The examples above and the theoretical outlines before them provide considerable food for thought. Every problem is essentially different from every other problem. If not, they would not truly be "problems." Constructing a mathematical learning environment which strikes a balance between challenge and support, then, will involve finding and posing suitably rich and engaging mathematical tasks, and then examining these to see ways in which the learner may be assisted through the problem solving process. The ideas presented here provide useful guidelines for this, but it will require some practise in order to become proficient. Look again, now, at a few of your "favourite problems," and try developing a series of graduated help formats for each. There are no right and wrong approaches here, but some will be better than others - hence a group approach would be very helpful in learning to look at the same situation through new eyes. Be patient, remembering that the teaching of problem solving has long been a most difficult and contentious aspect of mathematics education, possibly since we have paid to much attention for too long to the importance of challenge and not nearly enough to the vital role of support.

Sample Problem 3. References.

Challenge and Support Index