mathematics

The Role of `Using and Applying` in Primary Mathematics in Britain

You have probably noticed that people who are particularly good at mathematics often seem to think about issues slightly differently to others . For teachers of mathematics it will be their task to help pupils learn to think like mathematicians . Thinking mathematically is not an end in itself rather it is a process through which we make sense of the world around us . Learning to think mathematically is far more than just learning to use mathematical techniques , although developing a facility with

the tools of the trade is clearly an element . Mathematical thinkers have a way of seeing , representing , and analysing their world , and a tendency to behave like mathematicians - that is , to use mathematics to explain situations and solve problems . My argument then is that integrating a wide range of challenging tasks within teaching including practical investigation and extended problem solving , development of effective learning within using and applying in primary mathematics becomes something that develop metacognitive knowledge and problem-solving ability

`Using and Applying Mathematics ' deals with a number of interrelated processes associated with mathematical thinking . These processes underpin both the learning of new mathematics and the application of existing mathematical knowledge to real-life situations . At its heart these processes are about problem solving and investigation both in the application of mathematics and within mathematics itself . The aim of this Using and Applying was to focus attention on such problem-solving processes as well as on the content of mathematics

The position and nature of `Using and Applying Mathematics ' was fiercely contested from the outset and remains an area of hot dispute today . The dispute highlights two positions on the nature of mathematics . On the one hand are those who see mathematics as a body of knowledge consisting of facts and rules to learn off by heart and reproduce in examinations On the other hand are those who see it as a human construction for making sense of the world , emphasizing creativity , investigation , and problem solving . Clearly mathematical investigation and problem solving cannot exist in isolation from the body of mathematical knowledge Unfortunately , however , it is all too possible to teach mathematical content (badly ) in such a way that challenging problems , mathematical investigations , and real problems are not experienced (Burton 1984

The place of practical work in learning mathematics is often supported by reference to the work of developmental psychologists . Probably the most influential of these is Piaget . His work had a strong influence on the Nuffield Project team , who dedicated their first publication to him Piaget 's work is also referred to in books which discuss how children learn mathematics . For example , Liebeck (1984 ) discusses the theories of various psychologists talking in detail about Piaget , but also discussing the work of others . Liebeck 's own view is that young children learning mathematics should start with experience with physical objects Wood (1988 ) provides another comparison of theories of learning . In discussing the work of Piaget and Bruner , he points out...