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Problem Solving in Mathematics Instruction and Teacher Professional Development pp 167–184Cite as

Stepped Tasks: Top-Down Structure of Varying Mathematical Challenge

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Part of the book series: Research in Mathematics Education ((RME))

Abstract

Since each mathematics classroom is heterogeneous with respect to students’ mathematical potential, the quality of mathematical instruction results from matching the level of mathematical activities to different students’ potential. This is also true for classes that study mathematics at high level, in which mathematical challenge is a central element of effective learning. Varying mathematical challenge (VMC) is an approach according to which students are provided with opportunities to cope with mathematical tasks that are challenging with respect to their individual mathematical potential. In this chapter I draw a distinction between “opening” and “structuring” as two different approaches to VMC. I introduce a type of mathematical task – called “Stepped Tasks” – specially designed for students’ self-regulated VMC in teaching mathematics at high level. Stepped Tasks call for a top-down structure of problem-solving processing, which appears to be counterintuitive for many teachers and thus requires major didactical change.

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Change history

  • 01 February 2020

    The published version of this book included multiple errors in code listings throughout the book. These code listings have now been corrected and text has been updated.

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Acknowledgment

Development and implementation of the Stepped Tasks were made possible, thanks to the generous support of the Israeli Trump Foundation. I am grateful to the members of the Steps-to-5 project for their contribution to the task development and to teachers’ guidance at the implementation stage.

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Authors and Affiliations

  1. Department of Mathematics Education, RANGE (Research and Advancement of Giftedness and Excellence) Center, University of Haifa, Haifa, Israel

    Roza Leikin

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  1. Roza Leikin
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Correspondence to Roza Leikin .

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Editors and Affiliations

  1. Departamento de Ingeniería Matemática, University of Chile, Santiago, Chile

    Patricio Felmer

  2. Faculty of Education, Simon Fraser University, Burnaby, BC, Canada

    Peter Liljedahl

  3. Department of Science Teaching, Weizmann Institute of Science, Rehovot, Israel

    Boris Koichu

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Leikin, R. (2019). Stepped Tasks: Top-Down Structure of Varying Mathematical Challenge. In: Felmer, P., Liljedahl, P., Koichu, B. (eds) Problem Solving in Mathematics Instruction and Teacher Professional Development. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-29215-7_9

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  • DOI: https://doi.org/10.1007/978-3-030-29215-7_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-29214-0

  • Online ISBN: 978-3-030-29215-7

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