Developing Mathematical Thinking and Self-Regulated Learning: A Teaching Experiment in a Seventh-Grade Mathematics Classroom

摘要

Mathematics educators have found sociocultural models of teaching and learning to be powerful in their ability to describe and support the pursuit of instruction based on recent standards documents (e.g., National Council of Teachers of Mathematics [NCTM], 1989,2000). These models of instruction,however, have been criticized for their lack of explicitness. Detailed descriptions of cognitive processes within self-regulated learning (SRL) and attribution theories (e.g., Borkowski etal., 1988; Butler, 2002; Zimmerman, 2000)lend support for and provide examples of explicit instruction embedded within sociocultural models of mathematics instruction. Self-regulated learners are active participants in their own learning,are able to select from a repertoire of strategies and to monitor their progress in using these strategies toward a goal. In this article, we describe the collaborative efforts of a seventh-grade mathematics teacher and a university faculty member to develop students' mathematical thinking and self-regulation within one middle school classroom. We argue that implementing mathematics instruction consonant with NCTM(1989, 2000) standards documents makes the development of self-regulated learners possible and is at the same time dependent upon some degree of self-regulation within the community of practice. Several factors are crucial to this development: multiple representations and rich mathematic al tasks; classroom discourse; environmental scaffolding of strategic behavior; and varying needs for explicitness and support. This work constitutes beginning efforts to describe contexts that support the development of mathematical thinking and SRL in the middle school mathematics classroom.