The math ed establishment has shown a dead head reaction to the Peano Axioms. Not just my materials, but those of others. In terms of worked out examples, my materials may double what is available from others combined, but that has still not led to even one comment at e-vendors or a book review.
Place value notation is not recognized very widely as recursive. Nor is it emphasized enough that it logically depends on multiplication of natural numbers.
Grouping as a way to motivate place notation means that we are using grouping to keep our place in the count. This is the Peano Axiom mindset when we teach order first and teach that natural numbers and all their methods are about keeping our place in the count.
But why is the math ed establishment so not interested in the math behind elementary math?
There has to be a reason.
One reason is that the math ed establishment has given up on teaching math. They don’t believe in the schools. They don’t believe in the students.
Parents should take note of this. There is no point in having children in schools where the teachers and math ed establishment have given up on the students learning.