Bridging History of the Concept of Function with Learning of Mathematics: Students' Meta-Discursive Rules, Concept Formation and Historical Awareness

Autor/inn/en	Kjeldsen, Tinne Hoff; Petersen, Pernille Hviid
Titel	Bridging History of the Concept of Function with Learning of Mathematics: Students' Meta-Discursive Rules, Concept Formation and Historical Awareness
Quelle	In: Science & Education, 23 (2014) 1, S.29-45 (17 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0926-7220
DOI	10.1007/s11191-013-9641-2
Schlagwörter	Foreign Countries; Mathematics; History; Mathematical Concepts; Secondary School Mathematics; High School Students; Mathematics Instruction; History Instruction; Concept Formation; Experimental Curriculum; Courses; Denmark + Suchen Sie Ihr Suchwort? Ausland; Mathematik; Geschichte; Geschichtsdarstellung; High school; High schools; Student; Students; Oberschule; Schüler; Schülerin; Studentin; Mathematics lessons; Mathematikunterricht; History lessons; Geschichtsunterricht; Concept learning; Begriffsbildung; Kursangebot; Dänemark
Abstract	In this paper we present a matrix-organised implementation of an experimental course in the history of the concept of a function. The course was implemented in a Danish high school. One of the aims was to bridge history of mathematics with the teaching and learning of mathematics. The course was designed using the theoretical frameworks of a multiple perspective approach to history, Sfard's theory of thinking as communicating, and theories from mathematics education about concept image, concept definition and concept formation. It will be explained how history and extracts of original sources by Euler from 1748 and Dirichlet from 1837 were used to (1) reveal students' meta-discursive rules in mathematics and make them objects of students' reflections, (2) support students' learning of the concept of a function, and (3) develop students' historical awareness. The results show that it is possible to diagnose (some) of students' meta-discursive rules, that some of the students acted according to meta-discursive rules that coincide with Euler's from the 1700s, and that reading a part of a text by Dirichlet from 1837 created obstacles for the students that can be referenced to differences in meta-discursive rules. The experiment revealed that many of the students have a concept image that was in accordance with Euler's rather than with our modern concept definition and that they have process oriented thinking about functions. The students' historical awareness was developed through the course with respect to actors' influence on the formation of mathematical concepts and the notions of internal and external driving forces in the historical development of mathematics. (As Provided).
Anmerkungen	Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@springer.com; Web site: http://www.springerlink.com
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10