Surveying Middle-Grades Teachers' Reasoning about Fraction Arithmetic in Terms of Measured Quantities

Autor/inn/en	Izsák, Andrew; Jacobson, Erik; Bradshaw, Laine
Titel	Surveying Middle-Grades Teachers' Reasoning about Fraction Arithmetic in Terms of Measured Quantities
Quelle	In: Journal for Research in Mathematics Education, 50 (2019) 2, S.156-209 (54 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0021-8251
Schlagwörter	Teacher Surveys; Middle School Teachers; Middle School Mathematics; Mathematics Instruction; Mathematics Teachers; Fractions; Arithmetic; Inservice Teacher Education; Psychometrics; Measurement; Mathematical Logic; Problem Solving + Suchen Sie Ihr Suchwort? Middle school; Middle schools; Teacher; Teachers; Mittelschule; Mittelstufenschule; Lehrer; Lehrerin; Lehrende; Mathematics lessons; Mathematikunterricht; Mathematics; Mathematik; Bruchrechnung; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Lehrerfortbildung; Psychometry; Psychometrie; Messverfahren; Mathematical logics; Mathematische Logik; Problemlösen
Abstract	We report a novel survey that narrows the gap between information about teachers' knowledge of fraction arithmetic provided, on the one hand, by measures practical to administer at scale and, on the other, by close analysis of moment-to-moment cognition. In particular, the survey measured components that would support reasoning directly with measured quantities, not by executing computational algorithms, to solve problems. These components--each of which was grounded in past research--were attention to referent units, partitioning and iterating, appropriateness, and reversibility. A second part of the survey asked about teachers' professional preparation and history. We administered the survey to a national sample of in-service middle-grades mathematics teachers in the United States and received responses from 990 of those teachers. We analyzed responses to items in the first part of the survey using the log-linear diagnostic classification model to estimate each teacher's profile of strengths and weaknesses with respect to the four components of reasoning. We report on the diversity of profiles that we found and on relationships between those profiles and various aspects of teachers' professional preparation and history. Our results provide insight into teachers' knowledge resources for enacting standards-based instruction in fraction arithmetic and an example of new possibilities for mathematics education research afforded by recent advances in psychometric modeling. (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