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ERIC Number: EJ819413
Record Type: Journal
Publication Date: 2008
Pages: 8
Abstractor: ERIC
Reference Count: 33
ISBN: N/A
ISSN: ISSN-0819-4564
Differentiation from First Principles Using Spreadsheets
Lim, Kieran F.
Australian Senior Mathematics Journal, v22 n2 p41-48 2008
In the teaching of calculus, the algebraic derivation of the derivative (gradient function) enables the student to obtain an analytic "global" gradient function. However, to the best of this author's knowledge, all current technology-based approaches require the student to obtain the derivative (gradient) at a single point by implementing differentiation using first principles. This paper shows that the ability of spreadsheets to fit a polynomial to a set of discrete (x,y) points enables students to not just evaluate a gradient at a single point, but at a whole family of points, thus generating the analytic global gradient function of secants without doing any algebraic manipulations. Students can then perform "numerical experiments" to see the effect of taking the limit as the secants tend to tangents of the original function. Finally, students can derive the rules for differentiation through exploration and experimentation, again, without doing any algebraic manipulations. This approach enables the class to focus on the concepts being taught, rather than being hindered by the mechanics of (for example) trying to factorize a cubic polynomial. (Contains 4 figures and 1 table.)
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: office@aamt.edu.au; Web site: http://www.aamt.edu.au
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Australia