In Defense Of Skill-Based Practice
There are a few core beliefs we hold at Mathchops that seem odd or just wrong to a lot of tutors. One of them is that skill-focused practice is crucial. You should not spend all of your time taking practice tests, or even taking test-like questions. A significant portion of your practice should target specific skills directly. That means shorter questions, without multiple choice, in which the required skills are usually fairly obvious.
Maybe this sounds wrong to you too. Some of the really hard SAT questions are wordy. It can be hard to tell what they want you to do. Is it good for high scorers to practice questions that are skill-focused, and thus not exactly like the real test? Won’t the practice be too easy if you strip away a lot of the ‘reading comprehension’ aspects?
But I believe this type of skill-based practice is essential. You see it in every domain at the highest levels of performance. Think of tennis players practicing running forehands, improvisers practicing Giant Steps in all 12 keys in 9/4, chess grandmasters working on specific tactics and openings, basketball players working on turn-around jumpers from various spots on the floor…Wherever there are virtuosos, there is skill-based practice. They do not simply play matches or go to jam sessions. They isolate important skills and master them, so that they can then use them in real life. Similarly, students need to know how to factor, solve systems of equations, find the x-coordinate of a parabola’s vertex, and many other core skills if they want to earn high scores on a test like the SAT.
Of course, acquiring these skills is not enough. Some players have all the shots in practice but fail to hit them in the game. That’s why I still assign practice tests (and tennis players play matches, improvisers go to jam sessions, etc). But if you don’t have the skills, how could you possibly answer the ‘real test’ questions that require them?
If you still aren’t convinced, have your student try a Mathchops speedrun! It shouldn’t take more than 20-30 minutes if they have the skills. And if they don’t have them…then you’ve found some good practice material for your best students.
I agree, and the curriculum I use addresses skills.
One thing I've started to do lately (not enough to have strong evidence, and only for some students) is going over text that is well written but with various kinds of errors sprinked throughout. I start with legally usable/reusable text, edit to my view of grammatical perfection if it not already there, then use that as the baseline document to which I add errors. Then I make an "edited" version of it showing the errors. A student can work on their own or with me with the error-filled but uncorrected version, then we can refer to the edited version to a) identify what needed to be fixed, and then, just in case, b) keep track of which errors are SAT/ACT meaningful. (I try to avoid errors that are not tested.) So far I've used this only with ACT students, since the ACT directly simulates editing more than the SAT does.