Like most modern educrats, he was a believer in his own propoganda.

Children are capable of abstract thought when they use words to represent concepts. The digits that kindergartners use are abstractions of concepts that are in and of themselves abstractions. The symbols representing the operations of arithmetic are abstract and so is reading for that matter.

The question is what exactly is the principled difference between the abstraction in algebra and the abstraction the child is already capable of? (In fact, much that passes as algebra these days, rather than requiring high degrees of abstraction, requires almost no sentience at all–computers can be programed to solve the equations.)

What does “developmentaly appropriate” mean in the context of a task which a nonsentient calculator or computer can do?

Of course not, but that doesn’t mean that everyone will be ready for abstract thought at some point.

And Myrtle, I graduated salutatorian of my high school class, scored 1450 on my SAT’s (prior to the recentering of the mid-’90′s), and earned a 3.8 in science at Stanford. So the difficulty I had with calculus at age 17 had nothing to do with being dumb, lazy, or unprepared. I simply wasn’t ready for it. One year later, I was.

I would make that plural–”teachers”

Not just the right teacher in the 8th grade, but the students need to have had the right teachers in the 5,6,7th grades, the right curriculum, and pushy parents.

Middle schools should test students math abilities upon entry and start remedial efforts immediately.