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ERIC Number: EJ1272414
Record Type: Journal
Publication Date: 2020-Oct
Pages: 10
Abstractor: ERIC
ISBN: N/A
ISSN: ISSN-0025-5769
EISSN: N/A
Available Date: N/A
Developing Structural Reasoning with Diagrams
Lee, Hyung Sook; Yim, Jaehoon; Coomes, Jacqueline
Mathematics Teacher: Learning and Teaching PK-12, v113 n10 p812-820 Oct 2020
Children see and describe patterns in the primary grades when they develop the meaning of numbers by composing and decomposing. During their early years, they use patterns to learn properties of operations (Common Core Standards Writing Team 2011). While describing the intent of the third-grade standards for multiplication, the CCSS writers specifically identify the 9-Times pattern mentioned as an opportunity to examine patterns. Generating patterns by noticing the regularity from repeated calculations is an important first step. But the authors have observed that when students encounter difficulty abstracting regularity from patterns or justifying generalizations, it seems they have had little experience describing the underlying structure of the pattern. Narrowing in on this idea, this article suggests ways to incorporate structural reasoning into repeated reasoning. They also illustrate how to use structural reasoning as an opportunity to advance students' reasoning strategies, and they use students' diagrams throughout to illustrate how to incorporate structural reasoning and repeated reasoning.
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191. Tel: 800-235-7566; Tel: 703-620-9840; Fax: 703-476-2570; e-mail: publicationsdept@nctm.org; Web site: https://pubs.nctm.org/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Elementary Education; Higher Education; Postsecondary Education; Junior High Schools; Middle Schools; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A
Author Affiliations: N/A