Every day, in thousands of classrooms, excellent lectures are delivered on fascinating subjects, students and lecturers nod their heads in satisfaction, and on both sides of the podium there is the feeling that "everyone understands."
Then the students start trying to apply the new ideas. They have not yet absorbed the day's new concepts. They cannot yet use the material in any cognitive fashion. They find they must assimilate this new material a little bit at a time: reflect on the new concept, work a problem, study the result, and repeat that process until the new material is truly understood.
This understanding is a worthy goal - one which is not reached as frequently as it could be.
Our schools do much in the way of demonstration material, laboratories, video and computer presentations. Rensselaer Polytechnic Institute is an institution which has done extensive work in this regard, but in spite of those efforts, a prominent member of the faculty there has remarked, "They still cannot solve the problems." (Resnick 1972) Although twenty years have gone by since that remark was made, need for improvement still exists.
Homework problems have long been used to reinforce and develop the ideas presented in lectures and textbooks, but most students are unskilled in the problem solving process and repeatedly fail to achieve the desired learning experience. That failure leads to further uncertainties and a downward spiral in confidence begins at a time when just the opposite is needed.
An important obstacle has been the lack of an everyday, common sense, reliable approach to solving problems.
A reliable, consistent approach to solving problems makes it possible for students to
The process of developing meaningful problem solutions always leads to greater understanding of the subject matter. It is a constant process of building and reinforcing.
Success in problem solving breeds success in learning, and with success comes that upward spiral all of us would like to see for our students. Imagine what it would mean to double the number of truly capable graduates from our schools! Or to increase the average competency of all our graduates by even 10-15%.
Reliable problem solving does a great deal toward achieving that goal. It opens the door to greater achievement through mastering the subject matter and experiencing the satisfaction of success.
The importance of problem solving as an instructional tool cannot be overemphasized.
The burden of carrying out the mechanics of problem solutions is now greatly reduced by computer programs designed to take care of many routine functions. With the time-consuming, error-prone chores thus done quickly and reliably, the student is free to explore subject matter concepts. Genuine learning can then take place and the student can solve the problems.
A new emphasis on problem solving as a learning tool must take place, for today's students are the people who will run the world tomorrow. The tools they learn in school now will be applied to the many serious problems they will face in the "real world."
Solving problems is a straightforward process requiring:
1. Knowledge. All knowledge needs to be used, everything from commonplace daily observations to advanced study of specialized subjects. It may be old knowledge, perhaps from early childhood, or it may be new knowledge encountered today for the first time.
2. Rules. A few simple rules, easily understood and applied, are used to establish WHERE TO START and WHAT TO DO NEXT, in order to produce consistent, reliable solutions.
3. Practice. No one becomes an expert at anything by just being told how to do it. Consider baseball, basketball, golfing, pole vaulting, singing, dancing, or your own favorite skill. Practice must be done correctly in order to be beneficial. So it is with problem solving.
This discussion will first present the fundamental working principles of reliable problem solving. Then some of the research findings about problem solving will be examined.
Howard C. McAllister
Professor of Physics
University of Hawaii at Manoa
Honolulu, Hawaii 96822
mcallist@hawaii.edu
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