Mathematics is about understanding the properties of mathematical objects.
Just as things in the real world are made up of elementary particles, mathematical objects are also constructed using a modular principle. However, since the basic building blocks and construction rules do not need to be discovered through experimentation but are defined from the outset, the properties of mathematical objects can be understood and rigorously proven through careful analysis of how they are built.
This exact comprehensibility is extremely useful, as mathematical objects can be constructed in such a way that they closely resemble real-world objects. This makes it possible to simulate and predict real processes using mathematical models.
To participate in mathematics, a basic understanding of how and what is discussed in mathematics is required. Therefore, mathematics education should always include a kind of language course in which one learns
- how to construct mathematical objects,
- how to formulate statements about these objects,
- how to justify the properties of these objects, and
- how to describe real things using mathematical objects.
When you construct mathematical objects yourself and modify them in a purposeful way, you will naturally begin to formulate and test your own hypotheses about their properties. You will dive into the great thought experiment that is mathematics — and you’ll want more and more of it.
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