Before next time, ask each teacher to try the task with a class.
They should reflect on how effective it was; what progress students made with the development of problem-solving skills and be prepared to share their thoughts with the group at the next session.
Students can use drawings to help them look at a problem from many different perspectives.
In this tool we further explore the meaning of problem solving and what a problem in mathematics may look like.
One conclusion that may be drawn from these investigations is that individual differences in problem solving and decision making must be considered to adequately understand the dynamics of these processes (Stice, 1987).
Attention must be paid to both the problem-solving process and the specific techniques associated with important personal characteristics.Teachers often find it easier to think about the mathematical knowledge rather than the skills needed. Ask the teachers to consider: What particular skills would they like their students to develop? As a group, select a task (from the mascil classroom materials or from other sources) and discuss how you might use this in the classroom.The following (incomplete) list of skills can be used to prompt ideas: Ask the teachers if they agree with the items in this list. Alternatively, the group might consider how they could develop one or more of the sample tasks to increase the opportunities for problem solving.Firstly, ask the teachers to read through the sample tasks and then work in pairs to compare them, to identify the main features of each task and discuss the differences between the tasks.Suggested sample tasks: Task 1: Mixing paint Task 2: Fencing Task 3: Magic V investigation Task 4: Prism As a whole group, share the outcomes of your discussions and try to list the main features of each task.There is concurrent and parallel research on personality and cognitive styles that describes individuals' preferred patterns for approaching problems and decisions and their utilization of specific skills required by these processes (e.g., encoding, storage, retrieval, etc.).Researchers have studied the relationship between personality characteristics and problem-solving strategies (e.g., Heppner, Neal, & Larson, 1984; Hopper & Kirschenbaum, 1985; Myers, 1980), with Jung's (1971) theory on psychological type serving as the basis for much of this work, especially as measured by the MBTI (Myers & Mc Caulley, 1985).Discuss the demands on students of each task and how you might put the tasks into order according to the category.The activity is designed with this in mind so teachers are prompted to think further about what is involved in a problem-solving task).This paper relates a model of the problem-solving process to Jung's theory of personality types (as measured by the MBTI) and identifies specific techniques to support individual differences.The recent transition to the information age has focused attention on the processes of problem solving and decision making and their improvement (e.g., Nickerson, Perkins, & Smith, 1985; Stice, 1987; Whimbey & Lochhead, 1982).