A development perspective on mathematics teaching and learning: The case of multiplicative thinking

Abstract

This paper looks at the issue of mathematics learning from a developmental perspective. It begins by focusing on the importance for teachers of understanding how mathematical thinking develops. The New Zealand Number Framework is used as an example of a developmental progression that is of particular relevance to the teaching of mathematics. The paper examines data from the Numeracy Development Project gathered by teachers using the diagnostic interview--the Numeracy Project Assessment (NumPA). The data comes from almost a quarter of a million students whose teachers have participated in the Numeracy Development Project over the past three years. Two major developmental progressions are explored in the paper- the transition from counting to part-whole strategies, and the move from additive to multiplicative part-whole thinking. The final section of the paper looks at some practical ways of fostering multiplicative thinking using structured materials.