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Status:	Not Peer Reviewed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)
Related URLs:	Publisher

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