Tall, David (1986) A graphical approach to integration and the fundamental theorem. Mathematics Teaching, Vol.11 . pp. 48-51. ISSN 0025-5785.
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Abstract
In ‘Understanding the Calculus’ 3 I suggested how the concepts of the calculus could be approached globally using moving computer graphics. The idea of area under a graph
presents a fundamentally greater problem than that of the notion of gradient. Each numerical gradient is found in a single calculation as a quotient f(x+h)-f(x)h but the calculation of the approximate area under a graph requires many intermediate calculations. Using algebraic methods the summation in all but the simplest examples becomes exceedingly difficult. A calculator initially allows easier numerical calculations but these can become tedious to carry out and obscure to interpret. Graduating to a computer
affords insight in two ways: through powerful number-crunching and dynamic graphical
display.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Social Sciences > Institute of Education ( -2013) |
| Library of Congress Subject Headings (LCSH): | Mathematics -- Study and teaching, Mathematics -- Graphic methods, Calculus |
| Journal or Publication Title: | Mathematics Teaching |
| Publisher: | Association of Teachers of Mathematics |
| ISSN: | 0025-5785 |
| Official Date: | 1986 |
| Dates: | Date Event 1986 UNSPECIFIED |
| Volume: | Vol.11 |
| Page Range: | pp. 48-51 |
| Status: | Not Peer Reviewed |
| Access rights to Published version: | Open Access (Creative Commons open licence) |
| Related URLs: | |
| URI: | https://wrap.warwick.ac.uk/498/ |
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