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Teaching Maths: What Do Students Need to Know?

Teaching Maths: What Do Students Need to Know?
Teaching Maths: What Do Students Need to Know?

For math teaching to be effective and trouble-free, you need to make sure your math lesson has four parts: problem translation, problem integration, solution planning, and problem execution. Teaching Maths.

What does a person learning math have to do to solve a math problem? This is certainly one of the most common questions in the field of mathematics. Mathematics is a subject that usually causes difficulties for many students. How should effective mathematics teaching look like?

You need to be mindful of the key qualities students need to develop in order to learn and understand math. You also cannot forget about the learning process. Only then will you be able to teach math the right way.

To understand how math works, students must first learn four different aspects:

  • Linguistic and factual knowledge to create mental representations of a given problem.
  • Create your own schematic knowledge to comprehend all available information.
  • Strategies necessary to identify what the problem is asking.
  • Practical knowledge that allows you to solve the problem.

Moreover, keep in mind that these four aspects are also used in the following four steps:

  • Translate the problem.
  • Problem integration.
  • Planning a solution.
  • Executing the problem.
  1. Translate the problem

To solve a math problem, students first and foremost need to translate it into an internal representation. This will give them an overall picture of the available data and goals.

However, in order for a text to be translated properly, students must have a special language and factual knowledge. For example, they should know that a square has four equal sides.

Research suggests that students often focus on the superficial aspects of the text of a problem. This technique can prove useful when superficial words are moving towards the solution. When this is not the case, however, this approach creates even more difficulties.

The situation becomes even worse if the students do not even understand what their problem is asking for. It makes no sense for them to try to solve something that they cannot even comprehend.

This is why teaching mathematics must begin with teaching translation of problems and explaining the language of verbal problems. Many studies have shown that special training to create appropriate representations of mental problems can improve math skills.

  1. Problem integration

Once the student has translated the problem into a mental representation, they must take the next step that “binds” all the data together. To do this, they must recognize the purpose of the problem. Besides, students need to know what resources they have to solve it.

In other words, this stage requires students to have an overall perspective of the entire math problem

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Any mistakes made in integrating the data will leave students feeling confused and that there are issues they do not fully understand. At worst, the approach to the problem will go completely wrong.

Therefore, it is imperative to emphasize this aspect when teaching math as it is the key to fully understanding the problem.

As in the previous step, students tend to focus on the superficial aspects and ignore those that are important. When the time comes to define the nature of the problem, they don’t see the end in itself, but look to the least important data.

However, this can be remedied by giving detailed instructions and teaching students that the same problem can be presented in different ways.

  1. Planning and supervising the solution

Once students are able to fully grasp the problem, the next step is to create an action plan to find a solution. This is the moment to break down the problem into small tasks that will help you reach a solution gradually.

This is perhaps the most difficult part of solving a math problem. It requires cognitive flexibility and effort, especially when we encounter a new problem.

It seems impossible to teach mathematics around this aspect. However, research suggests that by using different methods we can improve our planning skills. To this end, three key assumptions should be made:

Generative teaching

Students learn better when they actively build their own knowledge. This is a key aspect of constructivist theories.

Instructions in context

Solving problems in meaningful and useful contexts helps students achieve a better level of understanding.

Cooperative teaching

Collaboration can help students share their shared ideas and fuel their knowledge with other ideas. Doing so also encourages generative learning.

  1. Execution of the problem

The last step that will allow you to properly solve a math problem is, of course, to find a solution. For this, it is necessary to refer to prior knowledge of how certain operations or parts of the problem can be solved. The key to problem performance is to internalize basic skills that help solve the problem without disrupting other cognitive processes.

Exercise and repetition are good methods to internalize these skills. However, there are many more. If we use other methods in mathematics (for example the meaning of numbers, counting, etc.), we will strengthen the learning processes.

So you can see that solving math problems is a complex mental exercise that involves the use of numerous cognitive processes. Teaching math in a systematic and rigid way is one of the biggest mistakes you can make.

Most importantly, if you want to have very gifted students, you must teach them to be flexible and to approach problems using the four aspects above.