The WaPo article is by Lynh Bui.
The math behind elementary math is not widely known. Even most mathematicians don’t learn it very well.
The Peano Axioms are a set of 5 rules for counting by one. I give versions that are easier to understand here:
Addition of whole numbers is counting on. But counting on is the same as the additive identities in Peano Arithmetic. I discuss a little of that here:
If the schools would adopt the prime notation for counting on by one, so 2 = 1′, then they could teach the rules for counting by one and teach addition as repeated counting on using this notation. This would teach the concepts.
Students stumble when they reach fractions. This is because they have not learned a) whole numbers as math objects 2) that counting on by one is itself a function 3) that addition as counting on is a function 4) that multiplication is repeated addition is also a function.
The complexity of fractions is then too much for them.