Completely incidental to the points the text is making (which are content-neutral), I've already found two examples of "good" grammar teaching that are rather distressing to me.
In the first, the answer is right but the definition wrong, in the second, only the definition, which is wrong, is given.
1. Definition of a Subject
The task is to identify the subject and the sentence is: "My mother was not happy." The student (A) in the example guesses "happy." The teacher asks for clarification from another student (B) and gets the definition that "The subject is what the sentence is about." The teacher says this is correct and then asks student A what the subject is again. Student A replies "mother." End example.
This is an example of the rule "No opt out," where students always are forced to give the right answer, even if they at first get the answer wrong. You might think that the teacher above was just going easy on student B to move the lesson along, but the next section of the book, "Right is right," is about how important it is not to pretend students are right when they're not, so I think we can safely assume that Lemov thinks this answer is right.
If you're wondering why the definition is wrong, it's easiest to just give some counterxamples:
1. It is raining. Grammatical subject: "it." Subject according to above definition: rain.
2. "It is a truth universally acknowledged that a single man in possession of a good fortune must be in want of a wife." Grammatical subject: "it." Subject according to the above definition: marriage.
2. Definition of a Noun.
The task is simply to define a noun. Lemov gives the example of a student who says "A person, place or thing." The champion teacher does not accept this answer but prompts a more thorough response, until given "A person, place, thing or idea."
The importance of the idea clause here is telling, because it is the vagueness of the concept "idea" that has let so many educated people believe this definition for so long. It is, after all, entirely obvious that not all nouns are people, places or things. However,if you consider that things like "liberty," "truth," and "proof" are ideas, conceptual entities if you will, then it seems like this definition might just do.
The trouble is many nouns are clearly actions. In fact, we have suffixes that let you turn verbs into nouns, thus creating newly minted nouns out of any action we please. Here are a few very simple cases of nouns that are not people, places, things or ideas:
"Destruction" as in "The hurricane resulted in devastating, wide-spread destruction."
"Liberty" as in "I am not at liberty to say."
How would I define "noun," you may ask. I teach students the following simple procedure for identifying a noun. It is not perfect, but it is close, and it doesn't include any out and out lies: "If for a given word X you can say "the X" but not "very X", then X is a noun." Every native speaker can apply my rule perfectly every time.