Mathematical thinking and task design

Abstract

Mathematical thinking is difficult to define pre-cisely but most authors agree that the following are impor-tant aspects of it: conjecturing, reasoning and proving, ab-straction, generalization and specialization. However, recent studies have shown that many sets of mathematical tasks produced emphasize lower level skills, such as memorization and the routine application of algorithms or procedures. In this paper we survey the literature on the design and use of tasks that aim to encourage higher level aspects of mathe-matical thinking in learners of mathematics at all levels. The frameworks presented here aim to guide task designers when writing a set of exercises.