Analyzing the Teaching of Advanced Mathematics Courses via the Enacted Example Space

Autor/inn/en	Fukawa-Connelly, Timothy Patrick; Newton, Charlene
Titel	Analyzing the Teaching of Advanced Mathematics Courses via the Enacted Example Space
Quelle	In: Educational Studies in Mathematics, 87 (2014) 3, S.323-349 (27 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-014-9554-2
Schlagwörter	Undergraduate Students; Advanced Courses; Mathematics Instruction; Algebra; Problem Sets; Mathematics Tests; Mathematical Logic; Learning Theories + Suchen Sie Ihr Suchwort? Fortgeschrittenenunterricht; Mathematics lessons; Mathematikunterricht; Problemstellung; Mathematical logics; Mathematische Logik; Learning theory; Lerntheorie
Abstract	Examples are believed to be very important in developing conceptual understanding of mathematical ideas, useful both in mathematics research and instruction (Bills & Watson in "Educational Studies in Mathematics" 69:77-79, 2008; Mason & Watson, 2008; Bills & Tall, 1998; Tall & Vinner, 1981). In this study, we draw on the concept of an example space (Mason & Watson, 2008) and variation theory (Runesson in "Scandinavian Journal of Educational Research" 50:397-410, 2006) to create a lens to study how examples are used for pedagogical purposes in undergraduate proof-based instruction. We adapted the construct of an example space and extended its application to the constructs of example neighborhood, methods of example construction, and the functions of examples. We explained how to use our new lens to analyze the collection of examples and non-examples that the students had access to. We then demonstrate our method by analyzing the collection of examples and non-examples of a mathematical group the professor of an abstract algebra class presented during lectures or assigned to students in problem sets or exams. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10