Mathematical thinking and task design

Mathematical thinking is difficult to define precisely but most authors agree that the following are important aspects of it: conjecturing, reasoning and proving, abstraction, 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 mathematical thinking in learners of mathematics at all levels. The; frameworks presented here aim to guide task designers when; writing a set of exercises.