How can it be that if we use “knowledge of children’s mathematics thinking” in our teaching
then we get no measurable improvement in their learning? Easy. We don’t have any
knowledge of children’s mathematics thinking. My own guess is that there are almost as
many different modes of mathematical thinking among children as there are children. I’m
happy with that. I wouldn’t particularly like to live in a world where children all approach
mathematics by thinking about it in the same or similar ways.