Volume 3, Issue 2
  • ISSN 2212-8433
  • E-ISSN: 2212-8441
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This article describes the interaction between mathematics and language, based on an analysis of how individual learners solve word problems in English as a foreign language (L2). It reports on a study conducted to investigate how the L2 influences mathematical thinking and learning in the process of solving word problems and how the construction of meaning unfolds. The research generated the Integrated Language and Mathematics Model (ILMM), which facilitates the description of the interplay between mathematics and language. The empirical results show, inter alia, that CLIL learners tend to use the given text more profoundly for stepwise deduction of a mathematical model, and conversely, mathematical activity can lead to more intense language activity. Furthermore, effective mathematical activity depends on successful text reception, and problem solving in a L2 provides additional opportunities for reflection, both linguistically and conceptually. The ILMM makes a major contribution to conceptualising content and language integration.


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  1. 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]
  2. Barwell, R
    (2005) Integrating language and content: Issues from the mathematics classrooom. Linguistics and Education, 16, 205–218. doi: 10.1016/j.linged.2006.01.002
    https://doi.org/10.1016/j.linged.2006.01.002 [Google Scholar]
  3. (2009) Mathematical word problems and bilingual learners in England. In R. Barwell (Ed.), Multilingualism in mathematics classrooms: Global perspectives (pp. 63–77). Bristol: Multilingual Matters.
    [Google Scholar]
  4. Bauersfeld, H
    (1995) ‘Language games’ in the classroom: Their function and their effects. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 271–292). Hillsdale, NJ: Lawrence Erlbaum.
    [Google Scholar]
  5. Berger, A
    (2013) Mathematiklernen im bilingualen Diskurs: Ein integriertes Sprache-Mathematik-Modell des Lösens von Textaufgaben mit Englisch als Arbeitssprache. [Learning mathematics bilingually: An Integrated Language and Mathematics Model (ILMM) of word problem solving processes in English as a foreign language.] Doctoral thesis, University of Vienna, Vienna, Austria.
    [Google Scholar]
  6. Blum, W. , & Leiß, D
    (2005) Modellieren im Unterricht mit der ‘Tanken’ - Aufgabe. [Mathematical modelling in the classroom by means of the “filling up“ task] Mathematik Lehren, 128, 18–21.
    [Google Scholar]
  7. (2007) How do students and teachers deal with modelling problems?In C. Haines , P. Galbraith , W. Blum , & S. Khan (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics: Proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications (pp. 222–231). Chichester: Horwood.
    [Google Scholar]
  8. Borromeo Ferri, R
    (2006) Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik, 38(2), 86–95. doi: 10.1007/BF02655883
    https://doi.org/10.1007/BF02655883 [Google Scholar]
  9. (2011) Wege zur Innenwelt des Mathematischen Modellierens: Kognitive Analysen zu Modellierungsprozessen im Mathematikunterricht. [Paths to the inner world of mathematical modelling: Cognitive analyses of modelling processes in mathematics lessons.] Wiesbaden: Vieweg & Teubner (GWV). doi: 10.1007/978‑3‑8348‑9784‑8
    https://doi.org/10.1007/978-3-8348-9784-8 [Google Scholar]
  10. Clarkson, P
    (1992) Language and mathematics: A comparison of bilingual and monolingual students of mathematics. Educational Studies in Mathematics, 23(4), 417–429. doi: 10.1007/BF00302443
    https://doi.org/10.1007/BF00302443 [Google Scholar]
  11. (2007) Australian Vietnamese students learning mathematics: High ability bilinguals and their use of their languages. Educational Studies in Mathematics, 64, 191–215. doi: 10.1007/s10649‑006‑4696‑5
    https://doi.org/10.1007/s10649-006-4696-5 [Google Scholar]
  12. (2009) Mathematics teaching in Australian multilingual classrooms: Developing an approach to the use of classroom languages. In R. Barwell (Ed.), Multilingualism in mathematics classrooms: Global perspectives (pp. 145–160). Bristol: Multilingual Matters.
    [Google Scholar]
  13. De Bot, K
    (1992) A bilingual production model: Levelt’s speaking model adapted. Applied Linguistics, 13(1), 1–24. doi: 10.1093/applin/13.1.1
    https://doi.org/10.1093/applin/13.1.1 [Google Scholar]
  14. Ehlich, K. , & Rehbein, J
    (1976) Halbinterpretative Arbeitstranskription (HIAT). [Heuristic Interpretative Auditory Transcription.]Linguistische Berichte, 45, 21–41.
    [Google Scholar]
  15. Ericsson, K.A. , & Simon, H.A
    (1993) Protocol analysis: Verbal reports as data (2nd ed.). Cambridge, MA: MIT Press.
    [Google Scholar]
  16. Khisty, L
    (1995) Making inequality: Issues of language and meanings in mathematics teaching with Hispanic students. In W. Secada , E. Fennema , & L. Byrd Adajian (Eds.), New directions for equity in mathematics education (pp. 279–297). New York: Cambridge University Press.
    [Google Scholar]
  17. (2001) Effective teachers of second language learners in mathematics. In M. Van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (pp.225–232). Utrecht: The Freudenthal Institute, Utrecht University.
    [Google Scholar]
  18. Kintsch, W. , & Greeno, J
    (1985) Understanding and solving word arithmetic problems. Psychological Review, 92(1), 109–129. doi: 10.1037/0033‑295X.92.1.109
    https://doi.org/10.1037/0033-295X.92.1.109 [Google Scholar]
  19. Knoblich, G. , & Öllinger, M
    (2006) Die Methode des lauten Denkens. [The think-aloud method.] In J. Funke (Ed.), Handbuch der Allgemeinen Psychologie – Kognition (pp. 691–696). Göttingen: Hogrefe.
    [Google Scholar]
  20. Levelt, W
    (1989) Speaking: From intention to articulation (5th ed.). Cambridge, MA: MIT Press.
    [Google Scholar]
  21. Lemke, J
    (2003) Mathematics in the middle: Measure, picture, gesture, sign, and word. In M. Anderson (Ed.), Educational perspectives on mathematics as semiosis: From thinking to interpreting to knowing (pp. 215–234). Ottawa: Legas.
    [Google Scholar]
  22. Liu, K.K
    (2015) The influence of the math classroom context on students’ academic English production. Journal of Immersion and Content-Based Language Education, 3(1), 127–147. doi: 10.1075/jicb.3.1.06liu
    https://doi.org/10.1075/jicb.3.1.06liu [Google Scholar]
  23. Moschkovich, J.N
    (2007) Examining mathematical discourse practices. For the Learning of Mathematics, 27(1), 24–30.
    [Google Scholar]
  24. Novotná, J
    (2004) Modelling the word problem solving process. An instrument to determine places suitable for teacher’s intervention. In H.-W. Henn (Ed.), Applications and modelling in mathematics education: Study Conference in Dortmund (Germany), February 13 - 17, 2004; pre-conference volume (ICMI study 14) (pp.193–198). University of Dortmund, Department of Mathematics IEEM.
    [Google Scholar]
  25. Novotná, J. , Hadj-Moussová, Z. , & Hofmannova, M
    (2001) Teacher training for CLIL - Competences of a CLIL teacher. In M. Hejny & J. Novotná (Eds.), Proceedings SEMT 01 (pp.122–126). Praha: Univerzita Karlova v Praze, Pedagogicka fakulta. Retrieved fromwww.content-english.org/data/Novotna.doc.
    [Google Scholar]
  26. O’Halloran, K.L
    (2005) Mathematical discourse: Language, symbolism and visual images. London: Continuum.
    [Google Scholar]
  27. Pimm, D
    (1987) Speaking mathematically: Communication in mathematics classrooms. New York: Routledge & K. Paul.
    [Google Scholar]
  28. Poulisse, N. , & Bongaerts, T
    (1994) First language use in second language production. Applied Linguistics, 15(1), 36–57. doi: 10.1093/applin/15.1.36
    https://doi.org/10.1093/applin/15.1.36 [Google Scholar]
  29. Reusser, K
    (1985) From situation to equation. On formulation understanding and solving “situation problems”. Technical Report 143. Boulder: University of Colorado, Institute of Cognitive Science.
    [Google Scholar]
  30. (1997) Erwerb mathematischer Kompetenzen: Literaturüberblick. Mathematische Textaufgaben als Unterrichts- und Forschungsgegenstand. [Aquisition of mathematical competences: Literature review. Mathematical word problems as an object of teaching and research.] In F.E. Weinert & A. Helmke (Eds.), Entwicklung im Grundschulalter (pp.141–155). Weinheim: Beltz Psychologie-Verl.-Union.
    [Google Scholar]
  31. Setati, M. , & Adler, J
    (2001) Between languages and discourses: Code switching practices in primary classrooms in South Africa. Educational Studies in Mathematics, 43, 243–269. doi: 10.1023/A:1011996002062
    https://doi.org/10.1023/A:1011996002062 [Google Scholar]
  32. Sfard, A
    (2001) Learning mathematics as developing a discourse. In R. Speiser , C. Maher , & C. Walter (Eds.), Proceedings of 21st Conference of PME-NA (pp.23–44). Columbus, OH: Clearing House for Science, Mathematics and Environmental Education.
    [Google Scholar]
  33. (2008) Thinking as communicating: Human development, the growth of discourses, and mathematizing. New York: Cambridge University Press. doi: 10.1017/CBO9780511499944
    https://doi.org/10.1017/CBO9780511499944 [Google Scholar]
  34. Sfard, A. , & Lavie, I
    (2005) Why cannot children see as the same what grown-ups cannot see as different? - Early numerical thinking revisited. Cognition and Instruction, 23(2), 237–309. doi: 10.1207/s1532690xci2302_3
    https://doi.org/10.1207/s1532690xci2302_3 [Google Scholar]
  35. Swain, M
    (2006) Languaging, agency and collaboration in advanced second language proficiency. In H. Byrnes (Ed.), Advanced language learning: The contribution of Halliday and Vygotsky (pp. 95–108). London: Continuum.
    [Google Scholar]
  36. Turnbull, M. , Hart, D. , & Lapkin, S
    (2000) French immersion students’ performance on grade 3 provincial tests: Potential impacts on program design. Final report submitted to the Education Quality and Accountability Office. Toronto, CA: University of Toronto. Retrieved fromon.cpf.ca/wp-content/blogs.dir/1/files/eqao-final-report-2001.pdf.
    [Google Scholar]
  37. Weir, C. , & Khalifa, H
    (2008) A cognitive processing approach towards defining reading comprehension. Cambridge ESOL: Research notes, 31, 2–10.
    [Google Scholar]
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