My six-year old knows the math lingo: equation, expression, construct, deconstruct, product, quotient, sum, factors, addends, commutative property, associate property, etc. Yes, the curriculum also weaves in the simpler terms as well, but she definitely knows her math vocabulary. She hasn't been confused by it and it wasn't difficult for her to learn. Being immersed in my daughters' education has shown me that we underestimate the ability of young people.
The spelling/language ones -- I'm going to have to spend some more time reading them carefully, but some of the principles embodied in them, and in the examples, are just wrong.
Some of the assertions about how English spelling works, for instance are inaccurate and emphasize rules far too much—the rules aren't really rules because English spelling isn't in and of itself logical.
Could you provide specific examples of wrong principles? I don't have much with which to compare but, yes, there is a lot of 'rules' my girls are being taught and so far I haven't come across any errors. I'll admit that initially when I glanced through the spelling workbook and saw words like predictable, easiest, and replacement, I thought, how in the world is a six-year old supposed to learn how to spell such big words? (She is a year ahead, though, so normally this is content a seven-year old would be learning. Still, it seemed like a huge jump from what it was previously) But as we've gone through it, it hasn't been a problem. Spelling lists are aligned with the vocabulary lessons that include the meanings of prefixes and suffixes, the "big" words are broken down to make spelling easier. Again, this is different than what my oldest had at that age, but it's more comprehensive and logical, IMO.
In regards to language arts, I really like that the literature includes a healthy dose of non-fiction. When my ten-year old was in K and first grade, all of the reading was fairy tales and nursery rhymes. Not so for my youngest. She's being exposed to a wide range of literature, and I think that's very beneficial. She's also being taught parts of speech in astonishing detail, along with the means of terms such as imagery, personification, and idioms. Again, not something my ten-year old learned at that age.
I'm not sure what will happen in the next school year, though. Our state has rejected CC after implementing it this year, so I have no idea what the curriculum will be like come August. I'll be sad, though, if we lose all that I've found wonderful this year.