Where do the children get the prior knowledge?
It’s certainly from their environment. There was some very interesting work done by the late Robbie Case at the University of Toronto and his colleague, Sharon Griffin, who’s now at Clark University, looking at children who enter kindergarten with a severe deficit in numerical understanding. The general assumption was that these kids just weren’t generally too bright. What Robbie and Sharon found was that’s not the case. There are very specific things these children don’t know. One of the most interesting things these children with learning problems have in the domain of arithmetic is not being able to judge which of two numbers is bigger. They can’t compare numbers for size. That’s a very strong predictor of how badly they will do in early formal mathematics instruction. What Robbie and Sharon did was to develop a test to assess children’s number knowledge prior to school, and then develop a curriculum based on that knowledge that would take them to a typical formal early mathematics
