# 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} }