[Drat -- my keyboard has gone glitchy and I inadvertently deleted the first part of this. I hope I can reconstruct it.]
I've been watching the Salaman Khan (of the Khan Academy) TED talk about better math learning through technology. Khan is a hedge fund manager turned math educator who has observed over his 5 years in the field that too many good students with good math teachers reach a point when for them prior achievement is no longer a predictor of future success. To a kid it can can feel like their quota of math success has been used up. From the outside it may seem that once their fund of math knowledge is longer a dependable platform for new learning, they turn into 'overnight unsuccesses'.
Khan has a great metaphor for what he (and I concur) believes is the underlying cause of this for most kids. He blames it on the holes in "the Swiss cheese" of kids' math learning that keep building throughout their foundation. Most of the kids I asked over the years said that this started happening for them in grade 5. I suspect that by then that the survival tactics (eg. finger counting) many kids develop to do arithmetic can't hold up under the demands of complex arithmetical questions. Over the next few years, a pattern of giving up on learning first one skill and then another evolves until a critical mass of failure is reached and they have a math melt down. From then on unless they get some effective intervention, they come to accept failure as the norm in math and begin to plan their lives around this deficit.
Khan wants to change math classes from being an environment characterised by an acceptable level of failure to one where the expectation is mastery. I think taken to it's logical conclusion this would mean the end of 'Remedial' or 'Essentials' or "A&W" (Apprenticeship and Workplace) courses which have, in a way, become a systematized acceptance of failure. We dress these courses up with nice names and convince ourselves and the public that they are in the best interests of the child, but they're still the system's way of saying: "You've now not learned enough math to prove that our past expectations of you were too high. Here's your ticket to the easier course. Just struggle for a couple more years and you can get out of math forever!!"
Khan's solution is to arm teachers with the data they need to know immediately when a student has become stuck and to increase what he calls the "student to valuable human time with the teacher" ratio so little sticking points don't turn into big holes in the cheese. I'm not sure if I buy his entire vision, but the fundamental shift to continuously collecting feedback to guide instructional decisions is critical. If I were the queen of teaching, I'd put an end to teachers demonstrating correct solutions on the board after quizzes and tests. Unless the students actively find out where their mis-learning has occurred and fix it, what carries forward is recall of the error or of an incompletely learned skill. I'd forgo 'scatter gun' homework assignments in favour of assigning fewer questions and looking at them more deeply to assure myself and the child that the work of learning a particular skill was done.
I think Khan's technological solutions can help, but first we need to make the fundamental shift (as he has) to believing that we are seriously underestimating people's ability to learn math. Then the work of preventive math dentistry -- of detecting and filling little learning cavities to be sure all kids leave school with a full set of math teeth -- can begin.