Flexibility and inflexibility in accurate mental computation: Two case studies

Heirdsfield, Ann M. & Cooper, Thomas J. (2002) Flexibility and inflexibility in accurate mental computation: Two case studies. The Journal of Mathematical Behavior, 21(1), pp. 57-74.

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Abstract

This paper reports on a study of two children’s mental computation in addition and subtraction, and compares their mental architecture. Both students were identified as being accurate, however, one student used a variety of mental strategies (was flexible) while the other student used only one strategy that reflected the written procedure for each of the addition and subtraction algorithms taught in the classroom. Interviews were used to identify both children’s knowledge and ability with respect to number sense (including numeration, number and operations, basic facts, estimation), metacognition and affects. Frameworks were developed to show how these factors interacted to explain the two types of accuracy in mental addition and subtraction. Flexible accuracy was related to the presence of strong number sense knowledge integrated with metacognitive strategies and beliefs and beliefs about self and teaching; while inflexible accuracy was a result of compensation of inadequate knowledge supported by beliefs about self and teaching.

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ID Code: 1145
Item Type: Journal Article
Refereed: Yes
Keywords: mathematics education, mental computation, addition, subtraction
DOI: 10.1016/S0732-3123(02)00103-7
ISSN: 0732-3123
Subjects: Australian and New Zealand Standard Research Classification > EDUCATION (130000) > CURRICULUM AND PEDAGOGY (130200) > Mathematics and Numeracy Curriculum and Pedagogy (130208)
Divisions: Current > QUT Faculties and Divisions > Faculty of Education
Copyright Owner: Copyright 2002 Elsevier
Copyright Statement: Reproduced in accordance with the copyright policy of the publisher.
Deposited On: 28 Apr 2005 00:00
Last Modified: 09 Jun 2010 12:24

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