Child-methods in secondary mathematics

An earlier research project, the Concepts in Secondary Mathematics and Science (Mathematics) project, identified both a hierarchy of levels of understanding in different areas of secondary mathematics, and a number of particular errors which were made by significant proportions of the children tested. Preliminary consideration of these errors and the strategies which appear to have given rise to them suggests that the use of informal naive methods which are limited in their applicability is widespread even at fourth-year level. The suggestion is made that there may be two systems of mathematics coexisting in the secondary school classroom: the formal taught system, and a system of child-methods which are based upon a counting, adding-on or building-up approach, and by which children attempt to solve mathematical problems within a human-sense framework. The difficulties which some children appear to experience in mathematics is suggested to be due in part to these children's non-initiation into the formal taught system. The implication of such a view for teaching and research are indicated.