The aims of mathematical education

 

The aims of mathematical education

 

The so-called ‘practical people’ merely state somewhat vaguely that mathematical that mathematics is necessary in practice, both in everyday life and in scientific work and industry, and so all mathematics ought to be practical – there are no other admissible reasons why children should learn mathematics.

 

Reflections will show that extremely little mathematics is in fact necessary in everyday life.  Multiplication is already largely superfluous, and the number of people who are going to need mathematics for their work is relatively small (they could easily be taught it as part of their vocational training).  Yet a large proportion of school time, both in the elementary and higher grades, is spent in studying quite detailed mathematics, with admittedly rather indifferent results.  It seems that we ought either to reduce the amount of mathematics learnt by children or be rather more clear about why we are making them learn it.  Perhaps we have something quite different at the back of our minds when we think about mathematical education --- something not entirely practical, namely a feeling that mathematics should add something to the quality of the person who has learned it by allowing him to participate in a cultural stream.  But it is quite clear that things have not worked out this way.  Mathematics is not used or enjoyed by people after they leave school, so that if our aim was to allow children to participate in this aspect of our culture, we have certainly largely failed.  It is legitimate to ask why this is so, and what it is about the present arrangement in mathematics-learning that prevents all but a number of relevant suggestions we might make on the practice of mathematics-learning as a result of the observations made in these experiments.

 

            Once we have agreed that our aims are not entirely practical, the whole question of what mathematics to teach children is immediately thrown wide open.  If mathematics-learning is to be regarded honestly as a cultural activity in the way we regard the appreciation of literature, art and music, then the present syllabuses immediately lose their sanctity.  Any syllabus would be suitable provided that with it most children could appreciate mathematics as a beautiful structure, irrespective of possible practical uses.  Many parts of mathematics are accessible to quite young children, as our work with all the experimental groups shows.  A great deal of the mathematics studied by these children has always been regarded as ‘higher’ mathematics, and for that reason difficult.  Yet there is considerable evidence, even apart from the work reported here, that certain mathematics is often regarded as easier by the lower grades than by the higher grades. A certain project, for example, had been giving fourth-and fifth-grade children algebra, including ‘difficult’ things like quadratic equations, and progress on the same syllabus had almost invariably been more rapid in the lower than in the higher grades. (Edited extract from Z.P.Dienes’ book “An Experimental Study of Mathematics Learning, 1964).