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A graphical approach to integration and the fundamental theorem
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Tall, David. (1986) A graphical approach to integration and the fundamental theorem. Mathematics Teaching, Vol.11 . pp. 4851. ISSN 00255785

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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 numbercrunching and dynamic graphical display.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Social Sciences > Institute of Education 
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:  00255785 
Date:  1986 
Volume:  Vol.11 
Page Range:  pp. 4851 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
Related URLs:  
References:  1. H Neill & H Shuard : Teaching Calculus (Blackie) 1982 2. M Powell: A numerical approach to integration, Mathematics in School, 14, 5, 4446 1985 3. D O Tall: Understanding the calculus, Mathematics Teaching 110, 4853 1985 4. D O Tall: The gradient of a graph, Mathematics Teaching 111, 4852 1985 5. D O Tall: Graphic Calculus II (Integration) for the BBC Computer, Glentop Publishers, 1986 
URI:  http://wrap.warwick.ac.uk/id/eprint/498 
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