Stepped Tasks: Top-Down Structure of Varying Mathematical Challenge

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.