Onmatu- General Math Learning Article
This article is the third from the series of articles describing the means you can use to help the student to learn Math better in the classroom. Let's talk now about principal divisions and principal questions.
6. The four phases. While we try to find the solution, we can change our point of view many times regarding the way we see our problem. We always need to change our position. Our thinking about the problem is in the beginning, after all the probabilities, rather incomplete; our way of seeing the problem is changing after some progress that we made; it's different again when we are close of finding the solution.
For us to group in the most convenient way the questions and recommendations from our list, we need to distinguish four phases of our work. First, we need to understand the problem; we must have a clear idea of what is required. Second, we need to see how are related between them the different elements, which is the relation between the unknown and the data of the problem, for us to make an idea over the solution, to make a plan. The third, to realize the plan. The fourth one, to look retrospectively the solution obtained, to revise it and discuss it.
Every of these four phases has its own importance. It can happen that a student to have a flash idea, to skip all the preparation steps and give directly the solution. These happy ideas are of course to be desired, but it can happen also something, which is not desirable at all and unpleasant, if the student skip one of those four phases and his idea is not a good one. The worst case is when the student starts to calculate and construct without understanding the problem. In general, it is not useful to clarify details before we understand the principal connection or before making a certain plan. So many mistakes can be avoided if, while making his plan, the student verifies each step. One of the best effects of the problem can be lost if the student misses to revise and reconsider the complete solution.
7. Understanding the problem. It's stupid to answer to a question which we don't understand. It's unpleasant to work for a goal which we don't desire. This kind of unpleasant and stupid things happen often, in school and outside, but the teacher should struggle to prevent their happening in the classroom. The student must understand the problem. But this is not enough, he must also have the will and pleasure to solve it. If the student lacks understanding or interest, it's not always his fault; the problem needs to be very well chosen, neither too heavy nor too light, natural and attractive and a certain time needs to be devoted to its natural and interesting exposure.
First we need to understand the verbal statement of the problem, its formulation in words. The teacher can verify this until a certain point; he asks the student to repeat the statement and the student must be capable of doing this in a fluent way. Also, the student must be capable of showing the main parts of the problem, the unknown, the data and the condition.
So the teacher can only sometimes dispense himself from the questions: "What is the unknown? What are the data? What is the condition? ". We will continue in the next article with an example to show how the process works. Thank you