Angle Measure, Quantitative Reasoning, and Instructional Coherence: An Examination of the Role of Mathematical "Ways of Thinking" as a Component of Teachers' Knowledge Base

Autor/inn/en	Tallman, Michael A.; Frank, Kristin M.
Titel	Angle Measure, Quantitative Reasoning, and Instructional Coherence: An Examination of the Role of Mathematical "Ways of Thinking" as a Component of Teachers' Knowledge Base
Quelle	In: Journal of Mathematics Teacher Education, 23 (2020) 1, S.69-95 (27 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Tallman, Michael A.)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1386-4416
DOI	10.1007/s10857-018-9409-3
Schlagwörter	Knowledge Base for Teaching; Mathematics; Logical Thinking; Secondary School Teachers; Experienced Teachers; Mathematics Instruction; Geometric Concepts; Secondary School Students; Affordances + Suchen Sie Ihr Suchwort? Teaching theory; Theory of teaching; Unterrichtstheorie; Mathematik; Mathematics lessons; Mathematikunterricht; Elementare Geometrie; Sekundarschüler
Abstract	This paper reports findings from a study that establishes empirical support for Harel's (Zentralblatt für Didaktik der Math 40:893-907 2008b) inclusion of "mathematical ways of thinking" as a component of teachers' professional knowledge base. Specifically, we examined the role of "quantitative reasoning" (Smith and Thompson, in: Kaput, Carraher, Blanton (eds) Algebra in the early grades, Erlbaum, New York 2007; Thompson, in: A theoretical model of quantity-based reasoning in arithmetic and algebra, Center for Research in Mathematics & Science Education: San Diego State University 1990; Thompson, in: Hatfield et al (eds) New perspectives and directions for collaborative research in mathematics education, University of Wyoming, Laramie 2011) on the quality and coherence of an experienced secondary teacher's instruction of angle measure. We analyzed 37 videos of the teacher's instruction to characterize the extent to which he attended to supporting students in reasoning about angle measure quantitatively, and to examine the consequences of this attention on the quality and coherence of the meanings the teacher's instruction supported. Our analysis revealed that the inconsistent meanings the teacher conveyed were occasioned by his lack of awareness of the conceptual affordances of students' quantitative reasoning on their ability to construct coherent, meaningful understandings of angle measure. Our findings therefore support Harel's notion that teachers' mathematical ways of thinking constitute an essential component of their specialized content knowledge. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01