farmerman wrote:I hope this makes sense.
I, fortunately had a great calc instructor , a Jezzie that was , to me, a rennaissance man, He knew so much about so much. He knew so much that he didnt mind speaking in our language. His explanations of similitude were outstanding. He left in my mind the lesson that " a given quantity or a measurable unit need not be excat" Exactness is not how stuff is solved. Be not afraid to jump in the problem and get it "sorta" right, then come back and straighten out the quantities. Small minds dwell on the exact values, the great minds always say "sorta"[.] He was a master in chemical diffusion, I had him in Math and in Physical chmistry I. (He was the "go-to" guy to understand how the equations worked and why they were relevant.
Part of the problem may be that students no longer need to work problems out on a pad of paper. They have calculators, and have little incentive to learn analog thinking. I've had young men or women ask me the time, and having shown them my watch, i've been obliged to tell them the time, because they only know digital, and actually cannot read an analog watch face.
They have calculators, and that is how they solve the problems. They enter the numbers, hit the appropriate button (the calculators have square-root buttons, fer chrissake), and await the response.
When i was taking advanced mathematics in high school, i had a slide rule. You got an approximate answer which allowed you to work backward, with pencil and paper, to the exact answer. The method for finding square and cube roots on paper involves such estimation. I would suspect that as students progress through courses in mathematics these days, they simply learn the appropriate entry method on a calculator, as opposed to learning what it is the calculator is doing to arrive at the correct answer.
None of this is to say i was ever very good at math, because i wasn't, and i didn't like it. The only math course in which i did well was geometry, because i could draw it. The only science in which i did well was chemistry, for precisely the same reason.