August 30, 2008 Mathematics is the only truly universal language. It describes the world and facilitates the vast majority of our advances in understanding. Mathematics underpins education: the only surefire cure to the world’s ills. Mathematics teaching is as vital as ever both in support of key fields such as life sciences, alternative energy development, or information technology, and also through its unique ability to develop problem solving skills. It should be highly relevant not just for the elite few but for all people in education. Recent research has shown that school students’ mathematical achievement is directly influenced by the students’ beliefs about mathematics and its teaching, teachers’ beliefs about mathematics and its teaching, and the ways in which teachers initiate and sustain learning opportunities. An attempt to re-energise mathematics teaching in Europe is being made in a new European Science Foundation (ESF) project examining a range of factors thought to influence achievement.
The new project was discussed at a recent workshop organised by the ESF, which brought together experts in different areas of mathematics education. "It was agreed that we would begin the process of developing a comparative project, involving between fifteen and twenty European countries, to examine the interrelatedness of the mathematics-related beliefs of teachers and students, teacher practices and student cognition," said Paul Andrews, the workshop's convenor and Senior Lecturer in Education at the Faculty of Education of Cambridge University in the UK.
Andrews pointed out that the solution to the mathematics teaching conundrum was complex and multi-dimensional, just like many of the great problems in the field itself. On the one hand, enthusiasm needed to be balanced with rigour in order to motivate students while also teaching skills and knowledge worth acquiring. "To assume that the development of enthusiasm is sufficient to guarantee achievement would be naïve as there are countries in which students have little enthusiasm for mathematics but achieve relatively highly and, of course, vice versa," pointed out Andrews.
There has also been a tension between immediate vocational objectives in response to the needs of employers, and the higher ideal of teaching logical thinking and deeper mathematical problem solving. European countries have to date resolved this tension in different ways, with the UK being at the vocational end of the spectrum, while Hungary has taken the purest approach with its traditions for mathematical rigour.
"One of the problems of English education is that students experience a fragmented and procedural conception of mathematics, due to underlying notions of vocationalism, and so rarely come to see the subject as a coherent body of concepts and relationships which can be worth studying for the intrinsic satisfaction it can yield," said Andrews. "The situation in countries like Hungary is almost the complete opposite - all students experience an integrated and intellectually worthwhile mathematics taught by teachers with little explicit interest in the applications of the subject but an enthusiasm for logical thinking and the problem-solving opportunities that mathematics can provide."
But the issue of mathematics teaching is not just about content, but also attitude, on the part both of pupils and teachers. One significant finding to emerge from the workshop was that the common practice of dividing pupils into sets defined by ability, which, in the UK context, is applied more for mathematics teaching than any other subject, can be counterproductive, even for the most able pupils. "Where teachers do not necessarily expect to teach students in ability groups but expect to work with the full ability range, achievement is generally higher across the board," said Andrews.
Another finding that perhaps contradicted common wisdom was that students often progressed best when taught to approach problem solving collectively instead of in isolation. This runs counter to the perception, manifested regularly in UK schools, that mathematics is a lonely endeavour pursued by individuals in competition rather than cooperation.
The workshop "The Relevance of Mathematics Education" was held in Cambridge, UK in January 2008. Each year, ESF supports approximately 50 Exploratory Workshops across all scientific domains. These small, interactive group sessions are aimed at opening up new directions in research to explore new fields with a potential impact on developments in science.
It remains to be seen whether the ESF project will lead to a radical shake up in mathematics teaching comparable to the introduction of the so called "new maths" in the 1980s in the place of the previous more arithmetically based approach. More likely it will lead to rebalancing of teaching, bringing greater consistency and rigour to deliver a more wholesome curriculum.