The Secondary School Mathematics AreaAuthor(s): Claude BirtwistleSource: Mathematics in School, Vol. 2, No. 5 (Sep., 1973), pp. 30-31Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30211082 .

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The Secondary School Mathematics Area

by Claude Birtwistle, Mathematics Adviser, Lancashire Education Committee

The importance of the environment in the understand- ing and learning of mathematics has been recognized at the primary level for some time. This is pure Piaget: through experience of the different things around him the child progresses to further levels of concept forma- tion. These ideas are put into practice by the primary teacher in methods of teaching and in the provision of appropriate materials within the classroom. New approaches have made new demands on the furnishing of classrooms, e.g. tables instead of desks.

But the demands have gone beyond furnishing to the actual design of the teaching area; the unit is no longer the classroom but the school itself and primary schools are now designed in open- or semi-open-plan structure so that every part of the school has a place and function in the education of the children therein. Buildings have to be adaptable to a wide variety of uses and, such is the cost of school building today, it is essential that there is maximum usage of all space.

New ideas are evident, too, in the design of secon- dary school buildings and it is worthwhile to consider the place of mathematics in these designs. At last there is recognition that the subject should no longer be regarded as being capable of being taught in any class- room or teaching space. However be it noted that such recognition has not come unilaterally; secondary schools are now designed with areas devoted to par- ticular fields of study, e.g. environmental areas, craft areas, science suites.

Influences already evident in primary schools are to be found in the design of these new secondary build- ings. Change in methods of teaching has come earlier at the primary level than at the secondary and since building design has to meet present and anticipate future needs of teachers, secondary school design is learning from recent design at the primary level.

So far as mathematics is concerned the idea of the mathematics laboratory has gained favour in the past fifteen to twenty years. The idea is first class: no longer is mathematics to be a subject learned by doing 30

endless examples from textbooks but one which demands activity with real things-mathematics stems from life itself. Unfortunately as schools grow bigger one mathematics laboratory becomes hopelessly inade- quate; each class gets a mere single lesson per week in the laboratory and what takes place there tends to be regarded as something different from mathematics, in a manner somewhat similar to the primary school which, a few years ago, had arithmetic timetabled for Monday to Thursday with Nuffield mathematics on Friday afternoon!

However it is not sufficient to string a number of mathematics laboratories together along a corridor and call this a mathematics suite. Provision of an area for mathematics demands careful thought and planning. What are teachers doing with their classes and how can the design of the buildings and equipment best help them in that work? Even more important remembering the life-span of school buildings, how can future needs be anticipated?

Some of the present trends in the teaching of secon- dary school mathematics include an increase in prac- tical work, a greater amount of individual working by pupils and topic and project work. There is need for group discussion at times but still a place for the more formal lesson. Experiments are being conducted in team teaching either within the subject or across a group of subjects. There are changes in equipment too, e.g. overhead projectors are becoming essential, com- puter terminals are increasing in number.

The first essential of a mathematics suite, therefore, is its flexibility; it has to be easily adaptable to a variety of uses. Can one meet this by providing a com- pletely open-plan area? Such an area clearly has the greatest flexibility but may not meet all requirements of the subject teaching. A subject which is concerned with ideas which are easily exchanged can be taught in a small discussion group within a larger area, but mathematics often requires ideas to be expressed in symbolism and there tends to be a need for a higher

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degree of formality. Thus mathematics teachers, for the present at least, tend to call for an area where a larger group may be brought together from time to time for a more traditional type of lesson.

Assessing these various factors my own view is that what is needed in a mathematics suite is a semi-open- plan design with general and more specialist areas. Basic teaching areas should be adaptable to individual and group work and at the same time allow a more formal lesson to be given without outside disturbance. Practical work clearly takes place at various levels of "prac- ticality" ranging from simple activities such as pattern drawing to more complex work demanding the use of large apparatus. The simple work can be done in the normal teaching area but some separate area is needed where the larger project can be undertaken and perhaps be left from one teaching period to the next.

Individual work often produces the need to go away to a quiet place or perhaps to an area where one can look up references and pursue personal interests un- disturbed. Such needs can be met by a small reference space containing occasional tables and chairs and two or three study carrels.

The need for taking groups of various sizes can be met by division rooms but since adaptability is the keynote, provision could be made for two division rooms to be combined to provide a teaching space of normal class size, i.e. about thirty places.

These ideas are exemplified by a mathematics suite at present under construction, a simplified plan of which appears in Figure 1. While this arrangement is attainable in new premises, adaptations of existing buildings frequently put limitations on what can be done. Figure 2 illustrates a mathematics suite which is to occupy part of one floor of an existing building and

has had to be designed to existing walls, doors, etc. The rest of this floor of the building is taken up with pro- vision for humanities in open-plan design. Although not so convenient in many ways as the area illustrated in Figure 1, this second design does incorporate a number of interesting features, particularly the small room for calculators and computer terminal which will isolate any machinery noise.

In both these cases, however, there is no provision for a large group such as a whole year or half a com- plete year to be taken at the same time as may be required in some team teaching situations where a "lead" lesson is being given. Provision of such an area is extremely difficult except in a true open-plan situa- tion, but Figure 3 gives a possible solution where classes may be taken in the areas marked Maths 1 and Maths 2. There are still practical and reference areas, but if pupils in Maths 1 and Maths 2 are faced towards the entrance to the suite it is possible to use the entire area to accommodate a large group of seventy or eighty pupils at a time when a "lead" lesson needs to be given. The teacher giving such a lesson would station himself somewhere near the entrance to the suite and provision for blackboard work, overhead projector, etc., would need to be made in this area.

From all this it should be apparent that the design of the teaching area is of some importance in the develop- ment of the teaching of mathematics. It can not only assist in the development of new and improved methods but actually encourage those who work therein to experiment in methods of class organization and teaching.

In the next issue, Bob Shaw writes about equipment for the mathematics room.

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