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Mathematics Education Research Journal

, Volume 29, Issue 1, pp 73–92 | Cite as

Children’s strategies to solving additive inverse problems: a preliminary analysis

  • Meixia Ding
  • Abbey E Auxter
Original Article
First Online:

Abstract

Prior studies show that elementary school children generally “lack” formal understanding of inverse relations. This study goes beyond lack to explore what children might “have” in their existing conception. A total of 281 students, kindergarten to third grade, were recruited to respond to a questionnaire that involved both contextual and non-contextual tasks on inverse relations, requiring both computational and explanatory skills. Results showed that children demonstrated better performance in computation than explanation. However, many students’ explanations indicated that they did not necessarily utilize inverse relations for computation. Rather, they appeared to possess partial understanding, as evidenced by their use of part-whole structure, which is a key to understanding inverse relations. A close inspection of children’s solution strategies further revealed that the sophistication of children’s conception of part-whole structure varied in representation use and unknown quantity recognition, which suggests rich opportunities to develop students’ understanding of inverse relations in lower elementary classrooms.

Keywords

Inverse relations Part-whole Addition and subtraction Children’s strategy 
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Notes

Acknowledgements

This study is supported by the National Science Foundation (NSF) CAREER program under Grant No. DRL-1350068 at Temple University and the NSF grant DUE-0831835 at the University of Nebraska–Lincoln. Any opinions, findings, and conclusions in this study are those of the author and do not necessarily reflect the views of the National Science Foundation.

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© Mathematics Education Research Group of Australasia, Inc. 2017

Authors and Affiliations

  1. 1.Temple UniversityPhiladelphiaUSA
  2. 2.Community College of PhiladelphiaPhiladelphiaUSA

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