Children’s implicit mathematical knowledge

Children’s implicit mathematical knowledge

It has long been accepted that pre-school children possess considerable implicit mathematical knowledge and experience, often to quite sophisti- cated levels of understanding (Gelman and Gallistel 1978). Hughes (1986) demonstrates that by the age of five most children can carry out a range of additions and subtractions in concrete and hypothetical situations. Many mathematics educators argue for teaching methods which acknowledge and build upon children’s individual knowledge and understanding. Liebeck (1984) bases her ELPS (Experience–Language–Pictures–Symbols) approach on the work of Bruner. She suggests that children should encounter mathematical situations initially through first hand experience (Experience) and should be encouraged to discuss what they see and do (Language). This will enable them to internalise their experiences. They should then be supported in representing the situations through draw- ings which are meaningful to them (Pictures) and finally, once they have fully grasped the significance of the underlying mathematical con- cepts and processes, they should be introduced to symbolic notation for recording their experiences (Symbols). The abstraction process (Skemp 1977), whereby learners come to represent and manipulate situations symbolically, is the most powerful feature of mathematics as a discipline. The ability to represent a physical act such as combining a set of three objects and a set of two objects with arbitrary symbols (e.g. 3 + 2) is fundamental to the abstraction process and is potentially the area most fraught with difficulty for the early years child. Mathematicians have taken centuries to devise and hone their procedures for performing calcu- lations in the most efficient and elegant ways and it is often expected that young children will learn these abstracted techniques within a few years of schooling.

With its roots firmly planted in constructivist principles, emergent writ- ing has become an accepted part of many teachers’ early language activ- ities. Less well known or adopted is ‘emergent mathematics’ which has been proffered as a means of identifying and developing children’s own math- ematical awareness and understanding. Whitebread (1995) describes emergent mathematics as an approach that assumes children will develop an understanding of numbers by playing around with them, using them for their own purposes, talking about them with each other and adults, beginning to represent mathematical processes in ways that make sense to them and becoming more aware of their own and their teachers’ math- ematical thinking. Although this approach originally underpinned the National Numeracy Strategy (DfEE 1999), in some classrooms the purposes With its roots firmly planted in constructivist principles, emergent writ- ing has become an accepted part of many teachers’ early language activ- ities. Less well known or adopted is ‘emergent mathematics’ which has been proffered as a means of identifying and developing children’s own math- ematical awareness and understanding. Whitebread (1995) describes emergent mathematics as an approach that assumes children will develop an understanding of numbers by playing around with them, using them for their own purposes, talking about them with each other and adults, beginning to represent mathematical processes in ways that make sense to them and becoming more aware of their own and their teachers’ math- ematical thinking. Although this approach originally underpinned the National Numeracy Strategy (DfEE 1999), in some classrooms the purposes