>This dynamic isn't unique to ECE 352, or even Wisconsin – I saw the same thing when TA'ed EE 202, a second year class on signals and systems at Purdue. The problems were FFTs and Laplace transforms instead of dividers and Boolean2, but the avoidance of teaching fundamental skills was the same. It was clear, from the questions students asked me in office hours, that those who were underperforming weren't struggling with the fundamental concepts in the class, but with algebra: the problems were caused by not having an intuitive understanding of, for example, the difference between f(x+a) and f(x)+a.

>When I suggested to the professor that he spend half an hour reviewing algebra for those students who never had the material covered cogently in high school, I was told in no uncertain terms that it would be a waste of time because some people just can't hack it in engineering. I was told that I wouldn't be so naive once the semester was done, because some people just can't hack it in engineering. I was told that helping students with remedial material was doing them no favors; they wouldn't be able to handle advanced courses anyway because some students just can't hack it in engineering. I was told that Purdue has a loose admissions policy and that I should expect a high failure rate, because some students just can't hack it in engineering.

I think that fundamentally the problem is in mathematics.

Our notation is from the 18th century at best, yet because it is hard people think it's meaningful.

Standard maths notation makes sense for polynomials: a_0 x^n+a_1 x^(n-1)+ ... + a_n = k is the only type of general expression one can write without the need to use parens. Everything else is a kludge added on top of that notation to fix one problem with it, but only in one specific field. Which leaves you with dozens of dsls to specific types of areas of maths/engineering/physics/etc

I'm a big fan of lispified typed lambda calculus. There are no exceptions, and any specific notation is defined in terms of rewrite rules. The fact that types are required also makes it clear what you're talking about.

Unfortunately I'm in a minority of one whenever I've talked to working mathematicians, even though I can tear through papers and proofs an order of magnitude faster than when I try and use standard notation.