Some problems with mathematical problem solving

The history of problem solving in schools has been problematic and this chapter outlines some of the background issues. Preferably problem solving has students' exploring unfamiliar problems and using a range of strategies that enhance their powers of analysis, reasoning, generalising and abstracting. Ideally students' should experience the beauty of mathematics and its power to make sense of their world. Good problems create opportunities for assessment of quality of student thinking and learning, producing data that is necessary for further planning of classroom activities. Problems are usually written and Newman's Error Analysis is a useful diagnostic procedure that links both problem solving and language concerns. From the diagnostic data different pedagogical strategies have been developed to overcome student difficulties. This chapter will highlight adaptations that contribute to problem solving and effective assessment for learning