Students' Difficulties with Definitions in the Context of Proofs in Elementary Set Theory

Autor/inn/en	Shaker, Hedieh; Berger, Margot
Titel	Students' Difficulties with Definitions in the Context of Proofs in Elementary Set Theory
Quelle	In: African Journal of Research in Mathematics, Science and Technology Education, 20 (2016) 1, S.80-90 (11 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1029-8457
DOI	10.1080/10288457.2016.1145449
Schlagwörter	Foreign Countries; College Freshmen; Mathematics Education; Majors (Students); Mathematical Logic; Disadvantaged Schools; Rural Schools; Mathematical Applications; Problem Sets; Theories; Definitions; Misconceptions; Comprehension; Difficulty Level; South Africa + Suchen Sie Ihr Suchwort? Ausland; Studienanfänger; Mathematische Bildung; Mathematical logics; Mathematische Logik; Rural area; Rural areas; School; Schools; Ländlicher Raum; Schule; Schulen; Angewandte Mathematik; Innermathematische Anwendung; Problemstellung; Theory; Theorie; Begriffsbestimmung; Missverständnis; Verstehen; Verständnis; Schwierigkeitsgrad; Südafrika; Süd-Afrika; Republik Südafrika; Südafrikanische Republik
Abstract	In this paper we explore first-year students' difficulties with the use and interpretation of definitions of mathematical objects as they attempt proof construction exercises in the area of elementary set theory. The participants are students at a historically disadvantaged university in South Africa. In this study the activities and utterances of 10 students who took part in consultative group sessions were observed and analysed. Consultative sessions were organised so as to encourage and develop students' active participation while engaging in the task of proof construction. The framework that was used to analyse students' proof comprehension and construction actions and contributions, particularly their interpretation and use of definitions, is described in the paper. The findings of the study resonate closely with those of researchers in the developed world. Students' difficulties with definitions of mathematical objects include their misinterpretation of definitions of objects such as the union of sets and the Cartesian product and their association of mathematical objects with a word or symbol contained in their definitions. (As Provided).
Anmerkungen	Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01