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Increasing the use of conceptually-derived strategies in arithmetic: using inversion problems to promote the use of associativity shortcuts

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posted on 30.01.2019 by Joanne Eaves, Nina Attridge, Camilla Gilmore
Conceptual knowledge of key principles underlying arithmetic is an important precursor to understanding algebra and later success in mathematics. One such principle is associativity, which allows individuals to solve problems in different ways by decomposing and recombining subexpressions (e.g. ‘a + b – c’ = ‘b – c + a’). More than any other principle, children and adults alike have difficulty understanding it, and educators have called for this to change. We report three intervention studies that were conducted in university classrooms to investigate whether adults’ use of associativity could be improved. In all three studies, it was found that those who first solved inversion problems (e.g. ‘a + b – b’) were more likely than controls to then use associativity on ‘a + b – c’ problems. We suggest that ‘a + b – b’ inversion problems may either direct spatial attention to the location of ‘b – c’ on associativity problems, or implicitly communicate the validity and efficiency of a right-to-left strategy. These findings may be helpful for those designing brief activities that aim to aid the understanding of arithmetic principles and algebra.

Funding

This work was supported by a PhD Studentship from Loughborough University Doctoral college. C.G. is supported by a Royal Society Dorothy Hodgkin Fellowship.

History

School

  • Science

Department

  • Mathematics Education Centre

Published in

Learning and Instruction

Volume

61

Pages

84-98

Citation

EAVES, J.M., ATTRIDGE, N. and GILMORE, C.K., 2019. Increasing the use of conceptually-derived strategies in arithmetic: using inversion problems to promote the use of associativity shortcuts. Learning and Instruction, 61, pp.84-98.

Publisher

© Elsevier

Version

AM (Accepted Manuscript)

Publisher statement

This paper was accepted for publication in the journal Learning and Instruction and the definitive published version is available at https://doi.org/10.1016/j.learninstruc.2019.01.004

Acceptance date

18/01/2019

Publication date

2019-02-21

Copyright date

2019

ISSN

0959-4752

Language

en

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