Posts tagged with: philosophy

I don’t know if you followed the kerfuffle between Jonathan Coulton and Glee a few weeks back. It’s old news now, but I watched it unfold at the time with great interest, and I’ve been thinking about it again the last few days. The incredibly short version: Jonathan Coulton is a fairly popular musician (on the Internet, anyway) who recorded a cover of Sir Mix-a-Lot’s “Baby Got Back” in 2005 (above). Glee did a note-for-note recreation of his cover without crediting him. Then Fox’s lawyers told him he should be thankful for the exposure he didn’t get because nobody credited him.

This is a case of morality and legality not completely overlapping, and that’s all very interesting if you’re into intellectual property law (which I know is very popular among high school students these days) but that’s not where I want to go with this. The reason I bring it up is that Mr. Coulton ended up announcing that rather than pursue recourse through the courts, he’d completely change direction and try to turn this into something positive for him, and for some great charities. And there’s an SAT lesson there: know when you’re beat, and do something about it.

Coulton’s indignation was justified, but he recognized early on that he’s not going to beat an army of Fox’s lawyers, so he shifted tactics. If what you’re doing isn’t working, try something else. This is what I’m talking about when I implore you to be nimble. It’s pretty good advice for life in general, and it’s particularly germane to the SAT, on which many of the most difficult questions are vulnerable to techniques that will allow you to sidestep the math solution, if you let them. Like this one, for example:

  1. Yesterday, a group of y friends went to the mall and each purchased p pairs of gym socks. If y > x > 1 and p is a positive multiple of 3, how many fewer pairs of gym socks would they have purchased if x of the members of the group had purchased only a third as many socks as they actually did?
    (A)   
    (B)   
    (C)   
    (D)   
    (E)   

If you’re looking for a top score on SAT math, you should be able to solve this with algebra, and you should also be able to solve it by plugging in. Being nimble in this way is how you work around the fact that you’re likely to see at least one problem on test day that thwarts your first attempt to solve it. Being comfortable solving a question like this two ways is also the best way to avoid careless errors—check your work by solving the way that you didn’t solve it the first time. If you get the same answer both ways, you’re almost certainly right. Both solutions below.

Let’s start with plug in

Say 10 friends go to the mall (y = 10) and each buy 3 pairs of gym socks (p = 3). So what actually happened yesterday is that the group purchased 10 × 3 = 30 pairs of socks. Now say 2 of the friends (x = 2) purchased a third as many socks as they really did. So 2 friends bought only 1 pair of gym socks each. 8 friends buy 3 pairs: 8 × 3 = 24, and 2 friends buy 1 pair each: 2 × 1 = 2. Total pairs of socks purchased: 24 + 2 = 26, or 4 fewer pairs of socks than were actually purchased. Look to your answer choices, and see which one gives you 4 when you plug in y = 10, p = 3, and x = 2.

(A) Does:   
(B) doesn’t:   
(C) doesn’t:   
(D) doesn’t:   
(E) doesn’t:   

So (A) is clearly the answer.

Now let’s do the algebra

Note that, since you’ve already spent some time working through the problem logically with plug in, the algebra should be a bit more intuitive now than it might have seemed at first. First, create an expression for what was actually purchased. That’s easy: y people purchased p pairs of socks each. Total pairs purchased: yp. Now, figure out how many would be purchased in the alternate scenario where x of the friends purchased a third as many socks as they really did. y – x purchased p pairs of socks, and x purchased p/3 pairs of socks. Total pairs purchased in alternate scenario:

Now just do some subtraction to find out how many fewer pairs of socks would have been purchased:

Unsurprisingly, we arrive at the same answer either way. Again, if you’re shooting for an 800, you really should be able to breeze through this question (and ones like it) both ways.

Bonus solution

As you might have deduced from the fact that the correct answer doesn’t contain y at all, y totally doesn’t matter. All that really matters is how many fewer socks the x friends would have purchased. If they were to purchase 1/3 of what they did, they would purchase 2/3 less than they did. Since the x friends purchased xp socks in real life, they would purchase 2/3 of that is . [See also: “Is there a math way?“]

If you’ve ever chalked up a math error to “carelessness”(and let’s be honest—you have) then this post is for you. So often do I see students blame their mistakes on “carelessness,” in fact, that the poor word has lost its meaning in an SAT context. This post is an effort to restore its dignity.

Carelessness, in my experience, can mean one (or more than one) of the following:

  • Misreading the question
  • Misbubbling the answer
  • Arithmetic or simple algebra errors
  • Self-delusion

To avoid misreading the question, always give the question one final read before you bubble your answer to make sure you found the answer the test is actually asking for.

To avoid misbubbling, bubble sedulously, and then double check your bubbling. You should check once as you’re bubbling, and then if you have time at the end of a section, go back through and make sure your answer sheet reflects the answers you’ve circled in your test booklet. This, by the way, is one great reason to actually use bubble sheets when you take practice tests. Because everyone misbubbles once in a great while, and if it happens to you during a practice test, you’ll be that much more likely to be careful on the real thing.

As anyone who’s ever taken a math test knows, it’s very difficult to avoid the occasional arithmetic or algebra error. Sometimes, the mind meanders. It’s also, unfortunately, very difficult to catch an error when you go back and look over your work. You can be staring right at 10 ÷ 5 = 5, but if you just wrote it 2 minutes earlier, you might not see what’s wrong with it. So to avoid bungling your simple calculations, do the following:

  • Check simple arithmetic on your calculator. I know you’ve done 6 × 7 in your head a million times correctly. Just make sure.
  • Try to do as many problems as you can multiple ways. If you arrive at the same answer with algebra as you did by plugging in, you can be doubly sure you’re right. Of course, you’ll need to find a healthy, comfortable balance here between caution and speed. Pro-tip: it’s usually not a good idea to sacrifice accuracy for speed. Favor caution.

As for self-delusion, this is the toughest one to fix, because it’s denial of a problem. Many students brush off every question they miss: “Oh, that was easy. Careless mistake!” This is a natural reaction—a good solution can look really obvious once it’s laid out in front of you, especially by a good teacher.

But if this sounds like you, know that you do yourself a disservice when you assume that, since a solution is obvious once someone else shows you how to do it, a similar solution will be obvious to you next time you see a similar question. By characterizing a mistake as “careless,” you tell yourself you don’t need to learn anything new about questions like the one you missed. And if that’s not true, then that question type will keep forcing you to make “careless” errors until you address your underlying knowledge gap. It’s OK not to know how to do something, and admitting that you need to learn is the first step towards doing so.

To be safe, try never to characterize a mistake as “careless” unless you’ve got a demonstrable history of cutting through similar questions like butter. Don’t even let the word “careless” enter your vocabulary until you’ve done 4 or 5 practice tests.

When a student asks me how to solve a math problem, my default response is to show, if possible, how to solve it by plugging in, backsolving, or guesstimating. I do this because I figure if the “math way” was obvious, the student wouldn’t be asking me for help in the first place. Besides, problem solving—in life, or on the SAT—isn’t about following a circumscribed set of procedures. It’s about creativity and flexibility. I’ve written before about the importance of being nimble. Consider this post a sequel.

It’s fun to be good at math, and it’s nice to understand how the underlying algebra on a tough word problem works. But if you’re aiming for top scores, it’s imperative that you cast a critical eye on your own ability to tease the “math way” of solving a problem out of the problem during the fairly tight time constraints imposed by the SAT.

If x + y = p and x – y = q, what is p2 + q2 in terms of x and y?

(A) 2(x + y)2
(B) 4xy
(C) 2x2 – 2y2
(D) 2(x2 + y2)
(E) 2(x2 – 4xy + y2)

Like all questions, there’s a “math way” to do this, but unlike all questions, this one is a prime candidate for plugging in. There will be some students who can breeze through the algebra in their head and identify the correct answer almost instantly. If that’s you, then great. You needn’t plug in. But if that’s not you, or if you only kinda think that’s you, then you should probably just plug in. It’s fast, it’ll get you the right answer, and then, later on you can go home, make an awesome couch fort, and figure out the algebra when you’re not pressed for time.

The plugging in solution

Say x = 3 and y = 2. Then 3 + 2 = p = 5, and 3 – 2 = q = 1. 52 + 12 = 26, so you’re looking for an answer choice to give you 26. Type the answer choices into your calculator carefully, substituting 3 for x and 2 for y, and you’ll be done in a hot second:

(A) 2(x + y)2 = 2(3 + 2)2 = 50
(B) 4xy = 4(3)(2) = 24
(C) 2x2 – 2y= 2(3)2 – 2(2)2 = 10
(D) 2(x2 + y2) = 2(32 + 22) = 26
(E) 2(x2 – 4xy + y2) = 2(32 – 4(2)(3) + 22) = –22

The algebra
Now add ’em up:
Not impossible, right? Totally doable. But arguably more involved than the plug-in solution above.
The bottom line

Look, I really just want you to be happy. If you want the algebra, I’ll give you the algebra. But I really think it’s a good idea for you to know how to plug in, too. Because if you have to ask me for the algebra on a question like this, that means it wasn’t obvious to you right away when you encountered it on the test. And that means there’s a good chance that when you sit down for the real thing, the algebra isn’t going to be obvious to you for every single question. And if, when the algebra isn’t obvious, you don’t have a backup plan, then you’re doing yourself a disservice.

Try the algebra first, if that’s your bent. But you should have a few other tricks up your sleeve for the questions where the “math way” isn’t jumping off the page onto your lap.

Although this site has amassed, over time, a fair amount of loyal readers (thanks guys! <3 u!) the single greatest source of traffic for this site is still Google. Which means a lot of people find their way here by searching for “SAT tips,” (I’ve got some) or “is C the most common SAT answer” (no) or, hilariously, “5 hour energy on day of test” (I wouldn’t if I were you).

I’ve done a fair amount of SAT-related Googling myself, so I know what else is out there. There’s some good stuff (for a sampling of what I think is good, see the “Brothers and sisters in arms” section in the left sidebar on this site). There’s also a lot of junk. Some of it’s benignly awful—space-filler articles in local newspapers that purport to tell you how to do well on the exam but actually just tell you to bring #2 pencils and get a good night’s sleep the night before. Those aren’t helpful, but they’re usually written by well-meaning people and they’re mostly harmless. Then there’s the more insidious stuff—the folks who try to squeeze large sums of money out of you or your parents by stoking your anxieties about the SAT, and then claiming they’re the only ones who can help you. You should avoid these charlatans like the plague. Which means you need to know how to identify them.

The two biggest, most glaring indicators that you should be skeptical about the efficacy of a test prep resource are big secrets and big promises. 

Big Secrets

The last major change to the SAT was in 2005, which means folks like me have had the better part of a decade to dissect and analyze the test in its current format. SAT prep is big business, and profitable business, so even though they’re not all blogging about it there are many sharp minds thinking about how to do prep the right way. On the fundamentals, there are more similarities than differences among expert test prep providers. Most of us use plug in and backsolve when appropriate, and we all talk about dangling modifiers and run-ons, even if we use different terminology for those techniques and concepts. Sure, many of us have little quirks that are fairly unique, but those are like the paint job on a car—a cool paint job is only worthwhile if the car actually runs.

Slick marketing and quality test prep don’t have to be mutually exclusive, but you need to make sure there’s steak behind the sizzle before you sign on the dotted line. If a potential prep provider claims to know something about the test that nobody else knows, or claims to have unlocked the secrets of the test, but won’t back up her claims until you’ve opened up your wallet, keep your wallet closed and find another resource that will be more forthcoming about the test prep process.

Big Promises

Nobody can sprinkle fairy dust over your head and raise your score 400 points; people who claim otherwise are suspect. A large score increase depends more on you and your hard work than it does on even the most adroit tutor. If someone on the Internet is willing to guarantee huge score increases in just a few hours of work before even meeting you, he probably either hasn’t been in this business long enough to be any good, or has his fingers crossed behind his back.

The Bottom Line

Gimmicks, secrecy, and salesmanship are all too common in the SAT prep world, but only good teaching is worth paying for. A good tutor or prep course teacher is good because she knows how to communicate concepts and ideas effectively—if you’re not resonating with her when she explains something the first time, she figures out your learning style and alters her approach accordingly. If you’re considering spending some money on test prep, seek good teaching.

Of course, it’s possible that I’m wrong and there is a tutor out there who can improve your score 700 points just by whispering some gibberish in your ear and doing a special dance. I’m just saying I wouldn’t bet my hard-earned money, or my precious time, on it.

[See also: Six questions to ask a potential SAT tutor]
If you don’t know li’l brudder you’ve got some viewing to do.

I don’t know if this is going to work or if it’s going to blow up fantastically in my face, but I’ve been toying with this idea for a while now (my original thoughts here) and I’ve decided I want to give it a whirl. I’m looking for a smallish group of students who would be interested in participating in an unorthodox and labor-intensive SAT experiment this summer.

Here’s the deal

I want to see if, collaboratively, a bunch of students can create a mock SAT—a whole test, from soup to nuts. I’ve talked to a few other test prep folks who might be interested in helping me advise the project (I won’t name names until they officially sign on) but my vision is that students do all the heavy lifting and research, and the other experts and I provide guidance along the way. If you participate, you’ll comb through tests in the Blue Book looking for patterns to decide things like how many run-ons should be tested in the 14-question final writing section. You’ll argue with each other about what the essay question should be, or how hard the final question on a math section should be. You’ll debate whether you’re really using a word properly in a sentence completion question. By the end of the summer, you’ll hopefully have a deep understanding of the content and structure of the SAT. My hypothesis is that this knowledge will increase your score.

Of course, it’s only a hypothesis. As far as I know this hasn’t been tried before, anywhere, and I obviously make no guarantees that you’ll see a huge score bump, or any bump at all. I really think you will, but if you decide to devote time to this you do so in full knowledge that it’s not a sure thing. Along those lines, I can’t guarantee that a finished product emerges from this. If you sign on, you take some of the responsibility for keeping this project going. If people lose interest halfway through, then it just fizzles and we all walk away.

logistics

I’m planning for most of the work to be done on a wiki, which will completely open to the public. Obviously, some work (like layout work) will need to be done offline, but that’s only in the final stages and we’ll cross those bridges when we come to them. Our finished product, and the wiki we used to create it, will remain available publicly, too. The idea is that if this works, other people might want to replicate and refine the process. Nothing is going to be bought or sold through this project. All content will be licensed with Creative Commons.

where do I sign up?

You don’t even have to! If you’d like to participate, you can access the project here. Just start contributing!

Feel free to tell your friends about this if you think they’d be interested, too.

As far as I’m concerned, the single most important difference between a good SAT taker and a truly adroit one is the ability to see the common threads that tie questions together. Pretty much everything you’ll find on this site was written to help you do that.

That’s why, if you try my math drills (1, 2, 3), the answer keys link you back to posts containing similar questions.  That’s why the Blue Book Breakdowns I’ve posted (Test 1, Test 2, Test 3, Test 11) do the same. That’s why, in my book, each chapter ends with a list of questions in the Blue Book to which the chapter applies. That list is meant to show you all the different ways the same concept can be tested, so that you can start to see the similarities, not the differences, between questions.

The lists also serve another purpose: they’re rough indicators of how frequently concepts are tested and how often techniques can be applied. Across sections, it’s important to internalize a sense of what you’re likely to see and what you’re not. The chances of you seeing an hard exponent question to which plug in might apply are pretty good. The chances of you seeing the word jejune (or any single vocab word) on the SAT are pretty small. The odds of you seeing a comparison error somewhere in the writing section? Incredibly high. And so on and so forth.

I’m spelling all this out now because it’s high season for self studiers, and I want to encourage you, if that shoe fits, to seek the forest behind every tree. As you take practice tests, focus not only on the mistakes you made, but the patterns that begin to emerge in the questions you’re getting right. Ask questions about your mistakes, sure, but remember that you’ll never see that exact question again, so the value of any explanation you get is in what you can take from it and apply to similar (or not-so-similar) questions going forward.

It’s easy to get hung up the details—and the details are important—but SAT prep is all about the big picture.

Source.

I came across a great LinkedIn group discussion recently about an in-school SAT class (not a big prep company running a course at a school, an actual class during school run by school faculty) and it really got me thinking about ways I would try to engage students in the SAT in a classroom setting given the luxury of time and the resources of a school system. I contributed a half-baked response before heading out for the day, but I’ve continued to ruminate on the idea ever since, so I figured I’d try to flesh it out a bit more here on my own blog. More so than most, this post will be a living document, in that I plan to add to it as more ideas come my way, and if I get any feedback from you all.

If I worked in a school, and was given the opportunity to run a semester-long, 5-days-per-week SAT prep course, I would spend the first few weeks teaching the requisite strategies and making students do practice drills and full tests. And then I would reinforce those first few weeks by making the class try to create an SAT of its own, from the ground up. The idea here is to really get students engaged in thinking about what the test is, and what it is not. I’ve toyed with the idea of question writing as pedagogy in the past, and although I’ve received pushback from students when I’ve proposed it, I remain convinced that under watchful, expert eyes, the construction of mock questions (and even a mock test) could be an incredible teaching tool.

I would model this part of class loosely around something that already exists in many schools: yearbook class. There would be, for example, people on a design team trying to emulate fonts, layout, and other design elements of the test. There would be teams dedicated to each subject, and possibly subteams to work on different question types. Depending on time constraints, I might or might not provide reading passages of my own choosing.

Learning objectives
  • Determine, based on available tests, what the most commonly tested concepts are.
  • Explore all the the different ways common concepts are tested.
  • Understand how incorrect answer choices are chosen. For example:
    • Common calculation missteps
    • Predictable misunderstanding of reading passage contents
    • Sentence Improvement questions that fix original problem, but introduce a new one
    • Phrases that “sound weird” but are grammatically correct
  • Learn how to write precise, unambiguous questions (and in so doing, gain an appreciation for how precise and unambiguous the SAT is).
  • Repeatedly reinforce important concepts and techniques as students emulate the style and substance of the SAT in their own questions.
  • If possible, administer both an official SAT Blue Book test and the student-built test to another group of students over a few weekends (some students do Blue Book test first, others do student-built test first).
    • Perform rudimentary statistical analysis to try to see how well the student-built test approximates the real thing.
    • Write report(s) on what worked about the process, and what didn’t.
Requirements

Of course, to pull this off a teacher would need really deep understanding of the test, to provide guidance and to keep students focused on designing an SAT—simply designing a really hard test that doesn’t feel much like an SAT might be a fun exercise but isn’t going to do anybody much good from a test prep perspective. And students would need to be motivated, curious, and not easily frustrated.

Last word

Difficulties and improbability of this ever being attempted aside, I really feel like in the right circumstances, this process could create some real powerhouse SAT takers. Aside from giving students some perspective on how the sausage is made, it would give the instructor tons of opportunities to go beyond teaching the basic test-taking strategies and really dig into students’ problem areas in a nontraditional way.

It could also, done right, be a lot of fun. Just sayin’.

* I don’t advocate violence towards cats (or other animals). “There’s more than one way to skin a cat” is a phrase that I used to hear all the time growing up, but that I now realize (having received some mortified stares at its utterance) that it’s not as common as I thought it was. It just means that a problem might have more than one solution. I still say it even though I have to clarify it now because I’m stubborn. 

I chimed in on a thread at College Confidential recently about a probability problem that apparently came from Dr. Chung’s book. The first few respondents provided completely legit (but rather technical) explanations of the problem using nCr, and then someone asked whether there was another way. So I jumped in with the way I prefer to solve most counting and probability questions on the SAT: short lists. For the most part, all the solutions offered in the thread were valid.

Why am I posting about that conversation here? Because it underscores an important fact: there are often multiple ways to solve SAT math problems. That’s one of the beautiful things about math in general, actually: it’s built on itself. That’s why you learned addition before multiplication, multiplication before exponents, geometry before trigonometry, etc. My recollection of learning nCr techniques was that they were slowly introduced to us as general solutions to simple combination problems we could solve with simpler counting principles—the kinds of problems you’ll see on the SAT.

I get a rush out of breaking a problem down until it’s so easy a caveman could do it. That’s one reason I’m a pretty good SAT teacher. But you’re probably not aspiring to a career in test prep; you’re probably just trying to score high enough on the SAT to move on with your life.

So it’s completely up to you whether you solve a combination/permutation problem on the SAT simply, the way I like to, or with robust, scalable techniques that would work just as well with many more elements. But I like to remind my students that you’ll never need nCr on the SAT; the numbers will stay small. Just like you’ll never need trigonometry or logarithms, even though you might once in a while spot a problem that can be solved with them.

At the end of the day, I’m all about information. In my ideal world, you’ll know more than one way to solve every problem, so you’ll be able to make informed decisions on whether to, say, plug in or do the algebra on a question-by-question basis, instead of being forced into algebra on every question because it’s the only way you know.

You’ve got a math teacher in school 5 days a week who will advocate the mathy way. You’ve got me, if you want, to show you alternatives. Once you’ve poked around and seen what’s out there, you decide the level of complexity that’s most comfortable for you and leads to your best score.

Sometimes, you make mistakes. I don’t care who you are, what your GPA is, or what your SAT scores are. Sometimes, you make mistakes. If you’re the kind of student who is able to finish sections before time is called, it’s pure hubris not to use that opportunity to check your work.

An anecdote: yesterday morning, I did a bunch of work typing up an explanation for the Q&A page, but then accidentally closed my browser and lost all my work before posting it. I was late for a train, so I didn’t have time to retype it all. I figured that once I got to campus—school has started again for me, too—I’d have a chance to retype it. And I did.

For the first time that I’m aware of, I posted an incorrect answer on my Q&A. And it’s not that I didn’t know how to do the question. I did all the “hard” math correctly. But when it came time to add 1 + 5 + 10 + 10 + 5 + 1, I got 22 instead of 32. And I posted that. It was up for about 18 hours before I woke up today, half-dazed, and muttered wait…22 isn’t a power of 2! (The super-fast solution I hinted at in that post is that the number of subsets of a set with n elements is 2n.) I got out of bed, changed one digit in a post, and went back to bed.

So what’s the point? I’m good at math. I’m sure-footed, especially when it comes to SAT-style problems. I don’t second guess myself. The fact that you’re reading this means that I have a reputation for being an authority on the topic. And still, I managed to make a very silly mental math error, the kind that costs people dearly on tests. And I posted it without checking my work. It was the first time in nearly a year of running the Q&A, so it doesn’t happen often, but I made a silly mistake and didn’t catch it. Sometimes, everyone makes mistakes.

Maybe some readers saw that I did all the work right, and just assumed it was a typo. That’s generous, and I thank them. But you know who won’t be as generous? You know who doesn’t care whether you did all the work right? You guessed it: the SAT. So do as I say, not as I failed to do yesterday.

Check your work if you have time.

I’m compelled, as I was when I wrote a similar post about the math section, to begin by saying this: If you’re striving for an 800 as a means to an end (admission to the school of your choice, etc.) you should know that close is probably good enough. An 800 is unlikely to open any doors that a score in the high 700s would not. I can relate to anyone who wants to hit 800 just to say she did it—I was that kind of student in high school, too—but it would be irresponsible of me to begin this post with anything other than a disclaimer that if you’re doing this for anything other than the thrill of the chase, you might look back at this time and think that you could have been spending this time doing something that might have brought you more personal satisfaction.

Phew! Now that we’ve got that over with, are you ready for a list of bullet points?!

  • You need to know all the common rules like the back of your hand. This should go without saying, but you absolutely must be able to spot a dangling modifier, a run-on, or a comparison error in your sleep. In fact, you should know everything on this page, and all the pages it links to. Want it all broken down even finer? Get Erica’s book.
  • Learn from every mistake. Some questions are trickier than others, but if you’re shooting for perfection then there’s no such thing as a bogus question. Every mistake is an opportunity not to make a similar mistake. Don’t get mad, get even.
  • Remember that the SAT loves to introduce new problems in the answer choices. In the Sentence Improvement section, one of the easiest ways to miss a question is to pick a choice that fixes the original problem, but introduces a new one (often a run-on). Make sure you read the sentence again with your choice inserted before moving on.
  • Leave no blanks. I advocate guessing in most cases, but especially in this one. If you’re even thinking about 800, then you should be able to correctly eliminate AT LEAST one incorrect choice on even the hardest problems. What’s more, if you’ve got a realistic shot at 800, then you won’t be missing enough to cost yourself points. A blank, in that case, is just as bad as an incorrect guess—so at least give yourself the chance at getting the question right.
  • The essay is important. Look, I know as well as anyone that it’s no fun to write a practice essay. And I’ve worked with enough students to know that no matter how many times I tell them to do a WHOLE test before I see them again, I’ve got maybe a 50/50 chance of them writing an essay. Practicing the essay is no fun. But if you don’t do it, then you’re putting yourself in the unfortunate position of sitting in your exam room at 8 AM with sweaty palms and no idea what to write. Or hand cramps and not enough time/space to fit in everything you want to say. You need to practice writing concise, convincing arguments in 25 minutes. If you don’t, you won’t.
  • The essay is not that important. You can get a 9 on your essay and still hit 800 with a perfect performance on the multiple choice section. So don’t obsess over scoring a 12. I’ve read essays I thought were awful that got 12s, and I’ve read essays I thought were great that didn’t get 12s. You’re at the mercy of nameless, faceless, overworked graders. If you can consistently write essays that score 10 or better, focus your energies on grammar rules and try to ace the multiple choice.
  • Don’t neglect the paragraph improvement section. It’s only 6 questions per test, so it’s easy to brush off preparing for this section. If you’re shooting for 800, though, then you can’t afford to be caught flat-footed. Remember that “in context” means you’re looking for sentences that make sense in the paragraph, and that transition nicely from the sentence before them, and into the sentence after them.
  • Don’t sweat idioms. Seriously, there are an incredible number of idioms that the SAT could test, but unlike vocabulary words which appear over and over again, there’s not much of a pattern to the idioms that are tested. That’s the bad news. The good news is that idiom questions are rare (usually 1 to 3 per test) and that you’ll often be able to get them by ear. Don’t become obsessed with idioms, because you’ll drive yourself crazy and start thinking all kinds of perfectly constructed phrases “sound funny.” Even if you miss an idiom question or two, you can still get an 800; the writing section is forgiving like that. So try to relax about idioms. If you want to do something productive that might have the happy side effect of making you better at spotting idiom errors, read lots of sophisticated writing; you might be exposed to a few idioms you haven’t seen before. And hey, you might also pick up some good vocabulary along the way. Reading is a good thing.
…Am I missing anything?

I just listened to a Planet Money story that I wanted to share with you. It’s a 4:26 long discussion of risk aversion and how some experts see it distorting the American housing market. I’m not recommending it because I think you need to be thinking about the housing market, though. I’m posting this because the whole time I was listening, I was thinking about the psychology involved in guessing on the SAT. To paraphrase one expert in the story, people are afraid to guess because losing feels more intensely bad than winning feels good.

I actually think the SAT is a better application of the theory in question than the housing market, since home buyers and sellers generally don’t get to buy and sell often enough for the “if you flip the coin 1000 times” argument to really make sense.

On the SAT, you lose 1/4 of a point for an incorrect answer, and gain a whole point for a correct one. Since there are 5 choices per question, if you are deciding whether to guess or leave a question blank more than a few times per test, you’re in a position where, statistically, random guessing is a complete wash (thorough explanation here). From there, if you feel like your guess is even a little bit better than random, the “rational” move is to guess, since the scales tip slightly in you favor once you eliminate even one incorrect choice.

I’m not saying you need to guess, but listen to the story, and see if any of it resonates with you. It may or may not inform your future guessing strategy on the SAT.

animal-camouflage-08

Dangling modifier (artist’s rendition)
Source.

As I see it, SAT prep has two main objectives:

  1. Discover the most efficacious ways to solve common problem types.
  2. Become proficient at recognizing opportunities to use those techniques in the wild.

It’s important that you devote equal time and effort to both. In other words, if you only take practice tests repeatedly, or if you only study techniques without ever taking a practice test, you’re doing it wrong. That’s why all smart tutors and good prep courses make you take full length tests in addition to showing you the important techniques. Because it’s one thing to be able to get a bunch of dangling modifier questions right when you know they’re coming. It’s another thing to have a dangling modifier jump right off the page for you when you’re taking the actual SAT and you’ll only see about two in a section.

If you’re going it alone, you should consider following a similar recipe to the one tutors and course use. Here’s a bare-bones SAT prep plan to help you go through this process:

  1. Take a full length practice test. Ideally you’ve already taken a PSAT so you sorta know what’s up, but the real test is twice as long, and it’s best you know up front what it’s going to feel like to test for 3:40. There are 10 tests in the Blue Book, and you’re probably going to want to buy that, but you can also download one test for free from The College Board, which might be a nice way to get started. The goal here is to get a true baseline score for yourself, and to identify some obvious weak areas right away, so take it seriously: no long breaks, no cell phone, no Facebook.
  2. Review the test. A lot. This is the hardest part for most people, but it’s one of the most important parts of the process. One of the major advantages of having a tutor or taking a good course is that they’ll force you to do this. Your goals here are to really understand your mistakes. Remember that the SAT is not subjective—there’s one correct answer and four incorrect answers to every question. Review the test until you feel like you could teach every question you got wrong to someone else. Take careful note of what kinds of questions (if any) flummox you so completely that you have no idea what’s going on at all.
  3. Hit the techniques. The SAT has a whole plethora of different question types, and you’re going to need to be dangerous with the weapons that can dispatch all of them. This site, in general, is my attempt to spell out tips and techniques (math, writing, reading) that I think are best, but I know I’m not the only fish in the sea and I encourage you to do some research and take what you find useful from a bunch of different sources.
  4. Take another practice test. Now that you’re good at solving plug-in questions when you know you’re looking at a plug-in question, it’s time to see if you can recognize what is and what is not a plug-in question when you’re taking a timed test. Be prepared to feel a little weird using some techniques, and don’t be discouraged if your score drops a bit. It’s the first time you’re taking a test in a new way. It probably won’t be smooth. Think of it like hitting live pitching after you’ve just gotten really good at hitting off a tee. Resist the urge to fall back on old methods when new techniques feel laborious. If you keep taking the test the same old way, you’ll keep getting the same old scores.
  5. Review the test. Even more than last time. Now that the timer’s off, go back through the test and see whether any of your mistakes came from not recognizing opportunities, or from trying to apply techniques when it wasn’t possible to do so. Look at the questions you got right, too, if it felt like doing them took too long. Maybe there’s a faster way. Again, one of the great values of a tutor or course is that this is done for you with an expert eye. If you’re acting as your own tutor, this process will take a long time, but it’s also where all the big improvements happen. There will be times that you won’t want to review a test after you take it and score it (probably, you will feel that way every time) but if you want to improve, you have to do it.
  6. Revisit the techniques. You won’t need to look at everything again, just the stuff that you didn’t know as well as you think you did when you took the test. Did you flub a few function questions? Brush up. If you have questions you don’t think you can answer yourself, ask an expert.
  7. Repeat steps 4 through 7 until you’re happy with your scores. 

It might take a long time, and it will be incredibly hard work, but big improvements can happen. I see them every day.

Disclaimer: This post is intended as pragmatic advice, not rebuke. Please don’t misconstrue anything herein as nastiness. This blog is still a big love fest, and any appearance otherwise is simply a result of a temporary inarticulateness. Promise.

I don’t like to talk about it in real life because honestly nobody wants to hear about it, but obviously part of my credibility as an SAT expert comes from the fact that I can score a 2400 myself, so I have to mention it here once in a while. I sometimes bolster my bona fides further by telling students that I was the valedictorian at my high school. Awesome, right? I know.

The point of this post isn’t to preen, though. It’s to point out that that I graduated, ran a summer victory lap that went horribly awry, and then matriculated to Brown, where I had to adjust very quickly to a new peer group. At Brown, nobody cared that I was valedictorian back home. About half of my friends had been, too, and many more had acquitted themselves well at high schools whose rigorous curricula put my own’s to shame. I struggled more in that first semester than I ever had in an academic setting, and than I ever have since. It was a semester-long lesson in humility and the nature of truly hard work.

After you graduate, it matters very little how you compare to the small group of peers in your high school class. When you apply to a competitive school, you’re pitted against everyone else who applies. The more competitive the school, the more competitive the applicant pool will be. Admissions officers do their best to admit the best class possible, based on the incomplete set of data they have in the form of innumerable applications, and what unknowable directives they have from their bosses*. This should go without saying, but it won’t matter whether you view the process as “fair.”

If you’re a straight-A student, if you’re smarter than all the other kids in your Spanish class, then congratulations. You’re a big fish in your small pond, and that’s commendable. But if you rest on your laurels, you do so at your own peril. Because many of the other big fish in the other small ponds continue to work hard, and those will be your peers in due time. Like it or not, all those other big fish are going to take the SAT, same as you. And the aforementioned admissions officers, for better or for worse, are likely to take their SAT scores into consideration alongside yours when they make their decisions.

It’s within your power, to an extent, to control how you’ll size up when that time comes. You can choose whether to

  • prepare fiercely, go toe-to-toe and blow-for-blow with the test, and walk out of the test center afterwards satisfied that you gave it your best effort, or to
  • sit back, relax, and hope you do well.

If you choose the former, I welcome you to this site with open arms. Leave comments; ask questions; use me as a resource as you prepare. That’s what I’m here for.

If you choose the latter, I hope the test goes well for you. I really do. I hope you’re as big a fish as you think you are. But please know that if it doesn’t go well, your mediocre scores probably aren’t indicative of any systemic unfairness inherent to the test. They simply mean that, to be where you want to be in the giant pond that contains all high school students, you’re going to have to work a little harder than you do to be be acing APUSH. So…whatcha gonna do?

* For more on this process, read John Carpenter’s Going Geek.

If you’ve been wondering why things have been a bit quieter around here for the past few weeks, there are 3 reasons:

  1. I’ve been scrambling to finish this book so that I can ship it off to print.
  2. I’ve been trying to keep up with all the great questions I’ve been getting at qa.pwnthesat.com.
  3. I started grad school this month and I’ve been trying to adjust after close to 10 years away from academia.
The third reason is pertinent right now, because for a class on finance (which I think will be quite good) I was assigned some preparatory work over the summer, which included some online quizzes. I want to quote a question from one of them here, and then explain why it’s a bad question. And then hopefully parlay my personal anecdote into insightful test prep advice for you, using my extreme perspicacity. Wouldn’t that be splendid?

If you have a present value and an interest rate, you can calculate a future value.

True / False

I don’t expect y’all to be experts in finance (nor should you expect me to be until a few months from now) but the formula being referred to here is a simple one: FV = PV(1 + i)n, where FV = future value, PV = present value, i = interest rate, and n = number of periods the investment will earn interest.
So if you have PV and i, you should be able to calculate FV for any n. In other words, if you know the  present value of an investment is $1000, and you know the interest rate is 5%, you should be able to tell how much that investment will be worth in 1 year, 2 years, 10 years, 100 years, etc. You should be able to find “a future value.” I picked “True.”
The answer they were looking for is “False” because you can’t solve the equation without also knowing n.
So yeah, I got a question wrong. Alert the media. But also take note of the imprecision in the way the question was written. The question asks whether one could find “a future value” given a present value and an interest rate. I maintain that one can: the value 2 years out is a future value, as is the value 3 years out and the value 8 years out. I can find all of them. So I can find “a future value.” Many, in fact.
If the question writer really wanted an answer of “False,” she should have asked whether one could find “the future value.” You cannot find “the future value” without knowing how many periods into the future the interest will compound.
This drove me absolutely nuts for days, but the bottom line is that not everybody writes tests the same way, and I had to adjust to the way these dumb online tests are written just like you have to adjust to the way your US History or Physics teacher writes tests, and just like you must adjust to the way the SAT is written.
In each question, in all three subjects, every single word matters, both in the questions, and in the answer choices. Every single word has been wrangled over and vetted by multiple test writing professionals, and is in there for a reason. The wording of questions on the SAT is extremely deliberate and precise. You will never, never have to wonder whether a test writer wrote “a” when he meant to write “the.” The sentence means exactly what it means. I take comfort in that, and I wish every other test I’ll ever have to take would follow the same guidelines.
Just like that simple finance question drove me nuts, the absolute precision of the SAT might drive you nuts for a while. But if you want to get to a place where you can dominate this test, you’ll have to adjust. Each and every word matters.

I’ve covered this before at length, but it’s important to remember that, in general, you’ll increase your score more by making fewer silly mistakes than you will by getting more of the hardest questions right.  I’ve always left the actual calculations and decision making in your court, though.

Well, the decision making is still in your court, but I’ve made the calculations a little easier for you. I went ahead and aggregated the scoring tables of a bunch of old tests, averaged the scaled scores, rounded them down to the nearest 10, and made a nifty little spreadsheet that you might find useful:

Based on multiple scoring tables…your particular scoring table obviously might vary a bit.

The bold rows are the rows that represent skipping the same number of questions per section. (For example, for a score of about 690, you can skip 6 questions, or two per section. If you just want to break 600, you can skip FIVE QUESTIONS PER SECTION if you get all the rest of the questions right. Seriously.)

This is not about limiting your scores; it’s about maximizing them. Questions on the SAT are arranged in order of difficulty, so you can predict very easily where the toughest ones will be. Take your time on the simple ones, make sure you collect all the easy points, and only then worry about the tough ones. If you run out of time and have to leave a few blank at the end, don’t worry about it. If you’re perfect (or almost perfect) on the ones you answer, leaving a few blank won’t hurt you much.