A Secondary School Student's Understanding of the Concept of Function--A Case Study

Autor/in	Sajka, M.
Titel	A Secondary School Student's Understanding of the Concept of Function--A Case Study
Quelle	In: Educational Studies in Mathematics, 53 (2003) 3, S.229-254 (26 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1023/A:1026033415747
Schlagwörter	Mathematics; Secondary School Students; Secondary School Mathematics; Symbols (Mathematics); Equations (Mathematics); Mathematics Education; Mathematics Instruction; Didacticism; Discussion; Case Studies; Learning Theories; Interviews + Suchen Sie Ihr Suchwort? Mathematik; Sekundarschüler; Equations; Mathematics; Gleichungslehre; Mathematische Bildung; Mathematics lessons; Mathematikunterricht; Didaktisierung; Diskussion; Case study; Fallstudie; Case Study; Learning theory; Lerntheorie; Interviewing; Interviewtechnik
Abstract	This article is concerned with an average student's understanding of the notion of function. It presents an analysis of a dialogue held with Kasia, a sixteen-years-old pupil of a general academic secondary school. The conversation concentrates on a non-standard problem--a functional equation. The theoretical framework used here is the PROCEPT THEORY formulated by Gray and Tall (1993, 1994). The article diagnoses Kasia's procept of function revealed during the dialogue. Her difficulties with understanding this notion can be described as based on a very limited procept of function and a misinterpretation of the symbols used in the functional equation. Three kinds of sources of the difficulties are identified: firstly, the intrinsic ambiguities in the mathematical notation, secondly, there stricted context in which some symbols occur in teaching and a limited choice of mathematical tasks at school, and, thirdly, Kasia's idiosyncratic interpretation of mathematical tasks. Moreover, the paper describes several important changes in understanding of symbols and of the concept of function that took place in the course of the dialogue. This article shows that we can use functional equations as both a research and a didactic tool in mathematics education. (Author).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10