I've figured out precisely why I'm skeptical about the common core standards. It's because they're vague and therefore susceptible to being gamed by textbook writers, districts, and teachers.
Here's an example. You can read the standards for proofs in geometry
on this page. If you click on the links about proofs, you'll see that they just say "Prove theorems about (stuff)."
The precise meaning of the word prove is open to interpretation.As a working example of how vague words can be interpreted, take the California standards:
Scroll to page 6 to see what I've copied here:
Students write geometric proofs, including proofs by contradiction.
2.1. Students write geometric proofs.
2.2. Students write proofs by contradiction
The standard says WRITE proofs. It doesn't say DEVELOP THEM FROM SCRATCH. Yes, I know: most or all people here will interpret
write as "develop from scratch." But the standard has clearly been interpreted differently. The Holt Geometry book my son used last year is a popular book in the state. I don't recall a single exercise in that book (and I looked) that required the kids to write a proof from scratch. Instead, they just had to fill in the blanks. The book typically listed the reasons and students had to copy stuff to a piece of paper and then fill in the appropriate theorem or postulate. Presto! They were
writing proofs.
As standards, they are supposed to represent a floor, a *minimum* of what will be taught, but there is nothing keeping a district from treating them as a ceiling instead.
Exactly. The teacher certainly never asked the kids to develop them, either. Her tests were always fill-in-the-blank style when they had proofs, which they often didn't.
