Creating Teaching Units for Student Inquiry
Creating Teaching Units for Student Inquiry

Author(s): André Heck, Lukáš Másilko
Subject(s): Higher Education , Educational Psychology, Cognitive Psychology, Pedagogy
Published by: Masarykova univerzita nakladatelství
Keywords: Student inquiry; developing mathematical thinking; memorisation; reasonong; cognitive demands;
Summary/Abstract: Tasks determine to a large extent how students develop mathematical thinking abilities and become fluent in applying mathematical methods and techniques. As Stein et al. (1996, p. 459) put it: \The mathematical tasks with which students become engaged determine not only what substance they learn but also how they come to think about, develop, use, and make sense of mathematics." They distinguish (p. 466) in mathematical tasks four increasing cognitive demands: (1) memorisation; (2) use of formulas, algorithms, or procedures without attention to concepts, understanding, or meaning; (3) use of formulas, algorithms, or procedures with connection to concepts, contexts, understanding, or meaning; and (4) \doing mathematics," including complex mathematical thinking and reasoning activities such as making and testing conjectures, framing problems, looking for patterns, and so on. Tasks at the highest level of cognitive demand are complex, possibly ill-structured, and require students to make strategic decisions, make connections between concepts and contexts, reason in a mathematical way, and explain their thinking. In other words, student are invited to work as a mathematician or as a professional using mathematics in her/his field.

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