Originally Posted by aeh
So that would suggest that quantity concepts in her everyday experience are intact. The quantities you've listed as not intuitive are all much harder to experience concretely in one's everyday life. That suggests to me that if there are (as there may well be) some underlying vulnerabilities in number sense, with her overall high level of cognition, the kind of concrete, multisensory experience with quantity that occurs in everyday life has remediated the smaller numbers sufficiently, but there might not be enough meaningful multisensory interaction with larger quantities (e.g., the higher multiplication facts, 100s, 1000s) to have created number sense at those levels. That suggests, too, that the smaller scale of number sense could be used to build up to larger scales. Which, incidentally, is very similar to teaching larger multiplication facts. E.g., she has a sense of 3 at a glance, and of 20 as an estimate. So 3x20=60 looks like three groups of 20.

Your testing methods are "qualitative". smile

Thanks AEH, we (I?) do spend a lot of time talking about ways of finding the simple patterns she does know and using them. We talk about how 40+70 (400+700) can be done as 4+7 as long as you maintain state on tens and hundreds. And she seems much more able to do that verbally than when faced with sums on paper. She will struggle with a problem, I will suggest a solution for working with parts of numbers separately and putting them back together, she can do that verbally, and then she can usually write that down at the end. But she rarely thinks to do that herself and rarely seems to be able to apply these skills that she has verbally to what she sees on paper in an equation for the same thing.

It's been useful to write that out. I do think that it is the case that she can work with concrete materials with me, OR do math verbally with me (with no concrete materials) at a far superior level to what happens when faced with sums on paper. She's far more likely to do quite random things with mixing up her place values on paper than she ever would verbally. I will try to test this on Monday.