A LONGITUDINAL-STUDY OF LEARNING TO USE CHILDRENS THINKING IN MATHEMATICS INSTRUCTION

This study examined changes in the beliefs and instruction of 21 prima ry grade teachers over a 4-year period in which the teachers participa ted in a CGI (Cognitively Guided Instruction) teacher development prog ram that focused on helping the teachers understand the development of children's mathematical thinking by interacting with a specific resea rch-based model. Over the 4 years, there were fundamental changes in t he beliefs and instruction of 18 teachers such that the teachers' role evolved from demonstrating procedures to helping children build on th eir mathematical thinking by engaging them in a variety of problem-sol ving situations and encouraging them to talk about their mathematical thinking. Changes in the instruction of individual teachers were direc tly related to changes in their students' achievement. For every teach er, class achievement in concepts and problem solving was higher at th e end of the study than at the beginning. In spite of the shift in emp hasis from skills to concepts and problem solving, there was no overal l change in computational performance. The findings suggest that devel oping an understanding of children's mathematical thinking can be a pr oductive basis for helping teachers to make the fundamental changes ca lled for in current reform recommendations.