Connecting Research to Teaching: Moving beyond Teachers' Intuitive Beliefs about Algebra Learning

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  • 1 Teaches at the University of Colorado, Boulder, CO 80309-0249
  • 2 Teaches at the Human-Computer Interaction Institute, Carnegie Mellon University, Pittsburgh, PA 15213

Think about this question: Why are algebra story problems considered to be the most difficult tasks facing algebra students? Teachers generally regard them as difficult (Nathan and Koedinger forthcoming), textbooks typically place these problems at the ends of chapters (Nathan and Long 1999), students find them least favorable, and even comic-strip folklore presents story problems as the bane of formal education. (See fig. 1). Are these perceptions held by teachers and textbook authors justified? This article examines teachers' judgments of the difficulty of algebra problems. Our findings may surprise readers, and we hope that they will motivate readers to reexamine some long-standing assumptions about mathematics learning and instruction.

Footnotes

Mitchell J. Nathan, mitch.nathan@colorado.edu, teaches at the University of Colorado, Boulder, CO 80309-0249. Mitchell J. Nathan interests are the study of student cognition and mathematical development, teacher cognition and its relation to instructional practice, and the design and evaluation of technology for learning and instruction.

Kenneth R. Koedinger, koedinger@cmu.edu, teaches at the Human-Computer Interaction Institute, Carnegie Mellon University, Pittsburgh, PA 15213. Kenneth R. Koedinger research attempts to overcome the “expert's blind spot” and uncover the subtle processes of mathematical thinking and learning that we overlook without careful study.

The Mathematics Teacher

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