Thinking mathematically by John Mason

John Mason in his book Thinking Mathematically demonstrated what we should do when encountering a conjecture (it is not necessarily a mathematical conjecture): (a) to convince ourselves; (b) to convince our friend; and (c) to convince our enemies. What he means by these is that we should describe the conjecture (as part (b) and explain it using formal language as proper as possible), and then see every statement as a conjecture and try to disprove it. These steps are significant in learning a mathematical concept.

But the below is what I feel valuable:

“Each version tends to become more abstract and formal, trying to be precise and to avoid hidden assumptions of informal language, but incidentally causing the reader to have to work harder at decoding the original insight and the sense of what is going on.” (p. 98)

This is why the math concepts are hard to read: the insights are covered under the intricate math signs. It might be helpful to demonstrate the true meanings of math concepts by showing students their origin.