And this even with DS11, whose math placement is much closer to where it needs to be than his reading placement. I don't know why. Maybe as some have mentioned, in reading it is easier to accelerate to the proper level on your own, and in math, most kids eventually need some kind of instruction to make the same progression so they are in a more dependent, helpless position.
I thought about this more last night. One you know the number line, there is no reason to hold back.
Math also has a tactile component to it. Discrete problems are solved by writing them out. In fact, most problems have to be written out. And ideal self-learning program would incorporate a tablet PC, HW recognition SW, plus a human-in-the-loop for discussion.
The math classes I learned the most in followed the Socratic method where we had to put our work up on boards and then we discussed it in turn. Sometimes the instructor would write a problem on the board and then cover it up and then you lifted the paper to reveal it and had to solve it in real-time. After a point, the instructor would lecture M and W and assign problems, and we would self-teach and critique. He or she would then critique methods or propose other lines not covered by the student.
While it may not be feasible to get advanced kids together locally, I can see an online virtual classroom working using the Socratic method to teach more mature students math. Using a projector screen for the class and a tablet PC coupled to a large monitor would be good. You could then record the sessions for the student to play back or for other students to learn from.
I am just thinking aloud!
