For my money, the answer is: figure out dangling modifiers.
Dangling modifiers are ubiquitous on the test, and they are especially ubiquitous in the multiple choice selections. Not infrequently, you can identify the correct answer simply by identifying the only answer that is not a dangling modifier.
This is so often the case that I now routinely read through the multiple choice options and cross out all the dangling modifiers (and the comma splices) before I even bother thinking about what's wrong with the sentence. I don't know whether that's a good idea for everyone, but it's a shortcut for me.
My goal with C. is to get him to the point where dangling modifiers 'jump' off the page at him, which is what they do with me.
Here's an example of what I mean (based on College Board materials, but clunkier):
One of the first women to serve in Congress, more than twenty significant laws were introduced by Jane Doe, making her a leader in her era.Choices A, B, C, and D all contain dangling modifiers. You don't have to read the final sentence to make sure it's correct because a dangling modifier is always wrong. Choice E has to be right, and it is.
(A) more than twenty significant laws were introduced by Jane Doe, making her
(B) Jane Doe's introduction of more than twenty significant laws made her
(C) introducing more than twenty significant laws made Jane Doe
(D) her introduction of more than twenty significant laws led to Jane Doe being considered
(E) Jane Doe introduced more than twenty significant laws, making her
The problem with a dangling modifier is that it isn't close enough to the thing it modifies, which is presumably why it is said to be 'dangling.' A dangling modifier is not firmly attached to the thing it modifies.
(Modifies means adds information to.)
When I get further along with Martha Kolln, I'll come back to this, but for now I'll say that generally speaking a modifier needs to be directly 'next door' to the thing it is modifying.*
Since the phrase "one of the first women" modifies (adds information to) Jane, Jane has to come next in the sentence -- and just Jane, not Jane-apostrophe-s. Jane-apostrophe-s isn't Jane-the-person; Jane-apostrophe-s is a modifier, too.
Choice A is wrong because "One of the first women to serve in Congress" modifies "more than twenty significant laws," which amounts to saying that the laws were women.
Sometimes you can see this better when you cross out the 'extra' words:
the laws, not Jane, were the first women to serve in Congress
the introduction of laws was one of the first women
introducing [20 laws] was a woman
the introduction was a woman
Jane Doe was [one of the first] women, which is correct.
I am positive that sentence diagramming would help with SAT writing.
Too bad no one knows how to do it.
update: Martha Kolln on dangling modifiers:
The participle can open the sentence only when its subject is also the subject of the sentence and is located in regular subject position. Otherwise, the participle dangles.
* I'm sure there's more to it that that.