Euler’s 1765 Algebra is very poor in conceptual thinking on whole numbers, addition of whole numbers and fractions. It is worse than Euclid in some ways.
Euler was very good at procedural thinking. He was a master at that. But at the concepts of elementary math, he was not so good.
If schools teach students in the Euler way using Euler type explanations, they won’t learn the 19th century answers as to what natural numbers are or what addition of natural numbers is or what fractions are.
Just teaching students to think like Euler doesn’t give them the right answers or to find the right answers on what natural numbers are or what addition of them is.
These things have to be taught. Even if schools taught their students to be Eulers, they still couldn’t self discover what natural numbers are or the definition of addition of natural numbers using the right additive identities and recursion.
Some parts of the core standards are New Math concepts like a function as a set of ordered pairs in which no two have a common first element and different second element. Euler struggled with the definition of function, but did not arrive at the 19th century definition with assurance.
Just teaching students how to think will not teach them 19th century abstractions or techniques. Those have to be taught as specific knowledge.
What is taught for natural numbers and addition and fractions is wrong or at least incomplete. These ideas run into problems and gaps. They don’t really add up. Just like Euler’s attempts in his 1765 Algebra book. He makes some assertions, waves his hands, but accomplishes nothing on the foundations of natural number or addition.
Read Euler, he doesn’t know how to explain it.
If the students can’t self discover that what is taught about these is wrong or incomplete, then it shows they are not being taught conceptual thinking.