To teach mathematics, and even mathematical language, most successfully, focus on the ideas—what things are, how they work, how they interrelate—and not on what they are called. Children learn their native language extremely efficiently by hearing vocabulary used in context — by using words to talk about things and ideas, not by talking about the words, themselves. Use good vocabulary, but keep the focus on the mathematics, not on the vocabulary.
Mathematics is about ideas — relationships, quantities, processes, ways of figuring out certain kinds of things, reasoning, and so on. It uses words, but it is not about words. When we have ideas, we often want to talk about them; that is when we need words. But knowing “denominator” and “addend” is not math and does not make one mathematical. Words help us communicate. Period. The ideas are elsewhere.
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