摘要:

Inside the scientific world it is not always understood that the mood of mathematics, which is a product and a part of culture, can change with time. This is partly why many have been surprised by the coming of the so‐called new mathematics.

ISSN:0020-739X    

DOI:10.1080/0020739750060201

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

This paper is an attempt, in a fairly light‐hearted fashion, to highlight the interconnection between vectors and geometry and to illustrace especially to students that in our elementary discussion of vectors we must necessarily assume some geometrical background.

ISSN:0020-739X    

DOI:10.1080/0020739750060202

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

This paper examines the educational desirability of introducing the teaching of statistics at the secondary level. A syllabus is proposed for a course in statistics at the secondary level and brief comments are given on each topic, indicating how they may be presented to students.

ISSN:0020-739X    

DOI:10.1080/0020739750060203

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

This paper discusses the role behaviourism is playing in the current development of school mathematics. A discussion of the underlying philosophy and wide‐spread use of behaviourism concludes with the recommendation that the behaviouristic model should not be used in constructing mathematics curricula. The behaviouristic approach to education seems appropriate only for those aspects of a curriculum which are concerned with skill development. Behaviourism equates training with education, and a blanket adoption of such a philosophy for all of school mathematics misses the heart and essence of the mathematics discipline. This paper argues against embedding mathematics curricula within the behaviouristic framework, and thus presents a plea for us to re‐evaluate the objectives of school mathematics.

ISSN:0020-739X    

DOI:10.1080/0020739750060204

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

Terms that are used to describe mathematical concepts are often used to describe psychological behaviour. In reading psychological writing which uses these terms, the reader does not always know whether the meanings of term as used in the two subjects are the same, similar, or dissimilar. In this article definitions of a selection of terms that are used in both subjects are compared and through a brief discussion the similarities and differences of meaning are identified.

ISSN:0020-739X    

DOI:10.1080/0020739750060205

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

Investigations into subject choice among upper sixth form pupils had revealed the not uncommon existence of adverse attitudes towards the advanced level mathematics course. A survey was undertaken to investigate this situation and to examine attitude and performance in a sample which was virtually the entire entry of a county and metropolitan area.

ISSN:0020-739X    

DOI:10.1080/0020739750060206

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

This paper briefly describes the basis of structural mathematics (N. Bourbaki), the elementary structures of genetic psychology (J. Piaget) and the matrix strategies in heuristics (G. Polya). It demonstrates, by epistemological analysis, that there are very close links between mathematical structures, psychological ‘structures’ and heuristic strategies and illustrates practical work according to heuristic matrix strategies by means of a simple example.

ISSN:0020-739X    

DOI:10.1080/0020739750060207

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

An elementary discussion that appears in at least two texts and purportedly suggests the basis of an argument for the derivation of Stirling's formula is reproduced, together with objections to two steps in the discussion that are essential to the simplification of the argument. These steps are the use of the Maclaurin expansion for In (1 +u)outside its circle of convergence followed by the deletion of certain terms which do not in fact individually tend to zero under the required conditions.

ISSN:0020-739X    

DOI:10.1080/0020739750060208

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

The nature of the art of applied mathematics is reviewed and three contemporary challenges are considered. These are the extended fields of mathematical application, the extension of applicable mathematics, and the problems associated with model building in the new fields. It is noted, however, that two aspects remain invariant: the difficulty of immaturity when making applications relevant and the essential problem‐solving theme of applied mathematics.

ISSN:0020-739X    

DOI:10.1080/0020739750060209

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

The paper presents a mathematical model of the problem of the politico‐economic stability of a welfare state. The variables characterizing the state of a government are identified. A sufficient criterion which ensures the damping out of the effects arising due to arbitrary perturbations in the variables, is obtained. The model assumes the prevalence of normal conditions, that is, times free from unforeseen calamities such as severe earthquake, outbreak of epidemic on a large scale, invasion by another country, acute famine, etc.

ISSN:0020-739X    

DOI:10.1080/0020739750060210

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor