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Chords, tangents and the Leibniz notation
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Tall, David. (1985) Chords, tangents and the Leibniz notation. Mathematics Teaching, Vol.11 . pp. 48-52. ISSN 0025-5785
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Abstract
In this article I continue my quest for “understanding the calculus” 1,2 by looking at a practical approach to the notion of a tangent and linking it to the Leibniz notation dy/dx in a meaningful way. The latter is a bête noire for students: it looks like a quotient, it acts like a quotient, yet the seeds of a classic psychological conflict are sown in their minds when they are told it must not be thought of as a quotient. I shall discuss how this conflict may be resolved so that the chain law allows cancellation.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Social Sciences > Institute of Education |
| Library of Congress Subject Headings (LCSH): | Mathematical notation, Calculus, Mathematics -- Study and teaching |
| Journal or Publication Title: | Mathematics Teaching |
| Publisher: | Association of Teachers of Mathematics |
| ISSN: | 0025-5785 |
| Date: | 1985 |
| Volume: | Vol.11 |
| Page Range: | pp. 48-52 |
| Status: | Not Peer Reviewed |
| Access rights to Published version: | Restricted or Subscription Access |
| Related URLs: | |
| References: | 1. D O Tall: Understanding the Calculus, Mathematics Teaching 110, 49-53 1985. 2. D O Tall: The Gradient of a graph, Mathematics Teaching 11, 48-52 1985. 3. P Couzens & D Butler: M.E.I. Programs for Mathematical Computing, Oundle 1983. 4. D O Tall: Supergraph, Glentop Publishing, Barnet 1985. 5. D O Tall: Graphic Calculus I: Differentiation, Glentop Publishing, Barnet 1986. 6. S M P : Additional Mathematics Part 2. 7. G W Leibniz: Nova methodus pro maximis et minimis, itemque tangentibus, qua nec fractas, nec irrationales quantitates moratur, & sinulare pro illis calculi genus, Acta Eruditorum 467-473, October 1684. 8. R Woodhouse: The Principles of Analytical Calculation, Cambridge 1803. 9. G Matthews: Calculus, John Murray 1964. 10. H Neill & H Shuard: Teaching Calculus, Blackie, 1982. 11. S M P : Advanced Mathematics Book 1, C.U.P. 1967. 12. A Orton: When should we teach the calculus? Mathematics in School, 14,2 11-15 1985. – 15 – 13. D A Quadling: Mathematical Analysis, O.U.P. 1955. |
| URI: | http://wrap.warwick.ac.uk/id/eprint/497 |
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