Ah, I love the collective wisdom of this forum. Thank you all!
The plan: We are going to step back a little, and not rush through this bit of math right now. DS has been doing tons of Scratch programming for the past month, and I really think that's where his learning is focused right now.
ZenScanner:
Maybe his "math lens" is broken such that he has it ingrained currently that math is memory based rather than cogniton based.
That is a good thought. I suspect DS thinks math comes in two flavors: the "boring" stuff (long division, fractions, etc) and the "fun" stuff (fractals, mobius strips, etc). He might think of the former as memory based, and then get frustrated.
Yesterday I asked him to show me what he had learned the previous week about a simpler way to compare fractions (he initially learned to convert the entire fraction, then DH taught him to cross multiply). At first he told me he couldn't remember how, and I could sense he was starting to feel frustrated. So I sat down at the white board and started to do a problem, when he completely took over and showed me. Yay! Maybe he just had more time to absorb the material and understand why it worked.
HK:
I'm also wondering if it is TYPICAL of him to struggle with verbal representations of symbolic mathematics. Some kids really struggle with translating the words into their mathematical equivalents.
I haven't noticed this to be the case so far, but much of the math he's had to do has been so beneath his level, he could do it in his head. So it's very likely true for newer concepts. For example, he's understood the concept of fractions for a long time, but since he learned it (on his own) long before he had to manipulate them, I never had to deal with drawing them for him.
Quantum: It's hard for me to know what he truly groks, because he sometimes has a hard time explaining his reasoning (true for many things, not just math.) And if he encounters an old problem in new clothes, I don't know if he has forgotten how to do the old problem, doesn't understand the new clothes, or just isn't thinking about it long enough to solve the problem. I suspect the latter much of the time.
phey: I am hoping to get to the end of the current book (we have just a few chapters left!), and then we might just drop the formal stuff for a bit to see how it goes.
CM: We will take a look at the video, thanks! DS adores Vi Hart, so her videos are pure gold.
