| Summary: | 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. === Education, Faculty of === Curriculum and Pedagogy (EDCP), Department of === Graduate
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