Solving Math Problems

For some pupils, solving math problems can be very difficult. There are, however, methods and strategies that can help both teachers and students.

To solve math problems, you need to know four basic elements. Only by teaching young students the whole process can we speak of an adequate and adapted education.

Pupils who start studying mathematics often think that it is a complicated subject, but it is possible that the difficulty is caused by the method of study or teaching. To understand how mathematical reasoning works, it is therefore necessary to know the four fundamental aspects that make it up.

Fundamental aspects of mathematical reasoning

Let’s see what are the main aspects of mathematical reasoning and how they can be developed:

• Possess appropriate linguistic and factual knowledge to construct the mental representation of problems.
• To be able to
  schematize

  to integrate all the information available.

• Possess strategic and metastrategic skills to guide the solution of the problem.
• Know the procedure that allows you to solve the mathematical problem.

These elements develop through four different phases. These are the various stages that lead to the implementation of actions for the solution of the problem, and can be summarized as follows:

• Translation of the problem.
• Integration of the problem.
• Solution planning.
• Running the solution.

Steps for solving math problems

1. Translation of the problem

The pupil who is facing a mathematical problem must first of all translate it to an internal representation. In this way it creates an image of the available data and the objectives of the question. To correctly translate the sentence, the pupil must know the specific and factual language. For example, you will have already learned that a square has four equal sides.

Thanks to the research it has been observed that pupils often let themselves be guided by superficial and insignificant aspects. This technique can be useful if the superficial text agrees with the problem. Otherwise, the pupil may not understand exactly what the question is and the battle would be lost before it even begins. If the student does not understand the problem, it will be impossible for him to solve it.

Mathematics education must begin precisely with teaching the translation of problems. Numerous studies have shown that specific training to create mental representations of problems improves mathematical ability.

2. Integration to solve math problems

After translating the problem statement into a mental representation, the next step is integration. To do this, it is very important to know the real goal of the problem. It is also necessary to know what resources we have available. Simply put, this task requires a global view of the mathematical problem.

Any mistakes made during integration can affect understanding. In these cases, the pupil feels the sensation of being lost. But the worst part is that it will tend to fix the problem incorrectly. Therefore, the need arises to emphasize this aspect in the teaching of this subject. It is a key point in learning how to solve math problems.

As in the previous phase, even during integration the pupil tends to focus on the more superficial aspects. When determining the type of problem, he pays attention not to the goal, but to the irrelevant characteristics. Fortunately, there is a solution: a specific teaching. That is to say, by accustoming the pupil to the fact that the same problem can be presented in a different way.

3. Solution planning and supervision

If the pupil has been able to understand the problem in depth, it is time to create an action plan. We are almost at the last stage of solving math problems successfully. At this point, the problem will have to be broken down into small actions. Each of them will help the student to approach the solution.

Perhaps this is the most difficult part of the process. It requires considerable cognitive flexibility and executive effort. This is especially true when the pupil faces a new problem.

Regarding this aspect, it almost seems that the teaching of mathematics is impossible. But research has shown that there are various ways to increase yield when planning. Let’s see what are the three essential principles on which they are based:

• Generative learning. Pupils learn best when they actively build their knowledge themselves. This is a key aspect in constructivist theories.
• Contextualized education. Solving math problems in a meaningful context fosters understanding.
• Cooperative learning. Cooperation favors the exchange of ideas between pupils. This allows them to reinforce personal opinions and generative learning.

4. Solving math problems: the solution

Here we are at the last step in solving math problems. Now the student can use what he has learned to solve some operations or part of a problem. The key to good execution is to familiarize yourself with the basic skills. These will help the student to solve the problem without interfering with other cognitive processes.

To develop these skills, practice and repetition are excellent methods. But it is also possible to introduce other methodologies for teaching mathematics (such as the notion of number and counting number lines), useful for reinforcing learning.

Bottom line: Solving math problems is a complex exercise. It requires an understanding of numerous processes related to one another. Trying to teach this subject in a systematic and rigid way will certainly not be useful. If we want students to develop math skills, we need to use flexibility. Only in this way will it be possible to favor concentration on all the processes involved.