index
Teaching Through Problem Solving
Ways in which We Learn Best
Steps in Helping Students in the Problem Solving Process
Assumptions
Examples

Teaching Through Problem Solving to top

We constantly solve problems. In many cases, there is a prescribed way of doing something and we fit our view of the situation and our reactions into that way of thinking and action. At other times, we may feel that the 'rules' do not apply, or that we are facing a new problem and we must then develop our own solution. Or the rules apply but the loss will be too great or the gain too unfair. It is then that we search for an alternative way of dealing with a problem and come up with a previously unused or a novel solution. In so doing, we learn and expand our parameters.

Teaching through problem solving is not always easy since many of us were taught by remembering facts whether or not they were related to each other, whether or not we were interested in the subject, and in some instances we were taught by rote. In fact, many teachers may say that problem solving in their particular subject area is not possible, not helpful, or only possible in limited parts of the subject matter.

However, everything that can be taught may be taught from a problem solving point of reference. The rest of this article is dedicated to this idea.

Ways in which We Learn Best: to top

It is sometimes helpful to look at the ways in which we learn more rapidly and fully.

We learn best by solving problems or have a personal stake in the outcome. It is then that we become interested in knowing the parameters, the details, the basis (assumptions) on which the problem is built, and the end results.
We learn best when we have discovered the answer for ourselves.
We learn best when we have contributed the answer or have a stake in its presentation.
We learn best when we have thought out the process by which the answer is achieved.
We learn best when we have opened ourselves to different possibilities - one of which is a possible answer.
We learn best when we have come up with a possible answer whether it is correct or not. If our answer is wrong, the 'wrong' answer will cause us to retrace and find out where we went wrong in our thinking and will reinforce the answer.
We learn best when we have examined our assumptions as to what will support the answer. Assumptions are very often the barrier to our learning and prevents us from achieving.
We learn best when we have to defend our answer against other potential answers.
We learn best when we have had to learn the supportive concepts and data which will provide us with the correct answer.
We learn best when we have a total environmental view of the data we are learning, its supports, its unknowns, or the controversies surrounding it.
We learn best when we have learned the different ways in which the data and the process of deriving it are used.
We learn best when we find different ways of arriving at the same answer.

Steps in Helping Students in the Problem Solving Process to top

1. Provide the basis for the solving of the problem
The student is often stymied by the lack of a basis from which to even begin the problem solving process.
     List the possible presumptions to be overcome in solving the problem.
     Identify tools & references needed to help in arriving at a solution.
     Give basic knowledge needed to begin searching for solutions.
     Support off-the-wall suggestions which may have some validity or
     may lead to other possibilities which are valid.
     Breakdown the problem into manageable component parts.

2. Discover the interest of the students. Many students are not interested in a particular subject. It is the teacher's challenge to illuminate the connection between the topic to be taught and the students interests.

3. Enter the world of the student. See the material to be learned from the student's viewpoint of what the student wants to do, know, experience.

4. Allow the student to create a project of personal interest which uses the material to be learned.

5. Multi-explanations or solutions. There is always more than one explanation for a phenomenon (some have been proven false long ago but were held to be true by the best minds of each preceding age). Alternatively, there is more than one way to interpret what we know, or more than one way to derive a solution. The differences should be brought up and discussed and the students given the task of defending different positions or of deriving the solution from different angles. Today there are many controversies still raging about certain phenomenon. What are they in your particular field?

6. Learning can be fun. This is a caveat of learning in childhood. Remember some of the ways in which children are taught from a unique and innovative perspective so that learning is actually enjoyable to the child. Translate these to the subject at hand. It is never too late to enjoy the experience of learning no matter how complicated the subject to be taught. We can learn from the simple methods used in the earlier years of childhood. Take a list of teaching techniques from the early years. Look at them from the perspective of the current topic. Which one fits or with a bit of imagination and innovation can be translated or upgraded to fit the current circumstances? It is often surprising the degree to which that which helped us learn the simpler lessons in life are still effective in later years.

7. We know that many subjects can be learned by rote. The only problem with this method is the incredible boredom of the task and the fact that once learned we have trouble expanding the knowledge to fit new situations. We know the material without knowing the reason for its existence or truthfulness. We do not know the supportive knowledge which helped our predecessors find the solution. There is no fun in learning by rote except the high percentage on our exam grades, or in the presentation before others. But there is little or no expansion of true knowledge.

I learned by rote parts of the Prologue to Chaucer's Canterbury Tales but to this day have no appreciation of Middle English or how it was transformed into modern day English, or how it limited the world view of those who spoke it, or the ability to rhyme with it, or what other works we still have today which were written in the same format, or how it related to the rest of the work, or to the perspective of the culture which produced it. In fact I did not even know the meaning of the words or the phrases until one day many years later I sat down and repeating it in my head, and attempted to assess its meaning and its true literary value.

8. Interrelationships - It is important that the student, whatever the project is that has been chosen, make an effort to interrelate the subject of the project with the other topics of the subject matter. This should be more than a simple descriptive relationship and should include ways of integrating the selected topic with the other knowledge learned in the class. Having an individual represent a historical figure in a debate on some topic may help learn everything about one person but all others presented in the class may be a blank for the student at the end of the semester.

9. Work towards the strengths of each student. It is important that each student realizes and understands the different capabilities brought by different students to a project. No capability or interest should be devalued. In a certain situation, each capability will help solve a specific problem. Collective problem solving should be emphasized over individual problem solving capabilities. Some students cannot see alternative solutions, or any solution at all. When confronted with a potential solution, the student may be able to contribute knowledge from other areas thus increasing interest and adding to the solution of the problem.

10. Support the discovery of what does not work. This discovery is often as important as the discover of what does work. The student can then be led to appreciate the lessons learned in the process.

Assumptions to top

We all believe in a specific order of things. We build our perceptual concepts (assumptions) on the basis of this belief. It is extremely difficult to change our perception because we fit our observations into the framework of this world view. And when a particular fact does not fit, we just say that there is not yet enough data to explain it or to account for its presence. Some of the assumptions which we use about the forces operating in a certain circumstance, the nature of the situation, any moral restrictions, and the probability of a certain outcome are all operating at each juncture in our decision or non decision processes.

In the development of a problem solving method for teaching any subject, some of the assumptions so often used in developing problem solving techniques are:
   The problem must relate directly to the subject being learned
   The solution must be logically derived from the problem
   The problem must be a real life problem using real information as its base.

All of these are not necessarily correct. A problem with none of these assumptions can be just as effective. The important point here is the use of or the finding of the answers or data which is to be learned. But even this is not necessary if the problem merely opens up the field, or expands perspective, or creates a more conducive or neutral environment within which thinking and exploring can take place.

The important point is that our assumptions must be checked and in certain cases overturned in order to produce fruitful predictions and results.

In the past, many more problems were created by commonly held the assumptions behind real world events.