Developing Structural Reasoning with Diagrams

Autor/inn/en	Lee, Hyung Sook; Yim, Jaehoon; Coomes, Jacqueline
Titel	Developing Structural Reasoning with Diagrams
Quelle	In: Mathematics Teacher: Learning and Teaching PK-12, 113 (2020) 10, S.812-820 (10 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0025-5769
Schlagwörter	Mathematics Instruction; Mathematical Logic; Teaching Methods; Elementary School Mathematics; Preservice Teachers; Mathematical Concepts; Concept Formation; Algebra; Visual Aids; Computation; Middle School Students; Secondary School Mathematics + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Teaching method; Lehrmethode; Unterrichtsmethode; Elementare Mathematik; Schulmathematik; Concept learning; Begriffsbildung; Anschauungsmaterial; Middle school; Middle schools; Student; Students; Mittelschule; Mittelstufenschule; Schüler; Schülerin
Abstract	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. (ERIC).
Anmerkungen	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/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01