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ERIC Number: EJ1417579
Record Type: Journal
Publication Date: 2024-Mar
Pages: 26
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0013-1954
EISSN: EISSN-1573-0816
Generalizing Actions with the Subtraction-Compensation Property: Primary Students' Algebraic Thinking with Tasks Involving Vertical Towers of Blocks
Karina J. Wilkie; Sarah Hopkins
Educational Studies in Mathematics, v115 n3 p433-458 2024
An important approach for developing children's algebraic thinking involves introducing them to generalized arithmetic at the time they are learning arithmetic. Our aim in this study was to investigate children's attention to and expression of generality with the subtraction-compensation property, as evidence of a type of algebraic thinking known as relational thinking. The tasks involved subtraction modelled as difference and comparing the heights of towers of blocks. In an exploratory qualitative study, 22 middle primary (9-11-year-old) students from two schools participated in individual videoed interviews. The tasks were designed using theoretical perspectives on embodied visualization and concreteness fading to provide multiple opportunities for the students to make sense of subtraction as difference and to advance their relational thinking. Twelve out of 22 students evidenced conceptual understanding of the comparison model of subtraction (subtraction as difference) and expression of the compensation property of equality. Four of these students repeatedly evidenced relational thinking for true/false tasks and open equivalence tasks. A proposed framework for levels of attention to/expression of generality with the subtraction-compensation property is shared and suggestions for further research are presented.
Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://bibliotheek.ehb.be:2123/
Publication Type: Journal Articles; Reports - Research
Education Level: Elementary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A