The Common Core Standards (CCS) are teaching behaviors not concepts. This is true because they have the wrong order. They have multiplication in grade 2 when teach place value in grade K. So they teach behavior not concepts.

Algebra is a type of codification of the logic of numbers. So if numbers are taught as behavior, students can’t understand the codification of numbers as algebra. So they learn algebra as a behavior as well. But algebra is supposed to be the concepts of numbers.

When they learn algebra, they don’t learn to do place value notation as a recursive algorithm with letters for each digit. This is done in my main book on Peano Axioms.

Because they don’t learn that, they are not learning to codify numbers with symbols. So they are not in fact learning the concepts of numbers. Instead, in algebra, they just learn more behaviors. This is why algebra is a brick wall for many students.

Common Core really hides the concepts and thus is a brick wall layer and builder. It stops forward progress by not teaching the concepts along the way. This accumulates until the student breaks down under the load of not understanding the number concepts and thus the meaning of the math they were supposed to have learned.

The whole Common Core Standards project is a fraud. Which is why it devolves into high stakes testing. HST itself turns classes into drill factories. That leads to homework bloat.

Zurich c. 1900 did not allow homework if there was afternoon classes. Assuming this was typical of German and even of Prussian education, this means they would regard today’s homework bloats as excessive. That includes the flipped classroom of watching hours of videos at home before class. Prussia would regard Khan Academy homework video viewing as child abuse.

This is what laziness by the math ed establishment results in. The math ed establishment refuses to learn the Peano Axioms or to learn elementary math in terms of recursion and math induction proofs. As Lance Rips et al would point out, they probably didn’t learn this because they tried to learn math induction with complicated math formulas. So they missed the real meaning. My books correct that by teaching math induction to prove the properties of arithmetic, which don’t involve complicated algebraic formulas.

The Common Core Peano Axiom Project will further hammer this home to a math ed establishment that is dead set against understanding the concepts behind elementary math. This is why their effort ends up as high stakes testing and drill factories. This leads to teacher strikes. Nor does it help disadvantaged students that the math ed establishment doesn’t understand the concepts of the math it claims to be teaching.

hello!

I am against the CCS for many reasons.

I have a question though, as algebra was a terrible brick wall for me. What do you mean by codify? Perhaps algebra would have registered in my brain if taught correctly.

A set of rules that summarize practice. So if you have say case decisions by judges, an advisory panel goes through the case decisions and extracts rules that come close to replicating them. Then the legislature passes the rules as laws that supersede the case decisions.

Algebra codifies specific numerical cases with rules that apply in any case.