What Does it Mean to Teach Mathematics Differently

In the past decade, many countries called for changes that result in students knowing a 'different' kind of school mathematics. This is due to a changed view of learning that requires different forms of teaching which are only beginning to be understood. In this paper, fmdings from research in primary maths classes with 'reform-oriented' culture are presented; examples drawn from these classrooms illustrate differences in teaching that influence the mathematics children learn. Two dynamic dimensions derived from this research are presented. Two aspects characterize the current attempts to improve mathematics education in many countries over the past decade. First is the influence of the 'cognitive revolution' in psychology that redefined how individuals learn, and second the attempt to change the perception of the discipline of mathematics in schoo1. Currently there is widespread acceptance of the view that learning is an active constructive process. It is thought that as students learn they impose their own interpretation and use these to make sense of the world (Bruner, 1990, 1996). Additionally, rather than conveying er view of mathematics as narrowly consisting of executing well-established procedures, the shift in goal is to present it as a subject that consists of patterns and relationships that are understandable through mental activity that involves mathematical reasoning and logic (Devlin, 1994)'. At the center of this reform in mathematics education at the primary level are two interrelated qualities that are thought to underlie children's learning that, when taken into consideration, designate significant changes in the nature of teaching. The first quality is the social nature of children's learning and the fact that rich social interactions with others substantially contribute to children's opportunities for learning (e.g., Bruner, 1990, 1996). The second aspect is the interplay of children's developing cognition and the unfolding structure that underlies mathematics (e.g., Nunes & Bryant, 1996). These qualities suggest that social situations for learning are needed that are different from those that exist in most primary maths classes (Wood, 2001). It follows from this that a different form of teaching is needed. Research shows that the quality and nature of students' mathematical learning in the 'reform classes' in the United States are significantly different from pupils' learning in conventional classes (e.g., Carpenter, Fennema, Chiang, & Loef, 1989). Cobb, Wood, Yackel, and McNeal (1992) found that, in particular, these classes could be distinguished by the differences in the quality of children's explanations and justifications they were required to give for their solution processes. Furthermore, these differences were found to affect the quality of children's thinking and reasoning about mathematics. Along with this, there are similar studies that examined teaching in these classes. The research has ranged from studies examining teacher beliefs to descriptions of changes in practice (Fennema & Nelson, 1998; Wood & Nelson, 2001). Yet, our understanding of these forms of teaching are is still not as clear as our knowledge of children's learning in these settings. For past decade, I have examined this teaching from a perspective grounded in the practice of teachers through the examination of the interaction patterns that exist in