Henningsen & Stein (1997)

Mathematical Tasks and Student Cognition: Classroom-Based Factors That Support and Inhibit High-Level Mathematical Thinking and Reasoning

The article Mathematical Tasks and Student Cognition: Classroom-Based Factors That Support and Inhibit High-Level Mathematical Thinking and Reasoning was written by Marjorie Henningsen and Mary Kay Stein and published in the Journal for Research in Mathematics Education in 1997. The article is available from NCTM at http://www.nctm.org/publications/article.aspx?id=17762 or from JSTOR at http://www.jstor.org/stable/749690.

Abstract

In order to develop students' capacities to "do mathematics," classrooms must become environments in which students are able to engage actively in rich, worthwhile mathematical activity. This paper focuses on examining and illustrating how classroom-based factors can shape students' engagement with mathematical tasks that were set up to encourage high-level mathematical thinking and reasoning. The findings suggest that when students' engagement is successfully maintained at a high level, a large number of support factors are present. A decline in the level of students' engagement happens in different ways and for a variety of reasons. Four qualitative portraits provide concrete illustrations of the ways in which students' engagement in high-level cognitive processes was found to continue or decline during classroom work on tasks.

Outline of Article Headings

Mathematical Tasks and Student Cognition: Classroom-Based Factors That Support and Inhibit High-Level Mathematical Thinking and Reasoning
- Importance of Mathematical Instructional Tasks
- Difficulties Associated with Implementing High-Level Tasks
- Ways of Supporting Implementation of High-Level Tasks
Conceptual Framework
Purpose of the Study
Methodology
- Prior Investigation
  - Data sources
  - Coding procedures
- Sampling for the Present Study
- Analysis Procedures for the Present Study
Results
- Maintenance of High-Level Cognitive Demands
- Factor Profiles for Specific Patterns of Decline
  - Decline into using procedures without connection to concepts, meaning, and understanding
  - Decline into unsystematic exploration
  - Decline into no mathematical activity
- Qualitative Portraits
  - Maintaining cognitive demands at the level of doing mathematics
  - Decline to procedural thinking without connection to meaning
  - Decline to unsystematic exploration
  - Decline to no mathematical activity
Summary and Conclusions

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APA

Henningsen, M. A., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549.

BibTeX

@article{Henningsen1997,
author = {Henningsen, Marjorie A. and Stein, Mary Kay},
journal = {Journal for Research in Mathematics Education},
number = {5},
pages = {524--549},
title = {{Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning}},
url = {http://www.nctm.org/publications/article.aspx?id=17762},
volume = {28},
year = {1997}
}