Nathan & Koedinger (2000) C&I

An Investigation of Teachers' Beliefs of Students' Algebra Development

• Authors: Mitchell J. Nathan and Kenneth R. Koedinger
• Journal: Cognition and Instruction
• Year: 2000
• Source: http://www.tandfonline.com/doi/abs/10.1207/S1532690XCI1802_03

Abstract

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

Corrolary

APA

Nathan, M. J., & Koedinger, K. R. (2000). An investigation of teachers' beliefs of students' algebra development. Cognition and Instruction, 18(2), 209–237. http://doi.org/10.1207/S1532690XCI1802_03

BibTeX

@article{Nathan2000b,
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 = {http://www.tandfonline.com/doi/abs/10.1207/S1532690XCI1802{\_}03},
volume = {18},
year = {2000}
}