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Applying Metacognitive Knowledge and Strategies in Applications and Modelling Tasks at Secondary School

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Trends in Teaching and Learning of Mathematical Modelling

Abstract

The importance of reflective metacognitive activity during mathematical modelling activity has been recognised by scholars and researchers over the years. The metacognitive activity (or lack of it) of secondary students associated with transitions between stages in the modelling process – especially in relation to the identification and release of blockages to progress – is considered. Productive metacognitive acts are identified as occurring at three levels. Routine metacognition together with metacognitive responses to Goos’ red flag situations are elaborated together with the notion of meta-metacognition being engaged in by teachers trying to foster students’ development of independent modelling competencies especially their metacognitive competencies.

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Acknowledgement

Examples used in this chapter are from research that was funded by the Australian Research Council linkage project, RITEMATHS (LP0453701), industry partner secondary schools and Texas Instruments.

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Authors and Affiliations

  1. School of Education (Victoria), Australian Catholic University (Ballarat), 650, Ballarat, VIC, 3350, Australia

    Gloria Stillman

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  1. Gloria Stillman
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Correspondence to Gloria Stillman .

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Editors and Affiliations

  1. FB Erziehungswissenschaft, Inst. Didaktik der Mathematik, Universität Hamburg, Von Melle Park 8, Hamburg, 20146, Germany

    Gabriele Kaiser

  2. Abt. Mathematik/Informatik, Universität Kassel, Kassel, 34109, Germany

    Werner Blum

  3. University of Hamburg, Germany, Doscherstrasse 1, Hamburg, 22083, Germany

    Rita Borromeo Ferri

  4. University of Melbourne, Australia, 23 Grampian Street, Victoria, 3072, Australia

    Gloria Stillman

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Stillman, G. (2011). Applying Metacognitive Knowledge and Strategies in Applications and Modelling Tasks at Secondary School. In: Kaiser, G., Blum, W., Borromeo Ferri, R., Stillman, G. (eds) Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0910-2_18

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