Mathematics Learning Through the Lens of Language Acquisition

Main Article Content

Michael J. Bosse Anass Bayaga Catherine Fountain Erica Slate Young Ashley DeMarte

Abstract

Previous theoretical research (Authors, 2018a; Authors, 2018b) has revealed conceptual similarities among a number of mathematical learning theories and theories regarding language acquisition. This intersection of ideas led to a novel framework defining four stages of mathematical learning: Receiving, Replicating, Negotiating Meaning, and Producing. Through qualitative research methods and transcripts of student communication and work, this study empirically investigates this theoretical construct. The findings herein demonstrate that this construct is helpful in characterizing where students are in the process of learning mathematics and how to help them attain the next level in the stages of learning.

Downloads

Download data is not yet available.

Article Details

How to Cite
BOSSE, Michael J. et al. Mathematics Learning Through the Lens of Language Acquisition. International Electronic Journal of Elementary Education, [S.l.], v. 12, n. 1, p. 103-113, oct. 2019. ISSN 1307-9298. Available at: <https://iejee.com/index.php/IEJEE/article/view/850>. Date accessed: 15 oct. 2019.
Section
Articles

References

Adu-Gyamfi, K., Bossé, M. J., & Chandler, K. (2015). Situating student errors: Linguistic-to-algebra translation errors. International Journal for Mathematics Teaching and Learning. Retrieved from http://www.cimt.org.uk/journal/bosse6.pdf
Adu-Gyamfi, K., Stiff, L., & Bossé, M. J. (2012). Lost in translation: Examining translation errors associated with mathematics representations. School Science and Mathematics, 112(3), 159-170.
Ansari, D., Lyons, I. M., van Eimeren, L., & Xu, F. (2007). Linking visual attention and number processing in the brain: The role of the temporo-parietal junction in small and large symbolic and nonsymbolic number comparison. Journal of Cognitive Neuroscience 19(11), 1845–1853.
Biggs, J. B., & Collis, K. F. (1982). Evaluating the quality of learning - The SOLO taxonomy. New York, NY: Academic Press.
Blomert, L., & Froyen, D. (2010). Multi-sensory learning and learning to read. International Journal of Psychophysiology, 77(3), 195–204.
Bloom, B. S., & Krathwohl, D. R. (1956). Taxonomy of educational objectives: The classification of educational goals, by a committee of college and university examiners. Handbook 1: Cognitive domain. New York, Longmans.
Bogdan, R. C., & Biklen, S. K. (2003). Qualitative research for education: An introduction to theories and methods (4th ed.). Boston: Allyn and Bacon.
Bossé, M. J., Bayaga, A., Fountain, C. A., Lynch-Davis, K., Preston, R., &, Adu-Gyamfi, K. (2018a). Fraction learners: Assessing understanding through language acquisition. International Electronic Journal of Elementary Education, 11(2), 113-124. https://www.iejee.com/index.php/IEJEE/article/view/649/374
Bossé, M. J., Ringler, M., Bayaga, A., Fountain, C.A., & Slate Young, E. (2018b). Acquiring math: Connecting math learning and second language acquisition. International Journal of Mathematics Teaching and Learning, 19, 223-252. https://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/151
Brown, M., Bossé, M. J. & Chandler, K. (2016). Student errors in dynamic mathematical environments. International Journal for Mathematics Teaching and Learning. Retrieved from http://www.cimt.org.uk/journal/bosse8.pdf .
Bruner, J. S. (1966). Toward a theory of instruction. New York: Norton.
Bruner, J. S. (1979). On knowing. Cambridge, MA: Belknap Printing.
Cabrelli Amaro, J., Flynn, S. & Rothman, J. (2012). Third language acquisition in adulthood. Philadelphia/Amsterdam: John Benjamins.
Chomsky, N. (1965). Aspects of the Theory of Syntax. Cambridge, MA: MIT Press.
Creswell, W. J. (2003). Research Design: Qualitative, quantitative and mixed methods approaches. (2nd ed.). London: Sage Publications.
Cummins, J. (1979). Cognitive/academic language proficiency, linguistic interdependence, the optimum age question and some other matters. Working Papers on Bilingualism, 19, 121-129.
Cummins, J. (1984). Bilingualism and special education: Issues in assessment and pedagogy. Clevedon, England: Multilingual Matters.
Cummins, J. (1991). Language development and academic learning. In L. Malavé & G. Duquette (Eds.) Language, culture and cognition. (pp. 161-175). Clevedon, England: Multilingual Matters.
Dienes, Z. P. (1960). Building up mathematics. London, England: Hutchinson Education Ltd.
Dienes, Z. P. (1971). An example of the passage from the concrete to the manipulation of formal systems. Educational Studies in Mathematics,3 (3/4), 337-352.
Dienes, Z. P. & Golding, E. W. (1971). Approach to modern mathematics. New York: Herder and Herder Co.
Kolkman, M.E., Kroesbergen, E.H., & Leseman, P.P.M. (2013). Early numerical development and the role of non-symbolic and symbolic skills. Learning and Instruction, 25, 95-103.
Krashen, S. (1977). Some Issues Relating to the Monitor Model. In H. D. Brown, C. Yorio & R. Crymes (Eds.) Teaching and Learning English as a Second Language: Trends in Research and Practice. (pp. 144-158) Washington: TESOL.
Krashen, S. D. (1982). Principles and practice in second language acquisition. Oxford: Pergamon.
Krashen, S. D., & Terrell, T. (1983). The natural approach: Language acquisition in the classroom. London: Prentice Hall Europe.
Lenneberg, E. H. (1967). Biological foundations of language. New York: John Wiley and Sons.
Lenneberg, E. H. (1975). The concept of language differentiation. In E. H. Lenneberg & E. Lenneberg, (Eds), Foundations of language development: A multidisciplinary approach (Vol 1). New York, NY: Academic Press.
Lyons, I. M., Price, G. R., Vaessen, A., Blomert, L., Ansari, D. (2014). Numerical predictors of arithmetic success in grades 1–6. Developmental Science, 17, 714-726.
Miles, M. B. & Huberman, M. N. (1994). Qualitative data analysis: An expanded sourcebook. Thousand Oaks, CA: Sage.
Moschkovich, J. 2005. Using two languages when learning mathematics. Educational Studies in Mathematics, 64, 121-144.
Selinker, L. (1992). Rediscovering interlanguage. London: Longman.
Selinker, L. (1972). Interlanguage. International Review of Applied Linguistics, 10, 209–231.
Swain, M. (1985). Communicative competence: some roles of comprehensible input and comprehensible output in its development. In S. Gass, S. and C. Madden, (Eds.), Input in Second Language Acquisition. Rowley, MA: Newbury House.
Swain, M. and Lapkin, S. (1995). Problems in output and the cognitive processes they generate: A step towards second language learning. Applied Linguistics, 16, 371-391.
Thompson, D. & Rubenstein, R. (2014). Literacy in language and mathematics: More in common than you think. Journal of Adolescent and Adult Literacy, 58(2), 105-108.
Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Orlando, FL: Academic Press.
Vygotsky, L. S. (1978). Mind in society. Cambridge, MA: Harvard University Press.
Vygotsky, L. S. (1986). Thought and Language. A. Kozulin, (Ed.). Cambridge, MA: MIT Press