Some old traditions in mathematics and in mathematical education
type: Item
instance of: scholarly article
title: Some old traditions in mathematics and in mathematical education
zbMATH Open document ID: 0938.01015
DOI: 10.1016/S0898-1221(99)00055-3
author: E. A. Galperin
publication date: 2000-01-20T00:00:00Z
review text: The author takes four cases. 1) Many applications of the calculus assume either left- or right-differentiability of a function, according as the interpretation of rate of change refers to the past or to the future respectively. 2) Similarly, temporal causality requires that velocity be conceived as a function of a function of time, the latter fulfilling certain conditions to ensure temporal priority. 3) Methods of optimization are compromised in generality of application by side or other conditions; but some methods manage to sidestep such restrictions. 4) `Integral calculus can be taught before differential calculus' (p. 16), and indeed there is a scrappy history of such procedures. It was John Bernoulli who imposed the priority of the differential, \textit{not} that the derivative was developed first (p. 16); in Leibniz `\(d\)' and `\(\int\)' are together, and on a par.
Mathematics Subject Classification ID: 01A50
Mathematics Subject Classification ID: 34A99
Mathematics Subject Classification ID: 26-03
Mathematics Subject Classification ID: 97D50
zbMATH DE Number: 1391518
Wikidata QID: Q115927394
reviewed by: Ivor Grattan-Guinness
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1391518