Mathematics and Language
Edited by Marsigit
Both our language, and our symbolic notation, have "just growed", although our notation has been subject to a slightly more rational process of selection.
To take a small example: I would much rather discuss geometry with nine-year-olds, by focussing on the interesting and important features of, say, plane figures, than by having them memorize that a triangle with only two sides equal is an isoceles triangle, but one with three sides equal is an equilateral triangle.
I would rather just say, "Let's look at the smallest number of sides we need to make a pen that would hold in a horse.... see, you can't do it in fewer than three.... now let's look at what we can say about three-sided figures ... how they can differ among each other ... what they all have to have in common... " and then go on to discover that all three-siders can have no sides equal, or two sides equal, or three sides equal. And then to look at the angles that we can have with each of these kinds of three-siders.
I think there are many areas in mathematics where, if we were starting over, we could make things much easier for ourselves and our students, if we could choose our vocabulary and notation.
Two more things -- from a longer list - which irritate me as being unnecessary impediments in learning mathematics:
(1) Conflating identities and equations and relations.
(2) Making the exponentiation operator implicit instead of explicit.
I wonder if others have any thoughts on this issue?