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ERIC Number: EJ1141516
Record Type: Journal
Publication Date: 2017-May
Pages: 40
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0021-8251
EISSN: N/A
Preservice Teachers' Reasoning about Relationships That Are and Are Not Proportional: A Knowledge-in-Pieces Account
Izsák, Andrew; Jacobson, Erik
Journal for Research in Mathematics Education, v48 n3 p300-339 May 2017
Past studies have documented students' and teachers' persistent difficulties in determining whether 2 quantities covary in a direct proportion, especially when presented missing-value word problems. In the current study, we combine a mathematical analysis with a psychological perspective to offer a new explanation for such difficulties. The mathematical analysis highlights numbers of equal-sized groups and places reasoning about proportional relationships in the context of reasoning about multiplicative relationships more generally. The psychological perspective is rooted in diSessa's (diSessa, 1993, 2006; diSessa, Sherin, & Levin, 2016) knowledge-in-pieces epistemology and highlights diverse, fine-grained knowledge resources that can support inferring and reasoning with equal-sized groups. We illustrate how the combination of mathematical analysis and psychological perspective may be applied to data using empirical examples drawn from interviews during which preservice middle-grades teachers reasoned with varying degrees of success about relationships presented in word problems that were and were not proportional.
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/
Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education; Elementary Education; Middle Schools; Secondary Education; Junior High Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A