There are really intelligent people out there who could never pass a calculus class, much less thermodynamics. Do you want them in your program taking up all the time of the teacher, stopping those proficient in math from getting the education they deserve?
It seems people get better at what they practice. I suspect anyone (barring genuine mental disability of some kind) could master calculus and thermodynamics if they were sufficiently motivated.
I'm basing it on both my time as a math tutor for Pima Community College and on people I have known.
People like my mother who, if she can quantify the data she can effectively do algebra, but as soon as X and Y appear she shuts down. She cannot make the jump to the abstract thinking of math, and it curtailed her ability to go back to college. It didn't help that her math teacher in 9th grade told her that she would never be good at math, much like many women from poor backgrounds. (I have no study, only the experience in tutoring on how many women said that a teacher told them not to bother, and could never make it over that hump.) Now you say that it's merely psychological for them and that they could. I'm telling you that for as much work as some of these people I tutored put in, they had a mental block that they simply could not overcome, fighting their way to a C in college algebra so they could get to where they're going.
I can give as an example my boyfriend, who can speak and teach two languages better than most people here can in their native language, and is a promising Ph.D candidate in his program. He worked for a month straight (with my help) to raise his GRE math to a minimum score. His limit may be calculus, but certainly not higher math, and not upper level sciences. Yet I have seen this man wake up, read, write, sleep, and repeat for weeks straight.
He's a gifted writer and academic, but even if he could muddle through (say...) managed information systems, he'd never be more than mediocre because his brain simply does not work that way. (He still asks for help with his Mac.) Square peg, round hole.
It doesn't benefit those who have a passion for the sciences to put him and dozens of others in the same class, wearing down the professor because they struggle to grasp concepts that future scientists understood in fifth grade.
1. I worked for a few years in the remedial math centre for mature students in my university, and one of my best friends did his doctorate in teaching mature students mathematics. Based on my experience, had I taken your attitude then I would have just not shown up for work.
2. I disagree that it doesn't benefit the stronger students. It was awfully hard for me to learn to teach mathematics, because I had never really had to learn it in a step by step way myself. However, when I did learn to teach an area, my understanding was orders of magnitude higher because I had the understanding of somebody gifted in the area but the method and the attention to detail of somebody who has learned it the hard way. If you mix classes with high and low skilled students, you just have to make sure you rely on the high skilled students as a teaching resource.
1. Just because I didn't believe they could do differential equations doesn't mean that I didn't believe they could learn college-leve. algebra with some coaching. I had more faith in them than they did of themselves, in many cases.
2. There have been many studies that have tried what you say. The problem is that the class must go slower to accommodate the slower students. Engineering degrees already have so much packed into them that they often can't take classes of interest -- are we going to make it even longer?
