In H. Forgasz & F. Rivera (Eds.) Towards equity in mathematics education: Gender culture and diversity (pp. 315332). Heidelberg, Germany: Springer. doi:10.1007/978-3-642-27702-3_28

    • Search Google Scholar
    • Export Citation
  • 9.

    BarwellR. (2014). Centripetal and centrifugal language forces in one elementary school second language mathematics classroom. ZDM—The International Journal on Mathematics Education46(6) 911922. doi:10.1007/s11858-014-0611-1

    • Search Google Scholar
    • Export Citation
  • 10.

    BarwellR. (2016). Formal and informal mathematical discourses: Bakhtin and Vygotsky, dialogue and dialectic. Educational Studies in Mathematics92(3) 331345. doi:10.1007/s10649-015-9641-z

    • Search Google Scholar
    • Export Citation
  • 11.

    BarwellR. (2017). Mathematical texts, alterity and the expropriation of mathematical discourse in second language mathematics classrooms. In J. Langman & H. Hansen-Thomas (Eds.) Discourse analytic perspectives on STEM education: Exploring interaction and learning in the multilingual classroom (pp. 119137). Cham, Switzerland: Springer. doi:10.1007/978-3-319-55116-6_7

    • Search Google Scholar
    • Export Citation
  • 12.

    BarwellR. (2018). From language as a resource to sources of meaning in multilingual mathematics classrooms. Journal of Mathematical Behavior50155168. doi:10.1016/j.jmathb.2018.02.007

    • Search Google Scholar
    • Export Citation
  • 13.

    BarwellR. ClarksonP. HalaiA. KazimaM. MoschkovichJ. PlanasN. Villavicencio UbillúsM. (Eds.). (2016). Mathematics education and language diversity: The 21st ICMI study. Cham, Switzerland: Springer. doi:10.1007/978-3-319-14511-2

    • Search Google Scholar
    • Export Citation
  • 14.

    BarwellR. MoschkovichJ. & Setati PhakengM. (2017). Language diversity and mathematics: Second language, bilingual, and multilingual learners. In J. Cai (Ed.) Compendium for research in mathematics education (pp. 583606). Reston, VA: National Council of Teachers of Mathematics.

    • Search Google Scholar
    • Export Citation
  • 15.

    BlackledgeA. & CreeseA. (Eds.). (2014). Heteroglossia as practice and pedagogy. Dordrecht, The Netherlands: Springer. doi:10.1007/978-94-007-7856-6

    • Search Google Scholar
    • Export Citation
  • 16.

    BoseA. & ClarksonP. (2016). Students’ use of their languages and registers: An example of the socio-cultural role of language in multilingual classrooms. In A. Halai & P. Clarkson (Eds.) Teaching and learning mathematics in multilingual classrooms: Issues for policy practice and teacher education (pp. 125141). Rotterdam, The Netherlands: Sense. doi:10.1007/978-94-6300-229-5_9

    • Search Google Scholar
    • Export Citation
  • 17.

    Bournot-TritesM. & ReederK. (2001). Interdependence revisited: Mathematics achievement in an intensified French immersion program. The Canadian Modern Language Review/La revue canadienne des langues vivantes58(1) 2743. doi:10.3138/cmlr.58.1.27

    • Search Google Scholar
    • Export Citation
  • 18.

    CivilM. & TurnerE. (Eds.). (2014). The common core state standards in mathematics for English language learners: Grades K-8. Reston, VA: National Council of Teachers of Mathematics.

    • Search Google Scholar
    • Export Citation
  • 19.

    ClarksonP. C. (2007). Australian Vietnamese students learning mathematics: High ability bilinguals and their use of their languages. Educational Studies in Mathematics64(2) 191215. doi:10.1007/s10649-006-4696-5

    • Search Google Scholar
    • Export Citation
  • 20.

    CrandallJ. (Ed.). (1987). ESL through content-area instruction: Mathematics science social studies. Englewood Cliffs, NJ: Prentice Hall Regents.

    • Search Google Scholar
    • Export Citation
  • 21.

    CreeseA. (2005). Teacher collaboration and talk in multilingual classrooms. Clevedon, United Kingdom: Multilingual Matters. doi:10.21832/9781853598234

    • Search Google Scholar
    • Export Citation
  • 22.

    CumminsJ. (2000). Language power and pedagogy: Bilingual children in the crossfire. Clevedon, United Kingdom: Multilingual Matters. doi:10.21832/9781853596773

    • Search Google Scholar
    • Export Citation
  • 23.

    de AraujoZ. RobertsS. A. WilleyC. & ZahnerW. (2018). English learners in K–12 mathematics education: A review of the literature. Review of Educational Research88(6) 879919. doi:10.3102/0034654318798093

    • Search Google Scholar
    • Export Citation
  • 24.

    DuffP. A. (1995). An ethnography of communication in immersion classrooms in Hungary. Tesol Quarterly29(3) 505537. doi:10.2307/3588073

    • Search Google Scholar
    • Export Citation
  • 25.

    DuffP. A. (1996). Different languages, different practices: Socialization of discourse competence in dual-language school classrooms in Hungary. In K. M. Bailey & D. Nunan (Eds.) Voices from the language classroom (pp. 407433). Cambridge, United Kingdom: Cambridge University Press.

    • Search Google Scholar
    • Export Citation
  • 26.

    DuffP. (2001). Language, literacy, content, and (pop) culture: Challenges for ESL students in mainstream courses. The Canadian Modern Language Review58(1) 103132. doi:10.3138/cmlr.58.1.103

    • Search Google Scholar
    • Export Citation
  • 27.

    DuffP. A. (2002). The discursive co-construction of knowledge, identity, and difference: An ethnography of communication in the high school mainstream. Applied Linguistics23(3) 289322. doi:10.1093/applin/23.3.289

    • Search Google Scholar
    • Export Citation
  • 28.

    DurantiA. (1997). Linguistic anthropology. Cambridge, United Kingdom: Cambridge University Press. doi:10.1017/cbo9780511810190

  • 29.

    ErathK. PredigerS. QuasthoffU. & HellerV. (2018). Discourse competence as important part of academic language proficiency in mathematics classrooms: The case of explaining to learn and learning to explain. Educational Studies in Mathematics99(2) 161179. doi:10.1007/s10649-018-9830-7

    • Search Google Scholar
    • Export Citation
  • 30.

    FarrugiaM. T. (2009). Reflections on a medium of instruction policy for mathematics in Malta. In R. Barwell (Ed.) Multilingualism in mathematics classrooms: Global perspectives (pp. 97112). Bristol, United Kingdom: Multilingual Matters. doi:10.21832/9781847692061-009

    • Search Google Scholar
    • Export Citation
  • 31.

    GibbonsP. (1998). Classroom talk and the learning of new registers in a second language. Language and Education12(2) 99118. doi:10.1080/09500789808666742

    • Search Google Scholar
    • Export Citation
  • 32.

    HeathS. B. (1983). Ways with words: Language life and work in communities and classrooms. Cambridge, United Kingdom: Cambridge University Press. doi:10.1017/cbo9780511841057

    • Search Google Scholar
    • Export Citation
  • 33.

    HymesD. (1974). Foundations in sociolinguistics: An ethnographic approach. Philadelphia: University of Pennsylvania Press. doi:10.4324/9781315888835

    • Search Google Scholar
    • Export Citation
  • 34.

    JonesD. V. (2009). Bilingual mathematics classrooms in Wales. In R. Barwell (Ed.) Multilingualism in mathematics classrooms: Global perspectives (pp. 113127). Bristol, United Kingdom: Multilingual Matters. doi:10.21832/9781847692061-010

    • Search Google Scholar
    • Export Citation
  • 35.

    KhistyL. L. (1995). Making inequality: Issues of language and meanings in mathematics teaching with Hispanic students. In W. G. Secada E. Fennema & L. B. Adajian (Eds.) New directions for equity in mathematics education (pp. 279297). Cambridge, United Kingdom: Cambridge University Press.

    • Search Google Scholar
    • Export Citation
  • 36.

    LermanS. (2001). Cultural, discursive psychology: A sociocultural approach to studying the teaching and learning of mathematics. Educational Studies in Mathematics46(1/3) 87113. doi:10.1023/A:1014031004832

    • Search Google Scholar
    • Export Citation
  • 37.

    LimC. S. & PresmegN. (2011). Teaching mathematics in two languages: A teaching dilemma of Malaysian Chinese primary schools. International Journal of Science and Mathematics Education9(1) 137161. doi:10.1007/s10763-010-9225-4

    • Search Google Scholar
    • Export Citation
  • 38.

    MaybinJ. (2006). Children’s voices: Talk knowledge and identity. Basingstoke, United Kingdom: Palgrave Macmillan. doi:10.1057/9780230511958

    • Search Google Scholar
    • Export Citation
  • 39.

    MaybinJ. & TustingK. (2011). Linguistic ethnography. In J. Simpson (Ed.) The Routledge handbook of applied linguistics (pp. 515528). Abingdon, United Kingdom: Routledge. doi:10.4324/9780203835654.ch36

    • Search Google Scholar
    • Export Citation
  • 40.

    MohanB. (2001). The second language as a medium of learning. In B. Mohan C. Leung & C. Davison (Eds.) English as a second language in the mainstream: Teaching learning and identity (pp. 107126). Harlow, United Kingdom: Longman.

    • Search Google Scholar
    • Export Citation
  • 41.

    MonaghanF. (1999). Judging a word by the company it keeps: The use of concordancing software to explore aspects of the mathematics register. Language and Education13(1) 5970. doi:10.1080/09500789908666759

    • Search Google Scholar
    • Export Citation
  • 42.

    MoschkovichJ. N. (2002). A situated and sociocultural perspective on bilingual mathematics learners. Mathematical Thinking and Learning4(2&3) 189212. doi:10.1207/S15327833MTL04023_5

    • Search Google Scholar
    • Export Citation
  • 43.

    MoschkovichJ. (2008). “I went by twos, he went by one”: Multiple interpretations of inscriptions as resources for mathematical discussions. The Journal of the Learning Sciences17(4) 551587. doi:10.1080/10508400802395077

    • Search Google Scholar
    • Export Citation
  • 44.

    MoschkovichJ. (2013). Principles and guidelines for equitable mathematics teaching practices and materials for English language learners. Journal of Urban Mathematics Education6(1) 4557.

    • Search Google Scholar
    • Export Citation
  • 45.

    Ní RíordáinM. & O’DonoghueJ. (2009). The relationship between performance on mathematical word problems and language proficiency for students learning through the medium of Irish. Educational Studies in Mathematics71(1) 4364. doi:10.1007/s10649-008-9158-9

    • Search Google Scholar
    • Export Citation
  • 46.

    OchsE. (1986). Introduction. In B. B. Schieffelin & E. Ochs (Eds.) Language socialization across cultures (pp. 113). Cambridge, United Kingdom: Cambridge University Press. doi:10.1017/cbo9780511620898.001

    • Search Google Scholar
    • Export Citation
  • 47.

    PlanasN. & SetatiM. (2009). Bilingual students using their languages in the learning of mathematics. Mathematics Education Research Journal21(3) 3659. doi:10.1007/bf03217552

    • Search Google Scholar
    • Export Citation
  • 48.

    RamptonB. (1995). Crossing: Language and ethnicity among adolescents. London, United Kingdom: Longman.

  • 49.

    RamptonB. MaybinJ. & RobertsC. (2015). Theory and method in linguistic ethnography. In J. Snell S. Shaw & F. Copland (Eds.) Linguistic ethnography: Interdisciplinary explorations (pp. 1450). London, United Kingdom: Palgrave Macmillan. doi:10.1057/9781137035035_2

    • Search Google Scholar
    • Export Citation
  • 50.

    SecadaW. G. (1991). Degree of bilingualism and arithmetic problem solving in Hispanic first graders. Elementary School Journal92(2) 213231. doi:10.1086/461689

    • Search Google Scholar
    • Export Citation
  • 51.

    SecadaW. G. (1992). Race, ethnicity, social class, language, and achievement in mathematics. In D. A. Grouws (Ed.) Handbook of research on mathematics teaching and learning (pp. 623660). New York, NY: Macmillan.

    • Search Google Scholar
    • Export Citation
  • 52.

    SetatiM. (2005). Teaching mathematics in a primary multilingual classroom. Journal for Research in Mathematics Education36(5) 447466. doi:10.2307/30034945

    • Search Google Scholar
    • Export Citation
  • 53.

    SetatiM. MolefeT. & LangaM. (2008). Using language as a transparent resource in the teaching and learning of mathematics in a Grade 11 multilingual classroom. Pythagoras671425. doi:10.4102/pythagoras.v0i67.70

    • Search Google Scholar
    • Export Citation
  • 54.

    SfardA. (2008). Thinking as communicating: Human development the growth of discourses and mathematizing. Cambridge, United Kingdom: Cambridge University Press. doi:10.1017/cbo9780511499944

    • Search Google Scholar
    • Export Citation
  • 55.

    StreetB. V. (1985). Literacy in theory and practice. Cambridge, United Kingdom: Cambridge University Press.

  • 56.

    Watson-GegeoK. A. & NielsenS. (2003). Language socialization in SLA. In C. J. Doughty & M. H. Long (Eds.) The handbook of second language acquisition (pp. 155177). Oxford, United Kingdom: Blackwell. doi:10.1002/9780470756492.ch7

    • Search Google Scholar
    • Export Citation

Metrics

All Time Past Year Past 30 Days
Abstract Views 153 153 41
Full Text Views 136 136 11
PDF Downloads 104 104 6
EPUB Downloads 0 0 0