Understanding and Describing Mathematical Knowledge for Teaching: Knowledge about Proof for Engaging Students in the Activity of Proving

Autor/inn/en	Stylianides, Andreas J.; Ball, Deborah L.
Titel	Understanding and Describing Mathematical Knowledge for Teaching: Knowledge about Proof for Engaging Students in the Activity of Proving
Quelle	In: Journal of Mathematics Teacher Education, 11 (2008) 4, S.307-332 (26 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1386-4416
DOI	10.1007/s10857-008-9077-9
Schlagwörter	Mathematics Instruction; Validity; Mathematical Logic; Elementary School Mathematics; Knowledge Base for Teaching; Grade 3; Student Participation + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Gültigkeit; Mathematical logics; Mathematische Logik; Elementare Mathematik; Schulmathematik; Teaching theory; Theory of teaching; Unterrichtstheorie; School year 03; 3. Schuljahr; Schuljahr 03; Schülermitarbeit; Schülermitwirkung; Studentische Mitbestimmung
Abstract	This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in, mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about proof is likely to be important for teachers to have as they engage students in the activity of proving. We explain that existing research informs the "knowledge about the logico-linguistic aspects of proof" that teachers might need, and we argue that this knowledge should be complemented by what we call "knowledge of situations for proving." This form of knowledge is essential as teachers mobilize proving opportunities for their students in mathematics classrooms. We identify two sub-components of the knowledge of situations for proving: "knowledge of different kinds of proving tasks and knowledge of the relationship between proving tasks and proving activity." In order to promote understanding of the former type of knowledge, we develop and illustrate a classification of proving tasks based on two mathematical criteria: (1) the number of cases involved in a task (a single case, multiple but finitely many cases, or infinitely many cases), and (2) the purpose of the task (to verify or to refute statements). In order to promote understanding of the latter type of knowledge, we develop a framework for the relationship between different proving tasks and anticipated proving activity when these tasks are implemented in classrooms, and we exemplify the components of the framework using data from third grade. We also discuss possible directions for future research into teachers' knowledge about proof. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10