The real exam was simply the practice exam but with different numbers for some the given information. I went over the practice exam and gave all the solutions and answered all questions about it. Many, many students failed the ream exam. I fear for future generations.
I gave a practice exam a week before the real exam

The real exam was simply the practice exam but with different numbers for some the given information. I went over the practice exam and gave all the solutions and answered all questions about it. Many, many students failed the ream exam. I fear for future generations.
Pretty typical.

The real exam was simply the practice exam but with different numbers for some the given information. I went over the practice exam and gave all the solutions and answered all questions about it. Many, many students failed the ream exam. I fear for future generations.
I avoid this problem by giving hard exams. All students struggle, but many impress me, and mostly we end up respecting each other.

I think the general point to be made here is that most students approach mathematical topics in completely the wrong way, largely because they've been taught incorrectly their entire lives. So much of primary and secondary education is taken up be teaching kids to memorize stuff, with no regard for obtaining a conceptual understanding of the material. If you asked 100 collegeeducated people to explain WHY 7 x 5 = 35, I'll be that 90 of them couldn't give you a remotely satisfactory answer.

Basically, any low attendance day, I say, after a specific problem I work through: I would study this for the exam, if you know what I mean, nudge, nudge, etc. The sad part is the idiots in the class who show up still get it wrong, and the smart ones who don't show up because they know the idiots will do this, can get 1/2 there...

The real exam was simply the practice exam but with different numbers for some the given information. I went over the practice exam and gave all the solutions and answered all questions about it. Many, many students failed the ream exam. I fear for future generations.
November 8, 2016 should've already told you to be worried about future generations.

If you asked 100 collegeeducated people to explain WHY 7 x 5 = 35, I'll be that 90 of them couldn't give you a remotely satisfactory answer.
Makes no sense
What doesn't make sense? People know that 7 x 5 = 35, but in most cases it is only because they memorized a multiplication table when they were in first grade. In other words, they think of it as an absolute fact, and could not prove that 7 x 5 = 35 (or even provide some basic intuition as to why it is true). This point becomes obvious when you change traditional math problems in trivial ways; for example, lots of people would be stumped if you asked them what (7/35) x 5 is, because they have no conceptual understanding of basic mathematical operations. A majority of college students would pull out a calculator to solve that problem.