TEACHERS STUDY CHANGES IN MATHEMATICS

Press, Volume CIII, Issue 30482, 2 July 1964, Page 11

TEACHERS STUDY CHANGES IN MATHEMATICS

in the Papanui High School every Thursday evening during the winter term, about 150 teachers from primary and post-primary schools, both State arid private, are “back-to-school” as students, participating in a course entitled "Modern Approaches to Mathematics." These teachers are giving up their time to bring themselves up-to-date and so become better prepared to teach the children in their charge along the lines currently being developed in most Western countries.

The course is under the direction of Mr D. M. Goldsmith, head of the mathematics department at Papanui High School, who Is assisted by senior teachers from three other city post-primary schools. Mr Goldsmith and his team have been experimenting now for several years with this “modern approach” material and have been responsible for much of the lecturing and tutoring at recent national. refresher courses for . post-primary teachers, organised by the Refresher Course Committee of the Department of Education.

Last year a similar course at Papanui was attended by about 70 teachers, but the course this year differs from that run last year in that this year a specific textbook is being examined. The text selected is one recommended by the Canterbury Mathematical Association as illustrating clearly the type of approach to mathematics suggested by contemporary thought in the United States, namely “Introduction to Mathematics,” by Brumfiel, Eicholz, and Shanks. Each evening a brief lecture Is given by one of the tutors on the mathematical background to the text material, and this is followed by a “workshop” session when the teachers become the class and work through and discuss problems from the text What is the history of, and the idea behind this upsurge in mathematical thought at the school level? .

The first noticeable activity commenced in the United States when in 1951 the University of Illinois Committee on School Mathematics was formed and commenced their researches into the teaching of mathematics and the understanding of mathematical concepts. With this initial impetus, various bodies , in the

United States, Great Britain, and Western Europe undertook further research the results of which are continually filtering into New Zealand. New Zealand teachers are not slow to recognise that much could be learned from these experimental programmes but many are naturally suspicious of educational development from the United States which operates, in mathematics at least, under a very different set of circumstances. However, more recently, material from the United Kingdom has shown that the traditional approach there is undergoing change, as is the approach in France, West Germany, Belgium, and Australia: New Zealand appears more prepared to accept these developments rather than the corresponding developments tn the United States.

In New Zealand there has just been produced a new infant manual for the teaching of arithmetic and this has shown that New Zealand thought in this field is well in line with, although perhaps less ambitious than, some of the most modem. American schemes.

In September 1961, a conference was held at Lopdell House in Auckland to study developments overseas, particularly the Illinois programmes, and again this year further conferences were held in March to consider the Standard 1 to 4 programmes, and in April the Form 1 to 6 programmes. The decisions of the Director of Education on the recommendations from these conferences is eagerly awaited by teachers all over the country, for it is hoped that a definite policy for future development will be framed. This development is likely to include much of the attitudes in approaches being developed in America, England and Australia, and, it is hoped, the genuine opportunity to test this work in external examinations. Broadly speaking, it would be fair to say that whereas elementary arithmetic and mathematics in the past has been taught as a series of isolated processes which must be learned largely by rote, the approaches are now emphasising understanding of broad basic concepts and principles and the application of these to a wide variety of situations. Many of these ideas are not “modern" but it is the awakening to them in the teaching situations which is new. Most teachers

have been aware that the operations in mathematics are supported by far-reaching fundamental principles, but these principles have not been taught to the children. Teacher training programmes in England, and university courses in New Zealand have certainly included these aspects in their development but the great body of teachers, particularly primary teachers, have not been trained in New Zealand with this background. Conversely, many of the ideas now being taught have been developed this century and may be considered modern; the study of situations of inequality as well as those of equality, number systems to bases other than 10 and the mathematical implications of . these, the “set” concept as one which in its language and ideas unifies many of the otherwise apparently diverging branches of mathematics, to name but a few.

Does this mean that our children will now be trained in mathematical ideas but will not be able to carry out simple basic calculations? Not at all; with a background of understanding developed alongside the development Of the skill, the child should be able to carry out more readily the many calculations which are part and parcel of the most traditional course, that is, if these still need be done.

With the coming change to decimal coinage approximately a whole year of arithmetic teaching time will be saved and this will mean that the teaching of genuine mathematical concepts will become an integral part of the primary teaching programme, and teachers must become equipped to undertake this task.

Through the officer for school mathematics, and members of the Education Department’s inspectorate, teacher training and retraining Is being carried out continually. The Canterbury Mathematical Association, along with other similar bodies throughout the country, is endeavouring to do its share of the work, but it is through evening classes for teachers such as that organised by Papanui High School, with the assistance of the Department of Education, that a great deal more can be done for it is under these circumstances that teachers from all branches of the profession can come together to discuss their common problems and by such practical participation, improve the educational opportunities of New Zealand's greatest asset, its children.