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ERIC Number: EJ1132834
Record Type: Journal
Publication Date: 2017-Mar
Pages: 20
Abstractor: As Provided
ISSN: ISSN-1033-2170
Children's Strategies to Solving Additive Inverse Problems: A Preliminary Analysis
Ding, Meixia; Auxter, Abbey E
Mathematics Education Research Journal, v29 n1 p73-92 Mar 2017
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.
Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Research
Education Level: Early Childhood Education; Primary Education; Elementary Education
Audience: N/A
Language: English
Sponsor: National Science Foundation (NSF)
Authoring Institution: N/A
Grant or Contract Numbers: DUE0831835