Nathan & Koedinger (2000) C&I

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An Investigation of Teachers' Beliefs of Students' Algebra Development


Elementary, middle, and high school mathematics teachers (N = 105) ranked a set of mathematics problems based on expectations of their relative problem-solving difficulty. Teachers also rated their levels of agreement to a variety of reform-based statements on teaching and learning mathematics. Analyses suggest that teachers hold a symbol precedence view of student mathematical development, wherein arithmetic reasoning strictly precedes algebraic reasoning, and symbolic problem-solving develops prior to verbal reasoning. High school teachers were most likely to hold the symbol-precedence view and made the poorest predictions of students' performances, whereas middle school teachers' predictions were most accurate. The discord between teachers' reform-based beliefs and their instructional decisions appears to be influenced by textbook organization, which institutionalizes the symbol-precedence view. Because of their extensive content training, high school teachers may be particularly susceptible to an expert blindspot, whereby they overestimate the accessibility of symbol-based representations and procedures for students' learning introductory algebra.

Outline of Headings

  • Influences on Teachers' Beliefs
    • Principles of Mathematics Education Reform
    • The Influence of Textbooks
    • Hypotheses of This Study
  • Method
    • Participants
    • Design, Materials, and Procedure
  • Results and Conclusions
    • Belief Instruments
    • Grade Level Differences
    • Teachers' Problem Difficulty Ranking
      • Start-unknown versus result-unknown problems
      • Story, word, and equation problems
    • Relating Teachers' Beliefs to Difficulty Ranking: A Regression Analysis
    • Summary
  • Discussion
    • Some Factors That Influence Teachers' Judgments
    • Grade Level Differences Among Teachers
    • Implications for Teacher Decision Making and Instructional Practice
    • Implications for Teacher Education


Nathan, M. J., & Koedinger, K. R. (2000). An investigation of teachers' beliefs of students' algebra development. Cognition and Instruction, 18(2), 209–237.
author = {Nathan, Mitchell J. and Koedinger, Kenneth R.},
doi = {10.1207/S1532690XCI1802_03},
journal = {Cognition and Instruction},
number = {2},
pages = {209--237},
title = {{An investigation of teachers' beliefs of students' algebra development}},
url = {{\_}03},
volume = {18},
year = {2000}