It develops thinking. Let's specify. There are different types of thinking – critical, abstract, logical, visual-imaginative, analytical. If a student solves math problems, he or she learns to highlight important things, analyze, arrange them, notice patterns and interrelationships, think abstractly and logically. Regular math practice develops the intellect.
It helps to learn other subjects better. Knowledge of mathematics can be transferred to, for example, drawing, where you need to correctly convey proportions or music, where you need to understand the tempo of the melody.
It develops accuracy, consistency, precision, and self-control. Once faced with solving a difficult example, a child will understand how important it is to follow the rules, take their time and double-check themselves. And these skills will be useful not only in other subjects or exams, but also in everyday life.
It helps you choose the best course of action. You can solve an example in several ways, and each can be correct, but one way will be faster and the other will not. The ability to identify all paths and choose the most appropriate will always be useful to everyone.
It teaches you to look at things with a skeptical eye. Sometimes the task seems easy and simple, but then it turns out that we were rushed. And so it is in life. It seems like allocating a budget for the month is easy, but when faced with it, you have to go through different options.
It gives you confidence. If you have a complex mathematical expression in front of you, divide it into parts and simplify it. Then everything will work out. This skill is useful everywhere. For example, if you need to clear up clutter in the house or prepare to move, you can break the whole into several parts-tasks and find the best way to solve each problem.
Talk about why children need math for a very long time. Recall the famous quote by Mikhail Lomonosov, "Math should be studied, because it brings order to the mind."