The point of learning math is there's an inflexible scorecard of reality for an incredibly complicated logic puzzle, and the only determiner of adequacy in the subject is persistence. Now if you want to excel you need the knack or genetics or whatever, but mere adequacy only takes a certain amount of sweat.
So it teaches that at least some times there's certain logical rules where one follows from the other or can be combined with another, and if you're persistent you can figure it out. Or just summarize to persistence and logic.
I really don't care if your wife can solve 2x=4 for x, but I would be unhappy to be under her care if she would give up on complicated situations (oh he's not breathing AND no pulse? I'll just give up), or refuses to notice cause and effect relationships.
Exactly. Math isn't a set of procedures, it's a way of thinking. Without understanding that way of thinking it is impossible to be an educated person.
"Most mathematicians at one time or another have probably found themselves in the position of trying to refute the notion that they are people with "a head for figures." or that they "know a lot of formulas." At such times it may be convenient to have an illustration at hand to show that mathematics need not be concerned with figures, either numerical or geometrical. For this purpose we recommend the statement and proof of our Theorem 1. The argument is carried out not in mathematical symbols but in ordinary English; there are no obscure or technical terms. Knowledge of calculus is not presupposed. In fact, one hardly needs to know how to count. Yet any mathematician will immediately recognize the argument as mathematical, while people without mathematical training will probably find difficulty in following the argument, though not because of unfamiliarity with the subject matter.
What, then, to raise the old question once more, is mathematics? The answer, it appears, is that any argument which is carried out with sufficient precision is mathematical, and the reason that your friends and ours cannot understand mathematics is not because they have no head for figures, but because they are unable [or unwilling, DRH] to achieve the degree of concentration required to follow a moderately involved sequence of inferences. This observation will hardly be news to those engaged in the teaching of mathematics, but it may not be so readily accepted by people outside of the profession. For them the foregoing may serve as a useful illustration."
College Admissions and the Stability of Marriage, Gale & Shapley, The American Mathematical Monthly (Jan 1962)
If all you're looking for is a scorecard for persistence and logic any rule based system will do, e.g. music. You also overestimate the general population's capacity for understanding math, in my experience. Your tone renders your comment equivalent to "The beatings shall continue until morale improves."
> I really don't care if your wife can solve 2x=4 for x, but I would be unhappy to be under her care if she would give up on complicated situations (oh he's not breathing AND no pulse? I'll just give up), or refuses to notice cause and effect relationships.
You really don't know what you are talking about here. How you can make the link from not being good or enjoying math to just giving up on something critical is completely illogical.
The point of learning math is there's an inflexible scorecard of reality for an incredibly complicated logic puzzle, and the only determiner of adequacy in the subject is persistence. Now if you want to excel you need the knack or genetics or whatever, but mere adequacy only takes a certain amount of sweat.
So it teaches that at least some times there's certain logical rules where one follows from the other or can be combined with another, and if you're persistent you can figure it out. Or just summarize to persistence and logic.
I really don't care if your wife can solve 2x=4 for x, but I would be unhappy to be under her care if she would give up on complicated situations (oh he's not breathing AND no pulse? I'll just give up), or refuses to notice cause and effect relationships.