Enjoyed exploring your site immensely. It is obvious to me that you are dedicated to real education at the highest human level...for its sake alone.
I sent along my contribution to your poll on the quote from Wired magazine and noticed that the numbers appear to indicate a leaning in favor of the education system here in the US. If I were to attempt to classify, I would say that your site is oft visited by teachers but I'm curious how many are math teachers.
While I'm certainly not an expert on the state of education here today, I was forced to participate in it in my youth and I spend most all of my free time reading about such things (for my own erudition). I perceive that my own pathetic instruction in mathematics was not an uncommon experience (I wish you had had even a few moments in my Geometry class in HS) and after all this time thinking about it (I am in my mid-forties) I have concluded that the system itself is to blame.
The colleges that train teachers, especially for the younger grades where children develop their ideas about education, focus on 'process', or learning how to learn, and social development. The factual nature of mathematics and the necessity to master the language needed to understand it are treated superficially by these teachers and when the level of abstraction increases in the later years, the students are ill-equipped to deal with it.
In addition, there is no acknowledgment of mastery in the compensation system. A teacher is financially rewarded for two things, staying with the system and attending courses that give them higher levels of certification. These courses, sadly, are generally more fluff on social aspects or learning how to learn.
My husband is gifted with the love of mathematics and took as many advanced courses as he could while handling a double major in sciences during his college (premed) years. Unlike his 'innumerate' wife, he is amused and comforted by the certainty and elegance of math challenges. Now we have two sons (teens) who fall neatly into the mother/father leanings, one who is quite talented in the subject and one who is indifferent.
The surprising thing about this is that they have been homeschooled pretty much all of their lives. My husband is unable to assist in their instruction due to his Orthopaedic practice and so it falls to the math-phobic wife to see to their accomplishments. Because I have felt so deeply the impact of fearing a subject that is so important to our everyday lives, I have always focused on the two ideas. One was that the memorization of the basics was not an option and two, that although they may stumble over math problems, it was not because they were incapable of understanding but that I was not explaining it correctly.
Over the years I have acquired dozens of texts on mathematics. Whenever my boys would scratch their heads over a tough one, we would start researching the books to see if a different approach to explaining it would help...and it almost always did. On quite a few occasions my husband would sit down and review their work, offering tips on how he dealt with that problem but time for him is limited.
The point to my rambling recollections is that these boys have had no one to learn from outside of books and videos while supervised by a 'teacher' who can only look in the answer book or work in the text side by side with the student. They test consistently in the upper ninetieth percentile on standardized tests-both of them. The only perceptible difference between them is that the 'indifferent' one knows he is expected to master it whether he enjoys it or not. The 'talented' one is more often apt to tell me, "This is cool!" when he conquers a problem.
Now, however, the 'talented' one (age fourteen) is approaching the need for a true believer. While the 'indifferent' one (age sixteen) is quite capable and comfortable in concrete math, he has no interest in pursuing the subject. He enjoys history, philosophy, and political science. But his brother has real talent and I would hate to see it wasted.
I am searching for a person here (Naples, FL) who will guide him in this important field so that his ability will reach full flower. The risk is that I will expose him to some untalented twit who will ruin his appreciation for math. So much better to take the time to find the right mentor...but how and where? I'm working on it.
Thanks for the great resource and the true belief.