Improvisational Understanding in the Mathematics Classroom

doi:10.1017/CBO9780511997105.013

12 - Improvisational Understanding in the Mathematics Classroom

Published online by Cambridge University Press: 05 June 2012

Lyndon C. Martin and

Jo Towers

Edited by

R. Keith Sawyer

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Lyndon C. Martin: Affiliation:
York University
Jo Towers: Affiliation:
University of Calgary
R. Keith Sawyer: Affiliation:
Washington University, St Louis

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Summary

In many mathematics classrooms, students learn largely by memorization; they memorize procedures, such as how to multiply two fractions, and they are then assessed by being presented with similar problems, which they can solve if they have memorized the procedure. The problem with this approach is that all too often, students fail to acquire any deeper understanding of mathematical ideas and concepts – for example, what does a fraction represent? How is it similar to a decimal, a ratio, or a percentage? What does it mean to multiply two fractions? Almost all experts in mathematics education agree that understanding mathematical ideas and concepts is a critical and desirable component of the mathematics classroom, yet teachers continue to struggle with meaningful ways to teach for mathematical understanding. Almost all teachers agree that understanding involves more than procedural knowledge and that it includes the ability to reason with and to make sense of what is learned, but the translation of this into concrete teaching strategies that can be implemented in the classroom remains a challenge.

Type: Chapter
Information: Structure and Improvisation in Creative Teaching , pp. 252 - 278

DOI: https://doi.org/10.1017/CBO9780511997105.013 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2011

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