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An initial framework for the language of higher-order thinking mathematics practices

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Abstract

This article presents an examination of the language demands of cognitively demanding tasks and proposes an initial framework for the language demands of higher-order mathematics thinking practices. We articulate four categories for this framework: language of generalisation, language of comparison, language of proportional reasoning, and language of analysing impact. These categories were developed out of our collaborative work to design and implement higher-order thinking tasks with a group of Grade 9 (14- and 15-year-olds) teachers teaching in a linguistically diverse setting; analyses of student work samples on these tasks; and our knowledge of the literature. We describe each type of language demand and then analyse student work in each category to reveal linguistic challenges facing students as they engage these mathematical tasks. Implications for teaching and professional development are discussed.

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Notes

  1. 2003 Connecticut Academic Performance Test (CAPT) released item, Connecticut State Department of Education 2003.

  2. Note that, in general, the fact that this is presented in a visual format gives students other ways to explain their ideas. Students can talk about the “left part” of the graph or the “right part.” This kind of language would not appear in a situation where a graph had not been provided or generated. This is another issue of which teachers might be aware. Thoughtfully done, the use of multiple representations can help students move away from language linked to the specifics of the representation being used towards the underlying mathematical relationships.

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Authors and Affiliations

  1. University of Connecticut, 249 Glenbrook Road, Unit 3033, Storrs, CT, 06269, USA

    Megan E. Staples & Mary P. Truxaw

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  1. Megan E. Staples
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  2. Mary P. Truxaw
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Correspondence to Megan E. Staples.

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Staples, M.E., Truxaw, M.P. An initial framework for the language of higher-order thinking mathematics practices. Math Ed Res J 24, 257–281 (2012). https://doi.org/10.1007/s13394-012-0038-3

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