One Secondary Teacher’s Use of Problem-Solving Teaching Approaches

This paper reports part of a larger study and examines one teacher’s use of problem-solving teaching approaches in Years 7 and 9. Thirteen problem-solving lessons were observed over an 18 month period during which the teacher devised and used 7 different problem-solving tasks. Three tasks are described in detail and analysed in terms of task structure and implementation, and how the teacher managed whole-class discussions. Analysis highlights changes in the design and use of the tasks. They became more open-ended and the teacher improved the quality of whole-class discussions to promote student learning and reflection. Anderson and White (2004) distinguish between problem solving, “the process of students exploring non-routine questions, using a range of strategies to solve unfamiliar tasks, as well as developing the processes of analysing, reasoning, generalising and abstracting ” (p. 127), and problem-solving teaching approaches, “investigations, open-ended questions, and modelling tasks, as well as providing opportunities for students to pose questions and explore new ideas ” (p. 127). Problem-solving teaching is therefore an approach in which “teachers see themselves as guides, listeners, and observers rather than authorities and answer givers” (Norton, McRobbie, & Cooper, 2002, p. 39). Problem solving is an important part of what it means to do mathematics and students require frequen