Advertisement

Educational Studies in Mathematics

, Volume 71, Issue 1, pp 43–64 | Cite as

The relationship between performance on mathematical word problems and language proficiency for students learning through the medium of Irish

  • Máire Ní RíordáinEmail author
  • John O’Donoghue
Article

Abstract

Ireland has two official languages—Gaeilge (Irish) and English. Similarly, primary- and second-level education can be mediated through the medium of Gaeilge or through the medium of English. This research is primarily focused on students (Gaeilgeoirí) in the transition from Gaeilge-medium mathematics education to English-medium mathematics education. Language is an essential element of learning, of thinking, of understanding and of communicating and is essential for mathematics learning. The content of mathematics is not taught without language and educational objectives advocate the development of fluency in the mathematics register. The theoretical framework underpinning the research design is Cummins’ (1976). Thresholds Hypothesis. This hypothesis infers that there might be a threshold level of language proficiency that bilingual students must achieve both in order to avoid cognitive deficits and to allow the potential benefits of being bilingual to come to the fore. The findings emerging from this study provide strong support for Cummins’ Thresholds Hypothesis at the key transitions—primary- to second-level and second-level to third-level mathematics education—in Ireland. Some implications and applications for mathematics teaching and learning are presented.

Keywords

Bilingualism Cummins’ thresholds hypothesis Educational transitions Mathematics word problems and language proficiency 

Notes

Acknowledgements

This research is funded by the Mathematics Applications Consortium for Science and Industry (MACSI), through Science Foundation Ireland (SFI), and in conjuction with the National Centre for Excellence in Mathematics and Science - Teaching and Learning (NCE-MSTL) at the University of Limerick. Any opinions, findings, conclusions or recommendations are those of the authors and do not necessarily reflect the views of the foundations. The authors are grateful for the comments from various reviewers during different stages of writing the paper.

References

  1. Adetula, L. O. (1990). Language factor: does it affect children’s performance on word problems? Educational Studies in Mathematics, 21(4), 351–365. doi: 10.1007/BF00304263.CrossRefGoogle Scholar
  2. Adler, J., & Setati, M. (2000). Between languages and discourses: language practices in primary multilingual mathematics classrooms in South Africa. Educational Studies in Mathematics, 43(3), 243–269. doi: 10.1023/A:1011996002062.CrossRefGoogle Scholar
  3. Allalouf, A., Hambleton, R., & Sireci, S. (1999). Identifying the causes of translation DIF on verbal items. Journal of Educational Measurement, 36, 185–198. doi: 10.1111/j.1745-3984.1999.tb00553.x.CrossRefGoogle Scholar
  4. Baker, C. (2001). Foundations of Bilingual Education (3rd ed.). Clevedon: Multilingual Matters.Google Scholar
  5. Baker, C., & Prys Jones, S. (1998). Encyclopedia of Bilingualism and Bilingual Education. Clevedon: Multilingual Matters.Google Scholar
  6. Barton, B., Chan, R., King, C., Neville-Barton, P., & Sneddon, J. (2005). EAL undergraduates learning mathematics. International Journal of Mathematical Education in Science and Technology, 36(7), 721–729. doi: 10.1080/00207390500270950.CrossRefGoogle Scholar
  7. Barton, B., & Neville-Barton, P. (2003). Language issues in undergraduate mathematics: a report of two studies. New Zealand Journal of Mathematics, 32, 19–28 Supplementary Issue.Google Scholar
  8. Barwell, R. (2003). Patterns of attention in the interaction of a primary school mathematics student with English as an additional language. Educational Studies in Mathematics, 53(1), 35–59. doi: 10.1023/A:1024659518797.CrossRefGoogle Scholar
  9. Bialystok, E. (1988). Levels of bilingualism and levels of linguistic awareness. Developmental Psychology, 24, 560–567. doi: 10.1037/0012-1649.24.4.560.CrossRefGoogle Scholar
  10. Bournot-Trites, M., & Tellowitz, U. (2002). Report of current research on the effects of second language learning on first language literacy skills. Canada: The Atlantic Provinces Educational Foundation.Google Scholar
  11. Cambridge Examinations Publishing (2002). Cambridge certificate of proficiency in English. Cambridge: Cambridge University Press.Google Scholar
  12. Capps, L. R., & Pickreign, J. (1993). Language connections in mathematics: a critical part of mathematics instruction. The Arithmetic Teacher, 4(1), 8–12.Google Scholar
  13. Clarkson, P. C. (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.CrossRefGoogle Scholar
  14. Clarkson, P. C. (2007). Australian Vietnamese students learning mathematics: high ability bilinguals and their use of their languages. Educational Studies in Mathematics, 64(2), 191–215. doi: 10.1007/s10649-006-4696-5.CrossRefGoogle Scholar
  15. Cummins, J. (1976). The influence of bilingualism on cognitive growth: a synthesis of research findings and exploratory hypotheses. Working Papers on Bilingualism, 9, 1–43.Google Scholar
  16. Cummins, J. (1977). Immersion education in Ireland: a critical review of MacNamara’s findings (with replies). Working Papers on Bilingualism, 13, 121–129.Google Scholar
  17. Cummins, J. (1979a). Linguistic interdependence and the educational development of bilingual children. Review of Educational Research, 49(2), 222–251.Google Scholar
  18. Cummins, J. (1979b). Cognitive/academic language proficiency, linguistic interdependence, the optimum age question. Working Papers on Bilingualism, 19, 121–129.Google Scholar
  19. Cummins, J. (2000). Language, power and pedagogy: Bilingual children in the crossfire. Clevedon: Multilingual Matters.Google Scholar
  20. Dawe, L. (1983). Bilingualism and mathematical reasoning in English as a second language. Educational Studies in Mathematics, 14(4), 325–353. doi: 10.1007/BF00368233.CrossRefGoogle Scholar
  21. Department of Education and Science. Education Act 1998, Dublin: Stationary Office.Google Scholar
  22. Ellerton, N. F., & Clarkson, P. C. (1996). Language factors in mathematics teaching and learning. In A. J. Bishop (Ed.), International Handbook of Mathematics Education (Vol. 4) (pp. 987–1033). Netherlands: Kluwer.Google Scholar
  23. Evans, S. (2007). Differential performance of items in mathematics assessment materials for 7-year-old pupils in English-medium and Welsh-medium versions. Educational Studies in Mathematics, 64(2), 145–168. doi: 10.1007/s10649-006-1634-5.CrossRefGoogle Scholar
  24. Fás ar an nGaelscolaíocht sa Ghalltacht (2005). Available at http://www.gaelscoileanna.ie (accessed on 10th January, 2005).
  25. Fredrickson, N., & Cline, T. (1996). The development of a model of curriculum related assessment. In N. Fredrickson, & T. Cline (Eds.), Curriculum Related Assessment, Cummins and Bilingual Children. Clevedon: Multilingual Matters.Google Scholar
  26. Galligan, L. (1995). Comparison of Chinese and English mathematical word problems: consequences of student understanding. In R. P. Hunting, G. E. FitzSimons, P. C. Clarkson, & A. J. Bishop (Eds.), Regional Collaboration in Mathematics Education (pp. 271–282). Melbourne: Monash University.Google Scholar
  27. Gorgorió, N., & Planas, N. (2001). Teaching mathematics in multilingual classrooms. Educational Studies in Mathematics, 47(1), 7–33. doi: 10.1023/A:1017980828943.CrossRefGoogle Scholar
  28. Hater, M. A., & Kane, R. B. (1975). The cloze procedure as a measure of mathematical English. Journal for Research in Mathematics Education, 6(2), 121–127. doi: 10.2307/748613.CrossRefGoogle Scholar
  29. Hoffman, C. (1991). An introduction to Bilingualism. Harlow, England: Longman.Google Scholar
  30. Johnstone, R. M., Harlen, W., MacNeil, M., Stradling, B., & Thorpe, G. (1999). The attainments of learners receiving Gaelic-medium primary education in Scotland. Sterling: Scottish CILT.Google Scholar
  31. Jongsma, E. (1971). The cloze procedure: A Survey of Research. Bloomington: Indiana University School of Education.Google Scholar
  32. Lasagabaster, D. (1998). The threshold hypothesis applied to three languages in contact at school. International Journal of Bilingual Education and Bilingualism, 1(2), 119–134.CrossRefGoogle Scholar
  33. MacDonnacha, S., Ní Chualáin, F., Ní Shéaghdha, A., & Ní Mhainín, T. (2005). Staid Reatha na Scoileanna Gaeltachta. Baile Atha Cliath: An Chomhairle um Oideachas Gaeltachta & Gaelscolaíochta (The Current State of Gaeltacht Schools).Google Scholar
  34. MacNamara, J. (1966). Bilingualism and primary education: A study of the Irish experience. Edinburgh: University Press.Google Scholar
  35. Marsh, H. W., Hau, K. T., & Kong, C. K. (2000). Late immersion and language of instruction in Hong Kong high schools: Achievement growth in language and non-language subjects. Harvard Educational Review, 70(3), 303–346.Google Scholar
  36. May, S., Hill, R., & Tiakiwai, S. (2004). Bilingual/Immersion Education: Indicators of Good Practice. Final Report to the Ministry of Education. New Zealand: Wilf Malcolm Institute of Educational Research, School of Education, University of Waikato.Google Scholar
  37. Mohan, B., & Slater, T. (2005). A functional perspective on the critical ‘theory/practice’ relation in teaching language and science. Linguistics and Education, 16, 151–172. doi: 10.1016/j.linged.2006.01.008.CrossRefGoogle Scholar
  38. Mohanty, A. K. (1994). Bilingualism in a multilingual society: Psychological and pedagogical implications. Mysore: Central Institute for Indian Languages.Google Scholar
  39. Neville-Barton, P., & Barton, B. (2005). The relationship between English language and mathematics learning for non-native speakers: A TLRI research report for NZCER. Wellington: NZCER.Google Scholar
  40. Newman, M. A. (1977). An analysis of sixth-grade pupils’ errors on written mathematical tasks. Victorian Institute for Educational Research Bulletin, 39, 31–43.Google Scholar
  41. OECD. (2006). Assessing scientific, reading and mathematical literacy: A Framework for PISA 2006. Available online at http://www.oecd.org/dataoecd/63/35/37464175.pdf [Accessed on 2nd February, 2007].
  42. Oller, J. W. (1975). Assessing competence in ESL. In S. Palmer, & B. Spolsky (Eds.), Papers on language testing. Washington, D.C.: TESOL.Google Scholar
  43. Pimm, D. (1987). Speaking mathematically: Communication in mathematics classrooms. London: Routledge.Google Scholar
  44. Romaine, S. (1989). Bilingualism. Oxford: Blackwell.Google Scholar
  45. Secada, W. 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. 623–660). New York: MacMillan.Google Scholar
  46. Smith, B., & Ennis, R. H. (1961). Language and concepts. Chicago: McNally.Google Scholar
  47. Stubbs, M. (1976). Language, schools and classrooms. London: Methuen.Google Scholar
  48. Swain, M. (1996). Discovering successful second language teaching strategies and practices: From programme evaluation to classroom experimentation. Journal of Multilingual and Multicultural Development, 17(2), 89–113.CrossRefGoogle Scholar
  49. 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. Education Quality and Accountability Office EQAO. Ottawa: OISE-UT, Modern Language Centre.Google Scholar
  50. Wall, E., & Burke, K. (2001). MICRA-T—Mary Immaculate College Reading Attainment Test (4). Dublin: Fallon.Google Scholar
  51. Williams, C. (2002). A language gained: A study of language immersion at 11–16 Years of Age. University of Wales, Bangor: Education Transactions.Google Scholar
  52. Yushau, B., & Bokhari, M. (2005). Language and mathematics: a mediational approach to bilingual Arabs. International Journal for Mathematics Teaching and Learning, (April, 2005). Available online at http://www.cimit.plymouth.ac.uk/journal/yashau.pdf, (accessed on 2nd November, 2005).

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsUniversity of LimerickLimerickIreland

Personalised recommendations