The Pedagogy of Mathematics: Is there a unifying logic?
The evolution of human civilisation engendered a need to develop systemic tools to measure and control human activity and natural phenomena. From early on this led to the development of systems of patterns, numbers and the logic of their interrelationships. Over time, commercial and other social activities influenced the development of arithmetic and mathematics. As an example, a basic calculation had to evolve to govern such relations as how to divide a family inheritance or measure assets. This gave birth to the logic of numbers in the governing of social and human development. Ishango bone, used by the “fishing and hunting” population in the Congo, is evidence of the social role of mathematics.
As South Africa’s modern economy emerged, founded on mining activity, the need for specialised skilled people in the sciences especially mathematical sciences grew. The College (now known as the University of Cape Town) started to focus its programme to support the mining industry, so was the Kimberley College which led to the formation of Wits University and the University of Pretoria. In this context access to maths and its teaching reflected the social engineering of the epoch. The teaching of maths was focused on creating students who would use maths in resolving issues that would support mining and other commercial activity, and buttress the socio-political relations of the time.
Mathematics is a science that exists and develops for its own sake, with a variety of branches. However, its utility is in supporting other sciences (including social sciences) and in underpinning the study of natural phenomena. Globally, the pedagogical system evolved in various parts of the world and assumed various forms depending on the level of development and culture of particular regions. The learning centres of China, Mali and Egypt were among the earliest formal expressions of this. Its modern expression can be traced to the evolution of educational systems of Europe and North America.
A number of countries seem to have performed relatively well in the teaching of mathematics; and examples in this regard include Hungary, Zimbabwe, China and Russia. The various dynamics that relate to such performance – development of curricula, systems of training of trainers, issue of language, popularisation of the discipline and so on – need further interrogation.
Given the socio-political history of South Africa’s educational system, the challenge is to build on the relative excellence attained in the education system of the privileged; and to correct the systematic undermining of the proficiency of teachers and leaners alike within the Black, and especially African communities. While improvement of the entire education system is critical to this – including management of schools, application by teachers and learners alike, involvement of parents and allocation of resources – the very issue of how mathematics is taught, and whether a unifying logic needs to be developed will be fundamental to the excellence that society yearns for.