Nathan & Koedinger (2000) JRME

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Teachers' and Researchers' Beliefs About the Development of Algebraic Reasoning


Mathematics teachers and educational researchers ordered arithmetic and algebra problems according to their predicted problem-solving difficulty for students. Predictions deviated systematically from algebra students' performances but closely matched a view implicit in textbooks. Analysis of students' problem-solving strategies indicates specific ways that students' algebraic reasoning differs from that predicted by most teachers and researchers in the sample and portrayed in common textbooks. The Symbol Precedence Model of development of algebraic reasoning, in which symbolic problem solving precedes verbal problem solving and arithmetic skills strictly preceded algebraic skills, was contrasted with the Verbal Precedence Model of development, which provided a better quantitative fit of students' performance data. Implications of the findings for student and teacher cognition and for algebra instruction are discussed.

Outline of Headings

  • Theoretical Framework: Factors Affecting Problem-Solving Difficulty
    • Unknown Values
    • Presentation Formats
    • Students' Solution Strategies
  • Method
    • Participants
    • Procedure
  • Results
    • Unknown Values
      • Teacher data
      • Researcher data
      • Relation to student performance
    • Presentation Format
      • Teacher data
      • Researcher data
      • Relation to student performance
    • Interactions
    • Summary
  • Discussion
    • Symbol Precedence View
    • Two Competing Developmental Models
    • Quantitative Model Comparison
  • Conclusions
    • Implications for Research and Student Cognition and Development
    • Implications for Research on Teacher Cognition
    • Implications for Mathematics Instruction


Nathan, M. J., & Koedinger, K. R. (2000). Teachers' and researchers' beliefs about the development of algebraic reasoning. Journal for Research in Mathematics Education, 31(2), 168–190. Retrieved from
author = {Nathan, Mitchell J. and Koedinger, Kenneth R.},
journal = {Journal for Research in Mathematics Education},
number = {2},
pages = {168--190},
title = {{Teachers' and researchers' beliefs about the development of algebraic reasoning}},
url = {},
volume = {31},
year = {2000}