Inaccurate mental addition and subtraction: Causes and compensation

Heirdsfield, Ann M. & Cooper, Thomas J. (2004) Inaccurate mental addition and subtraction: Causes and compensation. Focus on Learning Problems in Mathematics, 26(3), pp. 43-65.


This paper reports on a study of seven Year 3 students’ diminished performance in mental computation, and compares their mental architecture. Although all students were identified as being inaccurate, three students used some variety of mental strategies, while the other students 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 students’ knowledge and ability with respect to number sense (including number facts, estimation, numeration, and effect of operation on number), metacognition and affects. Two conceptual frameworks were developed, one representing the "flexible" mental computers, and the other representing the inflexible mental computers. These frameworks identified factors and relationships between factors that influence mental computation. The frameworks were compared with an ideal framework that had been developed from a study of proficient mental computers. These frameworks showed that inaccuracy resulted from disconnected and deficient cognitive, metacognitive, and affective factors; and in some cases might have been affected by deficient short-term memory. It appeared that students’ choices of mental strategies resulted from different forms of compensation for varying levels of deficiencies.

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ID Code: 1061
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: mathematics education, mental computation
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 2004 The authors / Center for Teaching/Learning Mathematics
Copyright Statement: Reproduced with permission of the copyright owners.
Deposited On: 06 May 2005 00:00
Last Modified: 29 Feb 2012 13:05

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