Here is something else, from my recent university experience. I taught for a while in a department of Statistics & Actuarial Mathematics (where some very funny things are happening in eduation, both for students and teachers alike) in the UK. In Spring 2009 I was asked to solve some exercises for an elementary probability class, for first or second year students. The students had taken calculus before. We had to compute a certain integral (related to a density function) and I asked the students to do this by themselves. I asked a student to tell me her answer and she, correctly, responded b-2b/3.
"So," I continued, "this is equal to what?"Apparently nobody knew how to subtract two thirds from 1.
"I don't know", replies the student (who had done the integra correctly), "I'm not good with fractions."
"What about the rest of the class?", I asked the handful of students who were present.
So, remembering my elementrary school days, I turned back to the blackboard, and drew a pie:
"So, if I cut a pie into three pieces and take out two, how many pieces remain?, I ask.When Jason, correctly, expressed his frustration with the teaching of fractions, he referred to elementary and middle school education. I repeat that the example above is taken, from personal experience, from university education.
"One", replies the student.
"Very good", I enourage.
"Oh, that was easy", says another, "even my daughter could have done this".
There seemed to be something very, very, wrong in this system. This is why I left.