Nobody has offered a precise definition of mathematics which reflects its nature and its entire specificity among the other disciplines – neither mathematicians nor philosophers. Therefore, we should not wonder much when our child does not understand a great deal from math class. But we must ask what the student is being taught and how it can ensure an adequate understanding. Such understanding amounts to seeing mathematics as both abstract and empirical, theoretical and applicative, language and structure, a collection of necessary truths as well as a method of acquiring them.

Even without a good understanding of mathematical concepts and mathematics as a whole, students still learn mathematical methods and procedures and come to apply them correctly in order to do their homework and pass their tests. In other words, they do classroom mathematics with little to no understanding of the concepts they use – and almost always their teachers are pleased with such results. This is possible due just to the nature of mathematics. On the basis of such double sufficiency (student’s and teacher’s), the idea is strengthened in the student’s system of beliefs that mathematics is something merely instrumental and calculational.

Of course, teaching methods enhanced through the new technologies (including web, video, and interactive media) are better than the old methods, but their advantage consists in capturing students’ attention and providing a certain cognitive-environmental comfort, not in the addition of new epistemic content. Making mathematics look “friendlier” is not sufficient for its understanding, first because the method of analogy is not sufficient for gaining understanding.

The studies on perceptual mathematics give us a promising premise: it is not mathematics itself that filters students in two categories – mathematically inclined or reticent about it; rather, all of us have innate mathematical perceptions and mathematical reasoning. the content of the mathematics courses, the way of teaching it, and the way mathematics is integrated in our own knowledge structures all cause a child to develop either "mathematical anxiety" or mathematical aptitude.

We recommend to students, parents, and instructors who want a detailed answer to the question in the title of this section our book What is Mathematics: School Guide to conceptual understanding of mathematics, a didactical unit necessary for the start of the adventure of understanding mathematics in its all complexity.

 

 

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