Mathematics and Society - OS X Lion Server

DIDACTICSTEACHING VIA PROBLEM SOLVINGSome types of problems are so important that often we deliberately p'rovide muchpractice so that they become exercises. For example, we do want our students to beable to calculate checkbook balances, gasoline mileage, interest, areas of floors,averages, . . . . What we may wish to avoid, however, is making these situationsexercises from the start ("Here's how to do this kind"). Initial work could wellretain the problem nature of the situations ("How do you think we might try tofigure this out?").Transfer through problem solving. Based on his studies, Brownell [1942] hasnoted that concepts and techniques are likely to be most useful in problem solvingwhen they themselves are learned through the solving of problems. As is noted inthe section Teaching for Transfer, working problems in many areas is one of thetechniques for maximizing transfer. Dealing with the various topics from Mathematicsin Science and Society should enhance a student's view of the applicability andimportance of mathematics.Motivation through problem solving.Many students are stimulated by challengeslike Problems 1-5 above, particularlyif the teacher seems to beenthusiastic and interested in theproblem. But many students are not"turned on" by such problems, unlessby chance they get caught up in theenthusiasm of other students, thegroup competition that might be used,or some other feature which may notbe entirely credited to the problem. Since the apathetic student is often the unsuccessfulstudent, it is perhaps of first importance to work for an optimisticattitude: (a) at first choose problems that look like they can be solved (Problems1 and 2, for example) or that have shown a great deal of appeal to former students,(b) present the problems so that the student's ego is not threatened (see the sectionStudent Setf-Concept in Number Sense and Arithmetic Skills, Mathematics ResourceProject) and (c) be optimistic yourself. [Johnson and Rising, 1972, p. 265]23