Math for the divergent mind

Something I've had to give up, as a teacher Mama to the intrepid Iggy, is that learning takes place in a linear way. The way I thought it went (and I think this is the way most schooling situations are set up) was....first you learn A and then when you really know A, you learn B and then when you really know B and so on. You did not skip to B or C until A was solidly known. Iggy's brain doesn't seem to absorb information that way. He doesn't want to interact with information in a linear way. We can't do A over and over until he seems to solidly know it and then go on to B and do the same thing. We do A over and over and he doesn't seem to "get" it, until we can go and fool around with B or even C. It seems like his brain can't grok A until he at least knows what B or C is.

I don't know if I'm making any sense, but addition and subtraction didn't seem to gel in his mind until we went far ahead and did multi-step multiplication. I showed him the procedure and he used an awesomely old fashioned tool called The Multiplication Machine for the multiplication facts that he hasn't memorized yet. He seemed to really enjoy something with so many steps. When we went back to simple addition and subtraction, he didn't seem to need his number line as much. Now, we just switch back and forth - from single digit addition with no carrying to multistep double digit multiplication. Sometimes we just hang around with manipulatives and place value. I wish I understood how this all works, but for now I'll take the fact that we're doing it at all as a success.