ABSTRACT
The English National Curriculum has as one of its aims that all pupils should be able to: solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions. Initially, young learners should be asked to recognise and re-create simple patterns and talk about what they see. Early skills include matching similar objects and sorting objects into categories they can describe. Two other ideas which are important when working with children on their mathematical thinking are specialising and generalising. Specialising is the process students use when they look at specific examples in order to get started on a problem. The ideas of specialising and generalising appear throughout mathematics.
