There is a huge indifference to improvements in math education. Poor students are the ones who need help with concepts the most.
The proof of the associative law of addition in the Peano Axioms is a key concept builder. This builds the concept of natural number.
This goes from Euler level bloviating and beating around the bush to the Grassmann Dedekind Peano actual working concept of a natural number with methods attached.
Schools still teach the Euler level of bloviating made up explanations that are not the concept of natural number nor of structure nor of proof.
This carries through the rest of math.
The place to learn structure in math is the natural numbers.
Symbolic logic notation is useful but for most people is a dead end. They don’t see how to build on it. In fact, mathematicians themselves don’t use that notation very much. It is useful, but does not have the same power to enlighten as does learning the associative law of addition proof in the Peano Axioms.
This massive indifference to teaching math is a huge problem for the students struggling with the concepts.
All the people saying they can’t learn it are not helping.
A simple approximately 10 page book that teaches the associative law of addition proof in the Peano Axioms is at the link.
This book also teaches mathematical induction avoiding complicated algebra formulas that Lance and Rips showed in their research is the stumbling block to learning induction proofs. They point out this is a stumbling block to understanding natural numbers and elementary math. This research in psychology at Northwestern is ignored even though it is known.
This is the massive indifference to teaching math concepts that permeates the colleges as well as the K-12.
Grassmann, Dedekind, Peano, Lance Rips, Jennifer Asmuth, et al, Alexandre Borovik, have recognized and promoted the Peano Axioms and these proofs but the math profession and the math ed profession do nothing. This is at the university level by professors who are supposed to know better. Instead they show massive indifference.