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Mathematical understanding and Tongan bilingual students’ language switching : is there a relationship? Manu, Sitaniselao Stan

Abstract

This study explores the relationship between Tongan bilingual students' language switching and their growth of mathematical understanding. The importance of this study lies not only in its ability to use the Pirie-Kieren Dynamical Theory for the Growth of Mathematical Understanding as a theoretical tool for examining the relationship between language switching and growth of mathematical understanding, but also in its ability to demonstrate the theory's applicability and validity in a bilingual context. Video case study was chosen as the most appropriate means of recording, collecting and examining the described relationship in a small-group setting. Two strands of data were collected between 2001 and 2002 from a selected number of bilingual students from five secondary schools in Tonga. Analysis of the students' language switching through the Constant Comparative Method resulted in the categorization of four main "forms" of language switching. These forms were identified, categorized, and developed from the data to provide a language for describing and accounting for the particular way Tongan students switch languages. The evidence from the data clearly demonstrates how language switching both did and did not influence and was and was not influenced by the students' growth of understanding through the construction of mathematical meanings. At the same time, language switching was found to definitely enable the expression of growth of mathematical understanding. This study proposes that the effect of bilingual students' learning and development of understanding in mathematics is largely dependent on the kinds of mathematical images each bilingual student associates with his or her language. Therefore this study introduces the notion of "evocative" language switching, used for identifying, retrieving, and guiding one's existing understanding and ability to work with images. The evidence from this study is certainly applicable to other Tongan-type bilingual situations that involve individuals using words with no direct or precise translation between a dominant Western language and an indigenous language. Ultimately, the findings of this study challenge the assumption that Tongan-type bilingual students have enormous problems in the classroom. Allowed the flexibility of language switching and thus access to appropriate terms and images in either language, they do not seem to be mathematically disadvantaged.

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