What does a student need to know to solve math problems?This is one of the most common questions in the field of math education. This subject often poses a multitude of problems for the student, but to what extent is it taught correctly?
It is important to consider the fundamentals students need to develop to learn and understand mathematics, as well as how this process develops.
Therefore, to understand mathematical functioning, the student must master four fundamental components:
In addition, it is important to bear in mind that these four components are developed in four different phases to solve mathematical problems, below we explain the processes involved in each of them:
The first thing the student has to face is a mathematical problem is to translate it into an internal representation, in this way you will get an image of the available data and its objectives, however, for the statements to translate correctly, It is necessary that the student knows both the specific language and the knowledge that is really appropriate. For example, that square has four equal sides.
Through research, we can see that students are often guided by superficial and insignificant aspects of statements. This technique can be useful when the surface text is consistent with the problem. However, when this is not the case, there are a number of problems with In general, the most serious problem is that students do not understand what they are asked to do. The battle is lost before it starts. If a person doesn’t know what to accomplish, it’s impossible to achieve it.
Therefore, the teaching of mathematics must begin by educating in the translation of problems. Extensive research has shown that specific training in creating good mental representations of problems improves math skills.
Once the statement of the problem has resulted in a mental representation, the next step is integration into a whole, for this it is very important to know the true purpose of the problem, in addition, we need to know what resources we are looking for. In short, this task requires an overview of the mathematical problem.
Any error in the integration of the different data will imply a feeling of misunderstanding and loss, which in the worst case will result in a completely wrong solution, so it is essential to emphasize this aspect when teaching mathematics because it is the key to understand a problem.
As in the previous phase, students tend to focus more on superficial aspects than on deeper ones; when determining the type of problem, rather than focusing on the objective of the problem, they get stuck with the less relevant features. it can be solved with a specific teaching and causing students to get used to thinking that the same problem can arise in different ways.
If students are able to fully understand the problem, the next step is to generate an action plan to find the solution. Now is the time to subdivide the problem into small actions that allow you to address the solution gradually.
This is perhaps the most complex part of solving math problems, as it requires great cognitive flexibility associated with executive effort, especially if we face a new problem.
It may seem that teaching math around this aspect seems impossible. But research has shown us that through several methods we can achieve an increase in planning performance based on three essential principles:
The last step in solving a problem is to find the solution, for this we need to use our previous knowledge of solving certain operations or parts of a problem, the key to good performance is to have basic internalized skills that allow us to solve the problem without interfering with other cognitive processes.
Practice and repetition are a good way to process these skills, but there are a few others. If we introduce other methods into math education (such as number teaching, counting, and number lines), learning will greatly improve.
As can be seen, solving mathematical problems is a complex mental exercise, consisting of a multiplicity of related processes, trying to teach this subject systematically and rigidly is one of the worst mistakes that can be made. math skills, we need to be flexible and focus teaching on the processes involved.