ERIC Number: EJ1334283
Record Type: Journal
Publication Date: 2022-Mar
Pages: 9
Abstractor: ERIC
ISBN: N/A
ISSN: ISSN-0025-5769
EISSN: N/A
Available Date: N/A
Beyond the Sign Rules
Bishop, Jessica Pierson; Lamb, Lisa L.; Whitacre, Ian; Philipp, Randolph A.; Schappelle, Bonnie P.
Mathematics Teacher: Learning and Teaching PK-12, v115 n3 p202-210 Mar 2022
In this article, the authors share frameworks for problem types and students' reasoning about integers. The authors found that all ways of reasoning (WoRs) were used across grade levels and that specific problem types tended to evoke particular WoRs. Specifically, students were more likely to use analogy-based reasoning on all-negatives problems than on other problem types, order-based reasoning on change-positive problems, and emergent reasoning on counterintuitive problems. Formal reasoning and computational reasoning did not follow any distinct patterns in the data. The videos themselves reflect these relationships: All but one problem in the videos illustrating analogy-based reasoning are all-negatives problems; all problems illustrating order-based reasoning are change-positive problems; and all problems illustrating emergent reasoning are counterintuitive. Although the authors presented these frameworks separately, they suggest that teachers integrate problem types and WoRs in their instruction.
Descriptors: Thinking Skills, Problem Solving, Mathematics Instruction, Logical Thinking, Computation, Video Technology, Teaching Methods, Kindergarten, Elementary School Students, Secondary School Students, Numbers, Arithmetic
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; Tests/Questionnaires
Education Level: Early Childhood Education; Elementary Education; Kindergarten; Primary Education; Secondary Education
Audience: Teachers
Language: English
Sponsor: National Science Foundation (NSF)
Authoring Institution: N/A
Grant or Contract Numbers: DRL0918780
Author Affiliations: N/A