Methods of solving text problems
The solution of the word problem is to find a way to present the content in mathematical form – saved as an action, several activities, a sequence of actions following one another, equations or inequalities, and then by performing the set mathematical operations and giving the result, the most common numeric, checking the correctness of the calculations made and formulating a verbal answer.
The teacher's task is to show students the method of solving problems, rather than treating tasks as individual cases requiring individual approach to each of them, in other words – teaching methods of solving problems.
Józef Kozielecki in the book: Troubleshooting, using the experience of educators and heurists, proposes five stages of problem solving, which can be very useful in developing word problem solving skills. Here is how the author puts it.
1. Seeing the problem – subject (pupil) sees the problem, that is, he discovers it and realizes it, that knowledge, which he has, it's not sufficient, to achieve the goal.
2. Analysis of the problem situation – the student analyzes the information contained in the initial phase and the goal, what is to be achieved. Well, what are the differences between these, what is given, and this, what is desired – searched.
3. Generating solution ideas – in this phase, the student generates new information necessary to solve the problem – solution ideas. These could be hypotheses, guesses, discovery projects, which will then be verified.
4. Verification of ideas for solving the problem – the purpose of this phase is to evaluate ideas for solving the problem, checking their value. As a result of the verification of ideas - the student accepts the idea as a solution or rejects it.
5. Return to previous phases – the student can go back to any previous solution stage, see new dependencies, a new solution idea or reject a previously approved one. Failures in the next phases may also be the cause of the return, and returns may be multiple.
The thinking process of solving problems, called productive thinking, is the so-called. a heuristic process (producing ideas for solving the problem). This thinking allows you to come up with ideas for solving a problem. Heuristics – means the ability to make discoveries from the Greek language. In modern psychology, heuristic methods are understood as all rules, rules, methods, tactics, tricks, which regulate the course of the productive process, but they do not guarantee the achievement of the planned result. Nevertheless, they are very useful in mathematics education, because like no other they develop the skills of a creative approach to tasks. It is different in the case of algorithmic methods, consisting in performing certain finite sequences of operations leading reliably to the result, and even to solve all the tasks of a given class. The discovery of a problem-solving algorithm often turns a difficult problem into a mechanical one. Algorithms quickly lead to a solution, but this method yields relatively simple tasks, stereotypical, hassle-free, and yet our task is to prepare the student for a creative approach to work.