Currently math ed for normal children is not based on the Peano Axiom root. We don’t have books that go from Peano Axioms through all of elementary math. I have started that, but it still does not exist yet.
K-8 math now is just a hodge podge that grew up. It is not structurally connected. It is behaviorally connected. It is 10 percent math and 90 percent behavior. Of the 10 percent math, very little is structural, say 1/10, so 1 percent total structural math in current K-8.
Now we go to math for deaf kids. Instead of going back to the root of Peano Axioms and elementary math built on that root with structure, math ed for the deaf goes to the already messed up structureless math taught to kids in regular schools.
But the regular school math is not a proper conceptual and structural version of elementary math. So when that is used as the base for math for deaf kids, they have to graft their different behavioral rules and situation onto a depleted math base that is jiggered to the behavioral situation of hearing kids and hearing teachers interacting and also with hearing parents.
With deaf kids, we get wrong compromises.
Imagine that regular math ed was an optimized subset of a Peano Axiom structured math that covered all of elementary math. It would be a subset that was optimized based on the behavioral component of normal classes.
Now we want to do this again for deaf kids starting from the Peano Axiom root together with their behavioral situation. The result is a different optimum subset of Peano Axiom math to be taught.
When we start as base a structureless aggregation of lessons for regular schools that is about their behavioral situation and rules more than math, then we get an unsuitable base for deaf kids. We have to go back to a structured base of elementary math and then adapt that to the behavioral situation of deaf kids and deaf classrooms.
Regular class room math is at best a sort of reduced form post optimization from the actual Peano Axiom root of elementary math. You can’t do an optimization from a reduced form and get the right answer. You have to go back to the original problem and then add in the new constraints of the deaf classroom and redo the optimization.
It is even worse because regular classrooms are not optimized to begin with. They are just an evolution that has wandered heavily through the configuration space, but never with a set of textbooks that cover elementary math from a structured base to look at.
That is, the teachers and curriculum builders themselves don’t even have access to a set of books that build out all of elementary math from the Peano Axiom root. These don’t exist yet. They are being created by me, but that is taking time.
The same applies to every disability, cognitive, behavioral, environmental, or situational.