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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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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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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