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ERIC Number: EJ819409
Record Type: Journal
Publication Date: 2008
Pages: 11
Abstractor: ERIC
Reference Count: 13
ISSN: ISSN-0819-4564
A Historical Perspective on Teaching and Learning Calculus
Doorman, Michiel; van Maanen, Jan
Australian Senior Mathematics Journal, v22 n2 p4-14 2008
Calculus is one of those topics in mathematics where the algorithmic manipulation of symbols is easier than understanding the underlying concepts. Around 1680 Leibniz invented a symbol system for calculus that codifies and simplifies the essential elements of reasoning. The calculus of Leibniz brings within the reach of an ordinary student problems that once required the ingenuity of an Archimedes or a Newton. One can mechanically "ride" the syntax of the notation without needing to think through the semantics. Calculus education typically has a strong routine aspect, focusing on methods for differentiation and integration without justifying these methods, since current teaching practice barely has time to discuss the underlying concepts. A question for the design of a teaching trajectory that focuses on ways to support the understanding of the underlying concepts is: How can students invent this? It is useful to look at the history of a topic to gain insight into this issue, to investigate concept development, and to analyze how and why people tried to organize certain phenomena without having any notion yet about the basic principles of calculus. In this paper, the authors will first review some highlights in the history of calculus. This review will lead into recommendations for an instructional sequence on calculus. The authors conclude with a plea for historical reflections in mathematics education as a method for changing routine-oriented practices. (Contains 5 figures.)
Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Australia