Fennema, Carpenter, Franke, Levi, Jacobs, & Empson (1996)

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A Longitudinal Study of Learning to Use Children's Thinking in Mathematics Instruction


This study examined changes in the beliefs and instruction of 21 primary grade teachers over a 4-year period in which the teachers participated in a CGI (Cognitively Guided Instruction) teacher development program that focused on helping the teachers understand the development of children's mathematical thinking by interacting with a specific research-based model. Over the 4 years, there were fundamental changes in the beliefs and instruction of 18 teachers such that the teachers' role evolved from demonstrating procedures to helping children build on their mathematical thinking by engaging them in a variety of problem-solving situations and encouraging them to talk about their mathematical thinking. Changes in the instruction of individual teachers were directly related to changes in their students' achievement. For every teacher, class achievement in concepts and problem solving was higher at the end of the study than at the beginning. In spite of the shift in emphasis from skills to concepts and problem solving, there was no overall change in computational performance. The findings suggest that developing an understanding of children's mathematical thinking can be a productive basis for helping teachers to make the fundamental changes called for in current reform recommendations.

Outline of Headings

  • Changing Instruction and Children's Thinking
  • The Study
    • The Teacher Development Program
      • The Research-Based Model of Children's Thinking
      • The Teacher Development Pedagogy: Building on Teachers' Knowledge
      • The Workshops
      • Support
  • Method
    • Overview
    • The Sample
    • Measuring Teachers' Instruction and Beliefs
      • Data
      • Procedures
    • Measuring Children's Learning
      • Tests of Learning
      • Procedures
      • Analyses
  • Results
    • Levels of Instruction
      • Level 1
      • Level 2
      • Level 3
      • Level 4
        • Levels 4-A and 4-B
    • Levels of Belief
      • Level 1
      • Level 2
      • Level 3
      • Level 4
        • Levels 4-A and 4-B
    • Relationship Between Levels of Instruction and Beliefs
    • Changes in Children's Learning
      • Concepts and Problem Solving
        • Overlap items
      • Computation
      • Relation of Instructional Change to Student Achievement
  • Discussion
  • Conclusions


Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use children's thinking in mathematics instruction. Journal for Research in Mathematics Education, 27(4), 403–434. doi:10.2307/749875
author = {Fennema, Elizabeth and Carpenter, Thomas P. and Franke, Megan Loef and Levi, Linda and Jacobs, Victoria R. and Empson, Susan B.},
doi = {10.2307/749875},
journal = {Journal for Research in Mathematics Education},
month = jul,
number = {4},
pages = {403--434},
title = {{A longitudinal study of learning to use children's thinking in mathematics instruction}},
url = {http://www.jstor.org/stable/749875},
volume = {27},
year = {1996}