Tall, David (1986) Lies, damn lies ... and differential equations. Mathematics Teaching, Vol.11 . pp. 54-57. ISSN 0025-5785.

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Abstract

The title of this article is a misquotation of Disraeli's comment on statistics, but there is every reason to apply it to the way we currently teach differential equations at A-level. The problem is that we try to make the theory ‘easier’ for the students by concentrating on
simple special cases, not delving too deeply into the technicalities. This tactic has two fundamental flaws. First, the oversimplification of the theory can lead to misrepresentation and falsification of the mathematical facts. Second, the presentation of the theory as a
number of special cases may lead to the mistaken belief that differential equations are solved by a number of isolated techniques (separation of variables, exact solutions, integrating factors, and so on), without any perceivable overall rationale binding the theory
together.

The arrival of the computer gives us the opportunity for a fresh look at the theory to give a clearer insight into the fundamental ideas. Using simple numerical methods it is possible to sketch the solutions of differential equations, showing visually how the theory works and under what circumstances there are likely to be difficulties.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Institute of Education ( -2013)
Library of Congress Subject Headings (LCSH):	Differential equations, Mathematics -- Study and teaching, 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. 54-57
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access (Creative Commons)
Related URLs:	Publisher

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