A Cross-Sectional Investigation of Students' Reasoning about Integer Addition and Subtraction: Ways of Reasoning, Problem Types, and Flexibility

Autor/inn/en	Lamb, Lisa A.; Bishop, Jessica Pierson; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.
Titel	A Cross-Sectional Investigation of Students' Reasoning about Integer Addition and Subtraction: Ways of Reasoning, Problem Types, and Flexibility
Quelle	In: Journal for Research in Mathematics Education, 49 (2018) 5, S.575-613 (39 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0021-8251
Schlagwörter	Problem Solving; Grade 2; Grade 4; Grade 7; Grade 11; Numbers; Addition; Subtraction; Case Studies; Academic Achievement; Mathematics Instruction; Mathematical Logic; Thinking Skills + Suchen Sie Ihr Suchwort? Problemlösen; School year 02; 2. Schuljahr; Schuljahr 02; School year 04; 4. Schuljahr; Schuljahr 04; School year 07; 7. Schuljahr; Schuljahr 07; School year 11; 11. Schuljahr; Schuljahr 11; Zahlenraum; Subtraktion; Case study; Fallstudie; Case Study; Schulleistung; Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Denkfähigkeit
Abstract	In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis of the WoRs also led to the identification of 3 problem types: change-positive, all-negatives, and counterintuitive. We found that problem type influenced student performance and tended to evoke a different way of reasoning. We showed that those with more experience with negative numbers use WoRs more flexibly than those with less experience and that flexibility is correlated with accuracy. We provide 3 types of resources for educators: (a) WoRs and problem-types frameworks, (b) characterization of flexibility with integer addition and subtraction, and (c) development of a trajectory of learning about integers. (As Provided).
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: NCTM@nctm.org; Web site: http://www.nctm.org/publications/journal-for-research-in-mathematics-education
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01