ABSTRACT
This chapter aims to introduce the reader to the variety of mathematical problem-solving tasks available for different ability levels of the pupils. The links between the Processes element of the National Curriculum, and the requirements of GCSE coursework are highlighted, as is the use of structured tasks for pre-GCSE work. Mathematical investigations are frequently used in the primary school classroom to engage and motivate the pupils. Much of the early learning in maths utilises practical activities where the pupils have hands-on experience of counting, grouping, selecting by criteria, sorting, identifying patterns, modelling and controlling the motion of a ‘Roamer’ to discover distance, direction and angles. However, as pupils progress through the school, less use may be made of practical activities and more emphasis placed on textbooks to practise skills and reinforce knowledge. Consequently, when pupils reach the end of Key Stage 3, there may be lower levels of enthusiasm for discovery and investigation in maths, leaving the GCSE teachers to find and rekindle the ‘detective’ in the pupil. The following sections illustrate the role of investigations in preparing students for GCSE coursework and offer a number of examples of the incline of difficulty that exists across the standard tasks in use in schools.
