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THE TEACHING OF

GEOMETRY IN SCHOOLS

A REPORT

PREPARED FOR THE

MATHEMATICAL ASSOCIATION, London.

LONDON

G. BELL AND SONS, LTD.
1923

CAJORI

THIS Report was prepared by a Sub-Committee appointed for the purpose on April 8th, 1922, by the General Teaching Committee of the Mathematical Association. It was presented as a unanimous Report, and accepted unanimously by the General Teaching Committee at a meeting held on November 3rd, 1923.

The Sub-Committee was composed as follows:

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Introduction

THE Committee responsible for this Report assembled first to consider the effects of diversity of sequences on the teaching of geometry, and the desirability and feasibility of a return to the uniformity that prevailed thirty years ago. But it was found unprofitable to proceed without a discussion of general principles, and these have applications to practical questions other than that which led to the discussion.

In the Report a Section on general principles comes first, and the teacher who is interested primarily to know what recommendations are made on specific details of practice is advised to begin at one of the later Sections; it is hoped that the Table of Contents will enable every reader to start at a congenial paragraph.

Section II describes the Stages which the Committee believes to be natural divisions of a course of geometry; this Section includes a minimum programme for the introductory Stage, arguments in support of the opinion that reference should be made continually to solid geometry, and an account of the manner in which solid geometry may be worked into every part of the course.

The next Section, which is the longest, is in some ways the most important part of the Report. It aims at providing something that to most teachers has hitherto been inaccessible, namely, a careful discussion of the principal difficulties encountered in the attempt to keep a course in geometry free from arguments that even the commonsense logic which is appropriate to the schoolroom must recognise as defective. There are several topics, such as the meaning of superposition and the use of limits, which many teachers approach with some uneasiness, aware that the way is said to abound in pitfalls. Some knowledge of the nature of the difficulties is necessary if the teacher is to discriminate between those he must ignore, those he can evade, and those which his class is capable of facing. The text-book, if it is prepared for the pupil without a companion volume for the teacher, cannot discuss these matters; it must adopt definite lines which the teacher, unless equipped to criticise them for himself, will suspect if they are easy and resent if they are hard. Section III is concerned with subjects of this kind.

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