Influences from Society - Mathematics learning

Schools and individual learners exist within societies and in our concern to ensure the maximal effectiveness of school mathematics teaching, we often ignore the educational influence of other aspects of living within a particular society. It is indeed tempting for mathematics educators particularly to view the task of developing

mathematics teaching within their particular society as being similar to that of colleagues elsewhere, largely because of their shared beliefs about the nature of mathematical ideas. In reality such tasks cannot deal with

mathematics teaching as if it is separable from the economic, cultural and political context of the society. Any analyses which are to have any chance of improving mathematics teaching must deal with the people - parents, teachers, employers, Government officials etc. - and must take into account the prevailing attitudes,

beliefs, and aspirations of the people in that society. The failure of the New Math revolution in the 60's and the early 70's was a good example of this phenomenon (see Damerow and Westbury, 1984).

It is therefore to explore those aspects of societies which may exert particular influences on mathematics learning. These may happen either intentionally or unintentionally. Societies establish educational institutions for intentional reasons - and formal mathematics education is directly shaped and influenced by those institutions in different ways in different societies. Additionally, a society is also composed of individuals, groups and institutions, which do not have any formal or intentional responsibility for mathematics learning. They may nevertheless frame expectations and beliefs, foster certain values and abilities, and offer opportunities and images, which will undoubtedly affect the ways mathematics is viewed, understood and ultimately learnt by individual learners.

Coombs (1985) gives us a useful framework here. In discussing various 'crises in education' he argues that education should be considered as a very broad phenomenon, rather than being a narrow one, and that there are d i fferent kinds of education. In his work he separates Formal Education (FE) from Non-formal Education (NFE), and Informal Education (IFE). Formal Education, he says, "generally involves full-time, sequential study extending over a period of years, within the framework of a relatively fixed curriculum" and is "in principle, a coherent, integrated system, (which) lends itself to centralized planning, management and financing" , and is essentially intended for all young people in society.

In contrast NFE covers "any organised, systematic, educational activity, carried on outside the framework of the formal system, to provide selected types of learning to particular subgroups in the population, adults as well as children" . In contrast to FE, NFE programs "tend to be part-time and of shorter duration, to focus on more limited, specific, practical types of knowledge and skills of fairly immediate utility to particular

learners" .

Finally IFE refers to "The life-long process by which every person acquires and accumulates knowledge, skills, attitudes and insight from daily experiences and exposure to the environment.... Generally informal education is unorganized, unsystematic and even unintentional at times, yet it accounts for the great bulk of any  person's total lifetime learning - including that of even a highly 'schooled' person" . We shall organise this contribution around these three different kinds of education, looking particularly at the influences from society

on the three kinds of mathematical education. Finally there will be a discussion of some of the significant implications which result from this analysis .

Societal influences through formal mathematics education (FME) It seems initially obvious that any society

influences mathematics learning through the formal and institutional structures which it intentionally establishes for this purpose.

P a r a d o x i c a l l y, at another level of thinking, it will not be clear to many people just what influence any particular society could have on its mathematics learners, in terms of how this will differ from that which any other society might have. Indeed, mathematics and possibly science have, I suspect, been the only school subjects assumed by many people to be relatively unaffected by the society in which the learning takes place.

Whereas for the teaching of the language(s) of that society, or its history and geography, its art and crafts, its literature and music, its moral and social customs, which all would probably agree should be considered specific to that society, mathematics (and science) has been considered universal, generalized, and therefore in some way necessarily the same Tom society to society. So, is this a tenable view?

What evidence is there? 

The formal influences on the mathematical learners will come through four main agents - the intended mathematics curriculum, the examination and assessment structures, the teachers and their teaching methods, and the learning materials and resources available. The last two aspects which are part of the implemented

curriculum (Travers and Westbury, 1989) will be specifically considered in the final two chapters of this book and therefore I will concentrate here on the first two, the intended mathematics curriculum, and the examinations. The intended mathematics curriculum If we consider the mathematics curricula in different countries, our first observation will be that they do appear to be remarkably similar across the world. Howson and Wilson (1986) talk of the "canonical curriculum" (p.19) which appears to exist in many countries. They describe "the familiar school mathematics curriculum (which) was developed in a particular historical and cultural context, that of Western Europe in the aftermath of the Industrial Revolution". They point out that "In recent decades, what was once provided for the few has now been made available to - 

indeed , forced upon - all. Furthermore, this same curriculum has been exported, and to a large extent voluntarily retained, by other countries across the world. The result is an astonishing uniformity of school mathematics curricula world-wide" . This fact has made it possible to conduct large-scale multi-country surveys and comparisons of mathematical knowledge, skills and understanding such as those by the International Association for Education Achievement (IEA) whereas such comparisons would probably be unthinkable in a subject like history. Indeed, one of the main research issues in the Second International Mathematics Survey (SIMS) was whether the 'same' mathematics curricula were being compared (see Travers and Westbury, 1989). 

It could be argued that such international surveys, and the comparative achievement data they generate, encourage the idea that the mathematics curricula in different countries should be the same, particularly when, as in this case, they are seeking the highest common  factors of similarity. At the very least, this approach could well lead to mathematics educators in many countries anxiously looking over their shoulders at their colleagues in other counties to see what their latest curricular trends are. One wonders what would result from a research study which sought to find the differences between mathematics curricula existing in different countries.