## Posts tagged with: philosophy

Much hay is made about what the SAT is actually testing. Does it function as some strangely-defined “college readiness” measurement? Is it a pure reasoning test? Is the SAT a test of innate intelligence, like an IQ test? Is it a completely meaningless hoop that you just have to jump through like a circus dog because everyone else does? The College Board claims only that the SAT tests “the skills you’re learning in school: reading, writing and math.” Is that true?

The indefatigable Debbie Stier asked me for my take on this the other day, and I realized that I had never written about it on this site. My answer to all of the above is a qualified “no.” There’s a bit of truth to each claim, and you won’t have to look too hard to find people who’ll argue for any of them. You might even have a friend with a crazy theory of his own (Duuude, the SAT is an awesome predictor of alien abduction!). I’ve been working with the SAT for a while now, and I’ve come to my own conclusions.

The short answer: there is no short answer. Each subject tests different things, and although there are overarching themes, you’re not giving the test fair treatment if you try to encompass the whole thing in just a word or two. What follows is a bit of a brain dump. Chime in in the comments if you think I’m missing something.

• Deep Reading: Are you able to interact with a passage in such a way that you understand the author’s tone? Can you draw inferences about how the author might respond to counterarguments or criticism of her point of view? Do you understand why she might have bothered to sit down and write the passage in the first place?
• Precision: Do you comprehend sophisticated writing (both in the passage and in the answer choices!) well enough to pick the one correct response from a list when the incorrect choices are often incorrect for subtle reasons? Often incorrect choices can be eliminated because of a single word in the choice! Do you know exactly what words mean? On hard sentence completions, it’s not good enough to have a vague sense that a particular word is “positive” or “negative.” You have to know precise definitions, and recognize appropriate use (not for every single word, mind you, but for enough to successfully eliminate incorrect choices).
• Vocabulary: This is a corollary to the above, but obviously you need to possess a decent vocabulary to score well on the CR section.
##### Math
• Umm…math: How are your fundamental math skills? Are you comfortable working with right triangles, exponents, and percents? Can you reliably translate word problems into mathematical equations? There’s no way around this; there are many techniques that can help boost your score, but if your fundies are weak your score will be also.
• Nimbleness: Do you see multiple ways to solve many of the problems? Are you willing to take shortcuts if they’re available (like on questions like these), or are you dogmatic in your methodology? Are you able to transition easily between techniques if the first one you try doesn’t bear fruit? Are you willing to try crazy things if you’re stumped?
• Stick-to-itiveness: Do you persevere when your first approach comes up empty? I’ve been teaching this stuff for years and I don’t get questions wrong when I take the test, but that doesn’t mean I still don’t end up at a dead-end once in a while on my first go-through of a problem. The highest scorers cock their eyebrows, learn from their missteps, and reroute when they run into trouble.
##### Writing
• Grammar: Can you spot common usage errors? The SAT doesn’t cover every grammatical rule, and it stays pretty far away from most grammar controversy. (Oxford comma? Not tested.) If you know the most common SAT rules, you’ll be in pretty good shape. If you’re looking for an exhaustive list of rules, Erica Meltzer’s got you covered.
• Flow: Can you identify (in the multiple choice) and execute (in the essay) a logically structured, well formed sentence or paragraph? Are you able to recognize when contrast or transition words are appropriate, or when an edit might drastically improve clarity and readability?
##### The Bottom Line
It’s quite difficult to say, concisely, what the SAT is testing, and attempts to do so are often uselessly reductive (it’s what you learn in school!) or dismissive and curmudgeonly (the SAT tests you on how well you take the SAT). Students who work assiduously in school (not students whose grades are exemplary because of cramming skills) tend to do well because there is a fair amount of overlap between SAT skills and the skills ostensibly taught in high school, but it’s also very possible to raise SAT scores a great deal with focused prep because the SAT is fairly predictable, despite its breadth.

A bunch of people have emailed me asking why I only post answers, and not full solutions, for my drills. That’s a fair question, so I figured I’d answer it publicly. I don’t post solutions because I think the best way to improve your skills is to figure the solutions out on your own. When I work with kids, I almost never give answers (although I’m almost always asked). What I do instead is help my students to find the path to the solution themselves and then keep them on it by reminding them to use all the weapons in our arsenal. To put it in old-school SAT analogy form:

Mike the tutor : SAT math :: lane bumpers : bowling

Although I’m not physically sitting beside you and acting as a bumper, I have provided on this site the tools you need to solve the problems in my drills, and I’ve linked to the relevant techniques for each question in the answer keys to point you in the right direction. If you want to be able to solve similar questions on test day, you’d do well to mess with the puzzle pieces now by yourself until you see how they fit together.

That said, it’s completely counter to my mission to frustrate you, so I’m happy to help if you’re really stuck. Ask me a for an explanation at PWN the SAT Q&A and I promise to get one to you as quickly as I can.

One last note: I don’t want to be unduly dogmatic about this. I know self-study is a lot different than sitting with a tutor, and I don’t want to force a round peg into a square hole. If enough people chime in, I’m happy to reevaluate my position.

Because there’s a penalty of ¼ raw score point for incorrect multiple choice responses on the SAT, many students experience extreme trepidation about guessing when they aren’t sure about an answer. I’ve stated my general advice on guessing before, but the truth is that while I almost always find that my students benefit slightly from guessing more, I’m open to adjusting that advice if it doesn’t seem to serve a particular student well. If you’re not comfortable just taking blanket advice from a stranger on the Internet, there’s actually a very simple experiment you can perform to help you settle on a guessing strategy that works for you.*

Here it is: always, ALWAYS, ALWAYS GUESS on practice tests, and make little marks on your answer sheet to remind yourself which choices were guesses. When you’re done, score your test twice: once with your guesses in there, and once with all your guesses replaced by blanks.

What you’ll probably find is that there isn’t much difference either way, but once you’ve done this on 3 or 4 tests, you’ll start to get a sense of how guessing works for you. By the time the real test comes along, you’ll be comfortable in your guessing strategy, knowing that it’s based not on superstition or blind faith, but science.

If you want to get really crazy and add a bit of granularity into this, that’s possible too. Replace the little mark you were using to signify a guess with a number. Rate your guesses on a scale of 1 (no idea whatsoever) to 3 (got a good feeling about this), and score your test first with all the guesses, then with only the 3-rated guesses, then with the 3- and 2-rated guesses, etc. You could similarly use numbers to note how many choices (if any) you were able to eliminate before you guessed. I wouldn’t go so far down the rabbit hole though; I’m just spitballing here.

__________
* Of course, the best guessing strategy is to never have to worry about guessing because you have prepared so well for the test that nothing can surprise you. But you knew that already, right?

About a month ago I realized that, as someone who blogs about SAT prep, I really should have an informed opinion on what’s out there in the online test prep space. With the June SAT prep cycle winding down, I’ve finally had time to sign up for a free trial and give Grockit a test spin for a few hours.

For the uninitiated, Grockit is web-based test prep built with adaptive learning technology (in other words: it assesses your skill level and tries to challenge you accordingly), garnished with a few rudimentary social gaming elements. Students are awarded ready-to-share achievements for things like “hot streaks” of questions answered correctly, and there’s a “Multi-Player” practice system in which students tackle problems together, and are encouraged not only to chat with each other about answers, but to reward each other with points for being especially helpful.

I started with math, because I rightly assumed it would be the most fun, and then moved on to reading and writing. My thoughts about all three experiences follow. I should note that I didn’t try every single thing Grockit has to offer; I didn’t enlist the help of any of Grockit’s tutors, for example (I thought that’d be weird). But I did enough poking around in the SAT sections of the site that I feel like I have a decent sense of what it’s about. I should also state the obvious: I am a grown up and a test prep professional myself, so I didn’t approach this exactly the same way a 16 year old might.

##### The Good

• Grockit does a fantastic job of encouraging interaction, and after adapting to the system I really enjoyed interacting with the few kids I joined in Multi-Player games. Of course, your mileage may vary, and I’m sure there are some trolls, but my interactions were nothing but positive. Multi-Player math practice was by far my favorite thing about Grockit, and while “playing” I actually lost track of time and stayed up far later than I had intended to. Students who aren’t shy will benefit from the locking-in of knowledge that occurs when they are able to explain it correctly to others.
• The adaptive learning system seemed to assess my math ability level quickly and started feeding me only high difficulty questions when I was in a “Solo” game. That kept me engaged and appropriately challenged.
• It was easy to view a summary of my performance, broken down nicely into different skill categories, each of which offered additional practice problems. This is an important part of the SAT prep process, and one of the hardest things for students to do by themselves.
• Grockit’s use of badges and achievements that can be shared with friends isn’t exactly breaking new ground, but if it succeeds in keeping kids on the site a bit longer (and I suspect that it does), then that’s a good thing. Who doesn’t like scoring points and leveling up?
• If you don’t want to be social on Grockit, you have the option to practice all by yourself. If you do want to be social, you’ll be able to find people to practice with quickly.
• If you only want to practice for 10 minutes, that’s fine. If you want to practice for 2 hours, also fine.
• The vocabulary in Grockit’s sentence completion questions was sufficiently challenging, but not ridiculous.
• At \$9.99 a month, Grockit is affordable.
• While most of the math questions I saw were decent approximations of the SAT’s style and some were quite faithful translations of questions I recognized from past exams, some of the questions were not carefully worded, and that frustrated me. An example:

A group of five radio stations participate in a Rock Concert ticket give away. The first two radio stations give away one ticket each hour on the hour, the third station gives away one ticket on the half hour, and the fourth and fifth radio stations give away n tickets on the nth hour (for example, 2 tickets will be given out at 2pm, 4 tickets at 4pm, 12 tickets at 12pm, and so on).

How many total tickets will be given away by these five stations between the times of 2:45 p.m. and 9:15 p.m.?

This was a grid-in question, and it hinges on one’s interpretation of “on the half hour” — does it mean “every half hour,” or does it mean 3:30, 4:30, 5:30, etc.? There is a question with the same phrase in the College Board’s own Blue Book (page 598 #17), but the meaning of the phrase is clarified in that question with a table: it means 3:30, 4:30, etc. To get the Grockit question correct, one actually needs to interpret the phrase to mean “every half hour.” That really stuck in my craw. Careful, precise wording of questions is the hallmark of a good standardized test question, and that doesn’t seem to have always been a priority for Grockit’s writers.

• After practicing for about an hour, I started to see algebra questions that looked very familiar. They had a few cosmetic changes, but were otherwise identical to questions I had already answered. That made me wonder how many total questions there were and how often I’d see repeats if I did it for a month. Repetition can be a good thing, but I’d prefer a little more variety.
• It’s hard to answer math questions on a computer screen. This is also, I’m aware, a valid complaint about my own site. Bottom line: you’re going to want to have scratch paper handy if you want to get anything out of your time on Grockit’s, my, or any online math practice.
• There’s no nicer way to say this: the reading comprehension passage games are just off:
• The timer for each question (4 minutes) is plenty of time once you’ve read the passage, but the fact that the timer for the first question begins as soon as the passage is revealed encourages bad behavior, like skipping back and forth between passage and questions without first understanding the passage as a whole. Students should be given time to read the passage holistically before the question timer starts.
• Some questions and answers themselves are poorly worded, and I fear they’ll instill a pernicious mistrust of the test in students who prepare using Grockit. The real SAT is very logical and precisely worded; it’s easy for a seasoned test taker to eliminate incorrect answers if he or she has understood the passage well. Grockit’s questions too often seemed to me (and I’m quite seasoned) to have either no fully satisfactory answer, or more than one. The SAT simply doesn’t do that, and causing students to believe otherwise is the opposite of preparing them well. This wasn’t true of every passage that I did, mind you, but it was true of enough of them that it’s a huge problem. In fairness, the reason you don’t see more reading comp practice on my own blog is that it’s really hard to do well and I’m afraid of becoming the target of similar complaints.
• Some of the explanations that accompanied answers were wrong. Here’s an example from a paragraph improvement question:

When teachers understand the complexities in the lives of their students, they will become more aware of certain issues as well.
“Their” is an ambiguous pronoun here.

Huh? Maybe “they” is ambiguous, but I think “their” is pretty clear.

##### The Ugly

Although many of the math questions were accompanied by completely adequate diagrams, the quality was very uneven and once or twice I came across some seriously bush league stuff. There exist numerous software solutions for making nice looking graphs, and Grockit can afford them. There’s just no excuse for these:

##### The Verdict

It’s my hope that if any Grockit folks stumble upon this post, they view it as I intend: as constructive criticism from someone who, like them, does a fair amount of thinking about how the web can be used to help kids on standardized tests. I support them in their use of technology for education (especially their appropriation of gaming psychology and adaptive learning), and I love their price point. I can see myself, in the future, becoming quite a fan. For now, here’s what I’ll say:

Grockit provides a decent service at a reasonable price for the math and writing sections of the SAT, but it falls short on the reading comprehension questions. Since the infrastructure is quite good, a little quality control on content would go a long way towards improving the product in all three subjects. Grockit is not a suitable substitute for assiduous Blue Book work, but if you’re looking for a low-cost, fun way to get some extra math and writing practice, you could do worse. Stay away from Grockit’s reading comprehension practice.

My sincerest hope is that when you loaded the page at College Board’s site that contained your May SAT scores, you were elated. If, however, the numbers on the screen left you dismayed, you shouldn’t waste time sulking. Pick yourself up, dust yourself off, and start plotting your revenge. Here, I’ll help:

• Is the June test an option? If your May test scores fell far below the practice tests you’d been taking, then you might have simply fallen victim to test day jitters. In such cases, it’s best to get right back on the horse if you can. You don’t want to internalize those lower scores and start considering them your new baseline, and the summer is a long time to have to wait if you feel that you’re already at peak test taking condition. The June test is one week from today, but you might still be able to take it on standby even if you haven’t signed up yet. A lot of kids will be thinking the same thing, though, and fewer schools give the SAT in June than do so in May, so you might have to do a bit of traveling, and you might have to sweat it out a bit on the morning of the test.
• Order the Question and Answer Service (QAS). For the May test, you can actually order a test booklet and a report of all your responses. That’s a great way to drill down into the areas of the test that caused you the most trouble, and will be a valuable tool this summer as you get lean and mean. If you ordered when you registered, you could have ordered online, but you can also order after the test by mail.
• Don’t wait for the QAS to arrive to start working on weak areas. If you prepped heavily for the May test, you probably already have a good idea of what areas are still soft for you, so start seeking out drills that focus heavily on them. If you struggle with circle questions, do every circle question you can get your hands on. If you don’t already know what your weak areas are, try my free diagnostic drills. The answer keys contain links to additional practice questions similar to the ones you missed.
• Prep smart, and you won’t have to prep as hard. Too many kids just take practice test after practice test and then get exasperated when the big improvements don’t come. It is important to take some full length practice tests on your journey, but you don’t need to do that every time. When a runner prepares for a marathon, she rarely runs marathon distances. Most of the training consists of shorter, focused workouts. So it is with the SAT. As you discover weaknesses, spend a few short sessions focusing on them until they’re strengths. You might find that you see big results with 20-30 minutes of prep per day.
• A large improvement comes in increments. You can improve 100 points on your overall score simply by improving your performance on each multiple choice section by one question. Seriously. Do that a couple times over the summer, and the SAT won’t know what hit it when you take it again in the fall.
• Don’t be afraid to ask for help. If you’re not taking a course or working with a tutor, that doesn’t mean you have to go it completely alone. There are plenty of people on the internet willing to help. As you probably know, I’ve got my own Tumblr Q&A service where you can submit questions.
• Don’t put it off. With the weather getting nicer by the day and school ending, it’s easy to say you’ll start studying for the SAT later. If you want to avoid the feeling you had this morning checking your scores, you’ll resist that urge and find a few minutes every day to study.

I remember taking a short, but very hard calculus test in high school, and watching my friend hand in his test 10 minutes before time was called. I shot him the requisite stink-eye glare, and got back to work, struggling to integrate a function that was giving me absolutely no love. I don’t remember the function all these years later, nor do I even remember if I ended up integrating it successfully or not. What I remember is walking out of the room in my typical post-exam delirium being approached by my speedy friend.

“I failed,” he said, hands in pockets and staring at his feet. “I saw that last problem and it just froze me in my tracks.”

COME. ON.

Don’t get me wrong. I have nothing but sympathy for people who struggle with difficult questions (that’s why I made this site — to try to be helpful), but I can’t muster any sympathy for you if you can’t muster the strength to persevere until time is called.

In fairness to my friend, some functions are impossible to integrate if you don’t know a particular rule, and unless you’re an evil genius you’re probably not going to be able to derive the rule on the fly in 10 minutes. But he still should have kept trying. Something might have come to him. The only thing that’s certain is that nothing was going to come to him with the test off his desk and his head on it instead.

Over my years doing test prep, I’ve watched countless of kids zip through an SAT section during a proctored test and then put their heads on their desks to wait for the next section to begin, especially in reading and writing sections. I don’t think I’ve ever seen one of those kids get through a section with 100% of the questions answered correctly. Much to my chagrin, many of them even leave difficult questions blank!

There’s no shame in getting a difficult question wrong. There is shame in giving up on yourself when there’s still time left in the section. There is shame in not catching silly mistakes that you could have caught if you had been checking your work instead of trying to catch a 5 minute nap. There is no glory in finishing early. There is only the potential for shame.

##### If you finish a reading section early

Pretend that you’re going to have to defend each of your answers to a room full of people, and find the relevant sections of text that support the answers you chose. If you can’t find support for the answer you chose in the passage, it’s probably not be the right answer.

##### If you finish a math section early

Check. Your. Work. Do problems a different way than you did the first time. If you did algebra, see if you arrive at the same answer when plugging-in. If you solved a tough question with geometry and the figure was drawn to scale, make sure your answer stands up to scrutiny by guesstimating. Perhaps most importantly, make sure you didn’t make any silly errors by misreading questions. Those mistakes sting the most.

##### If you finish a writing section early

Go back through and make sure you aren’t seeing errors where there’s really just complex construction. Just because you might choose to say something differently doesn’t mean the way it’s written is wrong. Do a scan to make sure you caught all the dangling modifiers and run-on sentences. Make sure you caught all the comparisons by looking for instances of possessives (Mike’s blog; Sam’s salary; the plight of the Mets fan). Look for lists that you might have missed the first time. Do all your verbs match their subjects? Do all your pronouns match their antecedents?

##### It ain’t over until it’s over

If you’re trying to maximize your score, there’s really no excuse for quitting on a section early. I don’t care how certain you are about your answers. I don’t care how rarely you make algebra mistakes. I don’t care how boring the passages were. You’re either working on improving your score, or you’re sitting there in the test room doing nothing. Get back to work. You’ll thank yourself when the test is finally, actually over.

You don’t need to move mountains to significantly increase your score; you just need to focus on weak areas, a few at a time, and make them strengths. This entire site is dedicated to the specifics of doing just that, but I wanted to take a bird’s eye view today and point out that in general, you can improve your overall score by about 100 points simply by making one fewer mistake per section than you made last time (not counting the essay, of course). Seriously.

Say your raw scores on Test 2 in the Blue Book looked like this:

CR: 53
M: 43
W: 42

That’d give you 650’s across the board (assuming an 8 essay). Now say you made one fewer multiple choice error in the 3 reading, 3 math, and 2 writing sections. That’s going to add points directly because of the correct answers, and it’s also going to erase incorrect answer penalties to the tune of 0.25 per answer.

CR: 53 + 3 + 0.75
M: 43 + 3 + 0.75
W: 42 + 2 + 0.50

Your new raw scores round up, so now they look like this:

CR: 57
M: 47
W: 45

Your score just went from 650 + 650 + 650 = 1950 to 690 + 690 + 690 = 2070. Get some.

Of course, the actual improvement you’ll see could vary a bit based on where you’re starting, but 100 points is a pretty good estimate for this kind of raw score improvement.

What does this mean for you? It means that if you can identify a few weaknesses that appear often on the SAT, you can really move your scores. Say you struggle with dangling modifiers, main idea questions, and questions that can be solved by plugging in. If you use focused practice on those kinds of questions until you’re a pro, you can see a big improvement, even if it’s late in the game.

The bottom line: If your score isn’t where you want it to be yet, don’t freak out, and don’t try to do everything at once. You’re not going to jump from 1800 to 2100 (or 2100 to 2300, or 1400 to 1600) in one test. But if you can identify a few weaknesses every time you take a test, and you’re able to make sure you don’t make those kinds of mistakes going forward, you can eventually see a huge improvement. Look at your practice mistakes closely to try to identify patterns, seek focused practice based on your personal weak areas, and set reasonable goals to improve your performance on those specific things. If you do so diligently, you’ll be happy with the results.

 Credit: the very talented Mike R. Baker

I’ve already covered the importance of a good vocabulary, and I hope that you’ve been clicking the red vocabulary links on this site as you meander through. They’re meant to teach you a few good words, and to show you that strong vocabulary doesn’t have to be shoehorned into writing; it can and should flow naturally. I basically taught myself javascript to make those links, which took an obscenely long time, but I did so because I think it’s useful. So, yeah: You should actively try to improve your vocabulary as you prepare for the SAT. Period.

I want to take a (slightly controversial) step back from that, though, and caution you that a single-minded obsession with vocabulary will, in all likelihood, backfire on you. Not only is there much more to the Critical Reading section than just vocabulary, vocabulary isn’t even #1 on the list of necessary skills!

Some folks incorrectly claim that the 19 Sentence Completion questions on the SAT test only vocabulary, but even if that were true those account for less than a third of the 67 questions in the section. Want to include the passage-based questions that ask you to define a word in context as pure vocabulary questions? That’s even more of a stretch, but including them still doesn’t get you to a third of the questions.

But I don’t want to argue about question distribution. The truth is, even the Sentence Completion questions test you on your comprehension skills as much as they test your vocabulary; not only do the difficult questions contain difficult words, they contain much more subtle context clues than do the easy ones. Let’s look at an example of a tough one:

1. Because of his devotion to economy of expression, the computer programmer’s code was ——- despite its incredible ——-.

(A) elegant . . complexity
(B) spare . . utility
(C) labyrinthine . . usefulness
(D) prosaic . . beauty
(E) mawkish . . magnanimity

This is an example of a question that goes to great lengths to make it difficult to predict the contents of the blanks. A good vocabulary might help you eliminate one answer, but without good comprehension skills it’s very difficult to nail this one down. There are two clues in the sentence:

1. The easier clue is the “despite” between the blanks, indicating that there should be some amount of surprise that both blanks are true about the same code.  If you know both words, you know that mawkishness and magnanimity have very little to do with each other, so you can kill (E). But even if you know all the other choices, that’s as far as you can go using the easy clue. All the rest of the choices kinda work: if something were prosaic it’d be slightly surprising to also call it beautiful; if something were labyrinthine it’d be a little strange to also call it useful; things that are spare do not always have great utility; elegance and complexity are often at odds.
2. The really difficult clue is the phrase “economy of expression.” Neither “economy” nor “expression” is a difficult word on its own, but think for a minute about what they could mean together. Sure, you read a lot about “the economy” in the paper, but what does “economy” mean here? When a car advertisement touts a vehicle’s “fuel economy,” what does that mean? It means the car goes a long way on one tank of gas. “Economy” means getting a lot out of a little. It means getting the maximum return on a limited resource (which, if I may just break the flow for one minute, is not what you’re doing when you study endless word lists). So “economy of expression” means, in the programming context, accomplishing a lot without using many lines of code.

And that, friends, is why the answer to this question is (B). Note one more devious aspect of this question: the relatively rare definition of “spare.” I doubt that word shows up on any SAT vocabulary lists, but it absolutely can mean “elegantly simple.” Just so we’re clear, I’ve changed some things about the question, but I based this on a real question from a real SAT that contained both “economy of expression” and “spare” used in the same ways they are used above. This kind of question exists.

##### So, what lessons have we learned?
1. The SAT will throw words at you that aren’t on most vocab lists. “Mawkishness” was on the May test, and most people who I’ve spoken to had no idea what it meant until they looked it up afterwards. THIS IS NOT A REASON TO STUDY LONGER LISTS! The other words in the question were much more common and would have been familiar to you if you spent a few hours with any well designed list of a few hundred words. You could have answered the question correctly anyway.
2. The SAT will often use common words in less common ways (like the obscure definition of “spare”). You won’t get those definitions from flash cards or word lists, you’ll get them from being a voracious, insatiable reader and coming across them in the wild.
3. Difficult Sentence Completion questions are difficult not only because of hard words, but because of complex sentence structure and esoteric usage. You will need to be a very good reader to get them right.
##### The bottom line

I’ve spoken with too many kids lately who seem hell-bent on memorizing all the words in Barron’s 3500 Word Black Hole From Which No Light Escapes, and it breaks my heart. If you do that, you will memorize literally thousands of words you won’t need for the SAT, and you’ll use valuable time doing so that would be better spent practicing your reading comprehension, writing practice essays, drilling circle questions, or trying to count the number of hairs on your head.

Remember a few paragraphs back, when we were talking about economy? Those were good times, right? Trying to memorize 3500 words is not good economy. To put it another way—and to finally incorporate the awesome illustration at the top of this post—if you pursue vocabulary obsessively, like Ahab did Moby Dick, your scores might remain in Davey Jones’ locker.

You, intrepid student, need to find a balance between the reasonable and the obscene. It won’t be easy, but nothing worth doing is. Godspeed.

Finally, here’s a thread where Xiggi, the much-ballyhooed College Confidential SAT guru, basically argues the same thing (and gets a lot of pushback, naturally).

Before we really get into this, let’s get one thing straight: It’s incredibly unlikely than an 800 will open any doors for you that a 770 or so won’t. In fact, it’s usually not a good idea to think of SAT scores opening doors at all. It’s better to think of high scores preventing admissions doors from being closed—your high score encourages an admissions officer to look into your application further. Nobody secures admission to an elite school on SAT scores alone. So if you’re looking at an 800 as a means to an end, you might want to reexamine your priorities. If you’re pining after an 800 just because you really like the challenge, though, then you and I are kindred spirits, and you should read on.

• Above all, you will need to be nimble. Read this post, and then read it again. And then again.
• You’ll need to be good at math, but you’ll also need a healthy helping of SAT technique. If you’re really going to be ready for everything the SAT can throw at you, then you’re going to need to be conversant with everything on this page. The SAT math section is not a math test, but there is a bunch of math on it, and if you’re shooting for perfection you’re going to need to be able to switch deftly between math wizard and test taking savant as different questions call for different approaches.
• There is no room for error. While there are some tests that will bestow an 800 on a student who’s missed one math question, most are less forgiving. A single mistake might drop you as low as a 760. So let that extirpate any misgivings you have about the guessing rule—if you want an 800, you have to guess even if you’re completely stumped. Of course, if you’re completely stumped, then you probably haven’t prepped sufficiently to be shooting for an 800 in math.
• It’s not enough to get all the hard ones. An obvious corollary of the rule above is that you’re going to have to be perfect on the easy ones, too. It always amazes me when I see a student who is consistently perfect on #15-20 miss #4, but I see it all the time. If you rush through the easy ones to get to the hard ones and you make a silly mistake along the way, you can kiss your perfect score goodbye.
• It only counts on the real thing. If you can get an 800 on a practice test then I’m impressed, but you don’t get to join the club until you’ve done it on game day. That’s because it’s different when you take the real thing. Have you ever been to the vet’s office with your pet? You know that smell in the waiting room? That’s the smell of concentrated animal anxiety, and it will smell like that in your testing room. I kid, but only sorta. You have to be able to overcome the pressure, the exhaustion, and the entropy that come along with testing first thing in the morning on a Saturday. Kid next to you has the sniffles? They’re mowing the lawn outside the school? The heat is blasting even though it’s unseasonably warm outside and you’re sweating bullets by section 2? Birds get into your testing room? All of these have happened.
• You must practice as you play. To mitigate some of the difficulties of testing day, you should simulate testing day as best you can when you practice. Wake up early on a Saturday to take practice tests. Take FULL practice tests—all three subjects. No long internet breaks between sections. No cell phone on your desk. No giving yourself an extra 30 seconds to finish a problem. No starting the next section early if you finish before 25 minutes is up. No smiling.
• You are not entitled to an 800. Even if you take every test you can get your hands on, even if you can do probability questions in your sleep, even if circle questions see you coming and just solve themselves to save you the trouble since you’re such a monster, the SAT might find a way to throw a question at you that’s unlike any you’ve seen before. That’s not unfair; that’s just how it works. You’re going to have to wrestle with a few very difficult questions when the pressure is on, and only if you come out on top will you earn your 800.
• If it were easy, everyone would be doing it. I know this post’s tone has been a bit less rosy than most of my others’, but that’s because I really want to set your expectations: an 800 is quite an accomplishment; it will require toil proportional to its resulting renown. If you expect to muscle through just because you’re really good at math, you might be disappointed. If you expect it all to come together on test day even though your practice tests have been in the low-mid 700s, you might be disappointed. Even if you hit 800 on your last three practice tests, you might be disappointed. But doing so, and enjoying the process, is the surest path to success.

Wanna try some hard problems right now? These drills are difficult, but you should be able to rip through it without making any mistakes if you’re shooting for 800. Good luck!

In fact, most math facts aren’t relevant to the SAT. It’s really important to remember that the SAT math section is NOT A MATH TEST. There’s some math on it, sure, but if you spend your time trying to absorb every arcane property and axiom you encounter, you’re not preparing effectively.

Test prep behemoth Kaplan surely feels pressure to have a constant presence on every social media platform known to man, but such ubiquity comes at a price. In this instance, the price is that Kaplan’s reputation as a tone-deaf, corner-cutting organization whose primary concern is not student improvement is, once again, reinforced.

Let’s be clear: you do NOT need to know what “relatively prime” numbers are for the SAT. I have seen every published test since the new test format debuted in March 2005, and although I suppose my memory could be failing me, I don’t remember ever seeing a question about relatively prime numbers. Furthermore, if such a question ever did appear or were to appear in the future, I can guarantee that it was or would be accompanied by a definition of what it means to say that numbers are relatively prime.

It’s disingenuous of Kaplan, which should have at least as much knowledge about the SAT as I do, to present it as something you might want to know for the SAT. As has been pointed out more methodically over at The Fat Envelope, sometimes the big test prep companies seem to be trying to perpetuate the mystification and panic that surrounds college admissions testing, because such confusion and fear benefit their bottom lines. I don’t know if this is an example of such cynical fear-stoking, or just the product of entrusting the job of drip-feeding the insatiable Twitterverse to a hapless intern without much SAT knowledge, but either way it’s pretty inexcusable from the likes of Kaplan.

Kaplan: I expect so little of you, and still you give less. Get it together.

UPDATE: Not long after I wrote this post Kaplan was at it again, posting the SAME TIP as an ACT tip of the day. Bell Curves founder and generally cool dude Akil Bello was all like “WHATTTT?” I took some screenshots of a truly bizarre exchange between him and Kaplan, and I submit them without further comment:

March SAT scores are out today and I’ve heard almost exclusively good news from the students I’ve worked with. The smiles and laughter of children, they are like manna to me. I know, however, that score day is never a happy day for everyone. If your results today fell short of your expectations, here’s some advice to help you avoid this feeling next time around.

1. Don’t panic. You have FIVE more chances to take the SAT before applications are due in the winter: May, June, October, November, December. Some seniors even get away with taking January. So you’ve got time.
2. Don’t sulk. Perhaps you’ve heard before that the best thing to do when thrown off a horse is to get right back on it. The same applies to the SAT. Feeling sorry for yourself won’t help; focused and assiduous prep will. Take today to lick your wounds, and start working in earnest tomorrow.
3. Set expectations. Most people will never score a 2400, and that’s OK. Figure out the scores you need to be comfortable in applying to the schools you like best, and make those scores your goal. If you’re having a hard time, check this post for more about how much you should be looking to improve.
4. Develop a plan. Taking the test the same way you did last time will probably result in a very similar score, so just doing a bunch of practice tests isn’t enough. You need to identify your weaknesses, and then focus on them to make them strengths. Start by doing a drill or two to help you identify weaknesses, like these ones!
5. Execute it. Whether you plan to take a course, work with a tutor, or prepare on your own, the key to your success will be your own personal commitment to improving. Even if you take a course for a few hours a week, you won’t see a huge improvement unless you also practice on your own. Today it felt crappy when you didn’t get the score you wanted. Remember this crap feeling every time you’re tempted, in the coming weeks, to blow off SAT prep. A huge improvement is possible, but only when accompanied by a huge commitment.
This site exists to help people like you do better than you were doing before. Consider subscribing to the blog, or following me on twitter: @PWNtheSAT. Good luck!

Here’s a question I love to throw at students early on in the tutoring process (let’s call this a grid-in for now, to keep things simple):

1. If $\fn_phv&space;\frac{4^{999}+4^{998}}{5}=4^x$, what is x?

It’s a beautiful question because no matter what, it’s going to show me something about the kid with whom I’m working. Almost everyone goes to the calculator first. Once it becomes clear that the calculator will be no savior I see a few divergent paths, all illuminating:

1. If my student says it can’t be done, I know one kind of question on which I’m going to have to drill her repeatedly.
2. If my student says x = 1997, then I know he just added the exponents in the numerator and completely ignored the denominator, so we’re going to need to review the exponent rules and get his vision checked.
3. If my student factors 4998 out of the numerator to see that everything else cancels out and x = 998, then I know I’m going to have to really challenge her to get her score higher than it already is (full solution explained at the bottom of the post).
4. And if my student starts wrestling with other, more manageable numbers (for example: $\fn_phv&space;\frac{4^{3}+4^{2}}{5}=16=4^2$),  to try to suss out a pattern, I know I’m dealing with a kid who knows how to struggle and who doesn’t back down from tough questions.

Let’s be clear here: it’s best to know how to do this question the right way, like the third student. She has a strong base of math knowledge, has seen enough similar problems not to misapply exponent rules, and is creative enough to try pulling out the greatest common factor to see if anything good happens (and it does). But I don’t know yet what she’s going to do when she gets to a problem that’s unlike any she’s seen before (and on the SAT, that will indubitably happen, and probably when it counts). So I’m going to keep watching her closely until I get to see how she reacts to a question that makes her squirm.

The fourth student is one who finds a way to claw out the correct answer when faced with an intimidating problem that his tools seem at first not to be able to solve. He might not be as conversant with math as the third student, but in the eyes of the SAT, she and he are exactly the same on that question. Because he’s scrappy. He’s nimble. And that will take him a very long way.

In sports, you’ll often hear a commentator say, “That’s why you play the game,” after an underdog wins a game it shouldn’t have. It doesn’t matter who looks better on paper. It matters who performs on game day. After seeing him work this question, I’m going to worry less about student #4 on game day.

If you want to take your place in the pantheon of great test takers, you’re going to have to be nimble. You’re going to have to grapple with tough problems sometimes. You’re going to have to, as poor Mario does in the video above, make mistakes, learn from them, and try not to repeat them. You’re going to have to be flexible, and willing to try more than one approach.

This is why I want you to know how to plug in, but I also want you to be able to do the math. This is why I want you to have a decent essay skeleton in mind when you walk into the test center, but I also want you to be able to handle a fakakta prompt like the one about reality TV. This is why it’s important to have a good vocabulary, but you’re wasting your time if you think the path to a higher reading score is through flash cards or word lists alone.

Kids sometimes complain that I ask too much of them. But the way I see it, I really only want one (admittedly multifaceted) thing out of my students: I want them to learn to be nimble.

##### Solution to the sample problem:
$\fn_phv&space;\frac{4^{999}+4^{998}}{5}=4^x$
$\fn_phv&space;\frac{4^{998}(4+1)}{5}=4^x$
$\fn_phv&space;\frac{4^{998}(5)}{5}=4^x$
$\fn_phv&space;4^{998}=4^x$
$\fn_phv&space;998=x$
 image source

It’s been over a week, and still not a day goes by that I don’t see a new article bashing The College Board for its decision to use reality TV as an essay topic. The topic caught me off guard just as it did everyone else, but I can’t justify all the hand-wringing that’s occurred in the days since.

Here’s the full text of the prompt:

Reality television programs, which feature real people engaged in real activities rather than professional actors performing scripted scenes, are increasingly popular. These shows depict ordinary people competing in everything from singing and dancing to losing weight, or just living their everyday lives. Most people believe that the reality these shows portray is authentic, but they are being misled. How authentic can these shows be when producers design challenges for the participants and then editors alter filmed scenes?

Do people benefit from forms of entertainment that show so-called reality, or are such forms of entertainment harmful?

I’m of the opinion that the prompt provides even television-less students enough information to opine about the benefits/harms of reality TV, regardless of whether they partake in the shows themselves.

A lot of test prep people are up in arms about the prompt because it caught them off guard, and they’re rightfully hearing from their students who felt unprepared to answer the question. That’s unfortunate for those who paid for prep that proved ineffective, but it’s not a fault of the test, whose stated goal is to assess how well a student develops a point of view, organizes an argument, and displays mastery of grammar and style.

A lot of us in the prep world encourage students to come prepared with a few “universal” examples ready to go — classic literature or historical figures, for example — and those weren’t exactly well suited for this prompt, but there’s no rule that the SAT has to use a prompt that will help students who’ve taken prep courses succeed. In fact, I’m sure the SAT writers are quite happy to be able to foil us once in a while.

This was a tough question, but it was fair. Different essay prompts are always accompanied by slightly different scoring tables for the writing section, and if this prompt really was more difficult than the others given on the March test, that difficulty will be reflected in a more lenient scoring table.

Believe me, I’m no member of The College Board’s booster club, but I just can’t bring myself to be mad at them for this one. I just have to tip my hat to them that they threw something at me that I didn’t expect, even after all these years.

 source.

I’m constantly reminding students to look for patterns. The key to transcendent scores is pattern recognition. If you want to be a truly adroit test taker, you’re going to have to devote yourself to taking every test you take actively. Obviously, you should be looking for patterns in the kinds of mistakes you’re making, but you should also be making mental (or hell, physical) notes of every question you see that strikes you as something new or novel.

Do you play Halo? Or COD? How about poker? Do you ever go outside and play baseball? When I was your age…

True domination in any of those games comes only after you have internalized the systems in which the game is played. If it’s a FPS, even if you’re good at FPS games in general, you’ve gotta spend time getting shot in the back right after you spawn until you’ve really learned the maps in a new game. You’ve gotta master the trajectories of projectiles that don’t go in a straight line (grenades, etc). You’ve gotta learn the timing of the sniper rifle. You have to learn the game’s physics, inside and out, and then you need to recognize the patterns of other players. Most guys run right for the rocket launcher when they spawn anywhere near it. How can you use that knowledge to your advantage? Once you’ve got all that down, you start teabagging. One time in COD4 some guy PREbagged me*. That guy knew every in and out of that game.

Good poker players do the same thing. Decent poker players know how to bet given the hand they have, because they know something about probability. Good poker players know what their opponents have based on how their opponents bet, if they’ve been playing together for a while. When a good poker player sits down at a new table, she spends time learning about her opponents. Who likes to bluff? Who plays fast, and who plays slow? What are these players’ tells?

And of course, there’s baseball. Professional baseball players don’t face a pitcher they’ve never seen before without reading a scouting report to try to learn what pitches they’re likely to see in which situations. Ever try to hit a curve ball before? That shit is hard. But you know what makes it a little easier? Knowing it’s coming. Pitchers do the same thing with batters. They know who not to pitch inside and low, etc.

A good vocab list based on prior tests is a nice start, but if you’re shooting for perfection you’re going to have to go further. And so it is with the rest of the test. This site is meant to help you to identify some of the more common patterns on the SAT, across all its sections, but you should really be looking to identify patterns for yourself too. When you make take possession of these observations, when you treat the entire SAT like a game of you vs. them, when you feel like you know what the SAT is going to throw your way before you even open the test booklet, you’re going to be in very good shape to knock it out of the park. And then teabag it.

*In COD4, you don’t see your body after you die; you see a kill cam replay of your death from your killer’s perspective. So this guy, who found me lying prone in what I thought was a pretty safe spot, teabagged me BEFORE he killed me, so I could see it happen in the kill cam. You have to respect that.

I’m getting a bit tired of all the focus on #20, which is usually the hardest math question on the test. I guess I’m a bit complicit in all the hype, since I like to illustrate techniques on here using difficult problems, but that’s only because I like to show how powerful those techniques can be. Seriously, let’s be very clear about this: #20 is the LEAST important question on the test. You shouldn’t be worrying about it at all unless you’re getting 780’s or higher every time.  Here’s an argument based on a simple economic principle.

If you’ve taken or are taking an economics course, you’re surely familiar with the concept of opportunity cost. Put succinctly, opportunity cost is the cost of a certain decision in terms of the best available alternative. For example, if you choose to go to the movies (which costs you \$10), but if there weren’t any good movies you you would have spent those two hours babysitting for \$15/hour, then your opportunity cost for going to the movies is what you paid plus what you COULD HAVE made instead (\$40). That’s an expensive movie, right?

Of course, opportunity cost is really just a way to codify the thought processes we have about the decisions we make: “if I didn’t do thing 1, I could have done thing 2 instead; the benefits of doing thing 1 are valuable enough to me that I will forgo the benefits of doing thing 2.” With that in mind, let’s look at some facts about the SAT math section:

Facts:

• Every multiple choice question is worth the same: +1 raw score point for a correct answer, -1/4 raw score point for an incorrect answer, +0 for a blank.
• Although they’re worth the same, questions vary greatly in difficulty.
• You have a limited amount of time to complete a section.
• In math sections, questions proceed in an order (roughly) from easiest to hardest*.
So here’s the argument:
1. Since the payoff for a correct response is exactly the same in raw score points no matter the difficulty, and since that’s the only thing that determines your final math score, the value of each question is exactly the same.
2. Since you can’t really be doing anything else during the 25 minutes in which you’re sitting there taking a 20 question math section, the opportunity cost for working on (and answering correctly) any given question is equal to the time it takes you to answer that question (time that you could otherwise be spending answering the next question correctly).
3. Since it takes longer to answer hard questions correctly than it does to answer easy questions correctly, questions on the math section have increasing opportunity cost (that is, they take longer) as you progress, even though their values are exactly the same.
4. Since your mission is to maximize your score (by maximizing the amount of raw score points you secure) in a limited amount of time, the most important raw score points to collect are the ones with the lowest opportunity cost associated with them.
5. Conversely, mistakes on easy questions are the most costly mistakes, since it would have taken so little extra time to get those questions right.
6. If #20 is the hardest question in the section (this is usually, but not always true), then it has the highest opportunity cost, and is therefore the least important to get right.
7. If it’s the least important question to get right, it’s also the least important question to attempt.

You should, therefore, be as positive as possible that you are correct in your response to every question you work on before moving on to the next question (which will have a higher opportunity cost for the same amount of raw score points). You should not even attempt #20 until you are sure you are correct on #19, which you shouldn’t even attempt until you’re sure you’re correct on #18, etc.

I’ve said it before but it bears repeating here: You’ll increase your score more by getting fewer easy questions wrong than you will by getting more hard ones right.

* In the section that has the grid-in questions, questions go from easiest to hardest twice, once in the multiple choice (#’s 1-8) and then again in the grid-ins (#’s 9-18).