Mathematical Thinking and Learning

Abstract

This chapter presents a selective review of the recent research on the development, learning, and teaching of mathematical knowledge and thinking. While school mathematics involves not only arithmetic but also algebra, measurement and geometry, and data handling and probability, the present chapter focuses on arithmetic only, a focus that reflects the preponderance of current psychological and educational research on mathematics education. And within arithmetic the emphasis is on number sense, whole number arithmetic, and word-problem solving—topics that have been stressed in recent reform documents because of their importance for the acquisition in children of basic competence in mathematics. The review is also selective with regard to age range, focusing on primary school children. As a framework for reviewing the literature, and for the presentation and discussion of research-based instructional interventions, we use a model for the design of powerful environments for learning and teaching mathematics that is structured according to four interrelated components, namely, competence (aspects of mathematical proficiency), learning (characteristics of productive mathematics learning processes), intervention (principles for the design of environments for mathematics learning and instruction), and assessment (forms of assessment for monitoring and improving mathematics learning and teaching). Keywords: classroom assessment; large-scale assessment; mathematical competence; mathematical learning; mathematical thinking; mathematics education; mathematics learning environments; mathemetics-related beliefs; multidigit arithmetic; number sense; single-digit computation; word problem solving