Those things which do not have to be the way they are, are called arbitrary. Those things which must necessarily be as they are, are called "necessary". The names we attribute to things, definitions we give to certain words, these are arbitrary. A square does not have to be called a square. It could be called a triangle.
There are others things, however, which cannot change. The three angles of a triangle add up to a half turn - this is a fact which is not merely based upon convention, but upon reality. The sum of the squares of two sides of a right triangle is equal to the sum of the square of the hypotenuse. This also is true in every instance, no matter what name we give to certain terms.
In my math class, I would try to allow my students time to work out those things which are necessary. Necessary things can be arrived at through intuition and through working out problems by oneself. Those things which are arbitrary, that need to be told to students, I would try not to spend as much time on. These things should be supplied as tools to the students, so that the students can proceed to work on those parts of mathematics which are not arbitrary, but necessary.
Good!
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