Bridging History of the Concept of a Function with Learning of Mathematics: Students’ meta-discursive rules, concept formation and historical awareness

Tinne Hoff Kjeldsen, Pernille Hviid Petersen

Research output: Contribution to journalJournal articleResearchpeer-review

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
Original languageEnglish
JournalScience & Education
Volume23
Issue number1
Pages (from-to)29-45
ISSN0926-7220
DOIs
Publication statusPublished - 2014
Externally publishedYes

Cite this

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title = "Bridging History of the Concept of a Function with Learning of Mathematics: Students’ meta-discursive rules, concept formation and historical awareness",
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",
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Bridging History of the Concept of a Function with Learning of Mathematics: Students’ meta-discursive rules, concept formation and historical awareness. / Kjeldsen, Tinne Hoff; Petersen, Pernille Hviid.

In: Science & Education, Vol. 23, No. 1, 2014, p. 29-45.

Research output: Contribution to journalJournal articleResearchpeer-review

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