That math thing

So, unless you are taking the LSAT, you need to know some math.  Perhaps you are taking the LSAT because you want to get an advanced degree but don’t want to know some math, in which case, that is a crappy reason to go to law school.  Maybe you should read this post too.

A lot of people think they don’t like math or that they can’t do math.  Others don’t mind it, but have forgotten everything they used to know and don’t use the skill currently.  For those of you who fit into either of these descriptions, this post is for you.  While the GMAT, GRE, and SAT don’t actually try to test your math skills comprehensively, you do have to be really comfortable with some math.  And for the tiny slice of the discipline that you have to understand, you have to understand it really really well.

But that is okay!  It will serve you really well to learn this stuff!  Particularly if it currently gives you nightmares.  It just sucks to go through life as a professional, competent adult who is scared of math.

The stuff you need to know

The most important three skills for all the math-y tests are estimation, number sense, and basic function manipulation skills.  Estimation is an important TestSmashing skill — it isn’t particularly tested directly.  By number sense, I mean, do you understand zero?   fractions?  negative numbers?  what operations start to behave crazily in which bits of the number line?  Also, what are the differences between even and odd numbers?  Can you factor numbers into their prime factors quickly?  Cope with exponents? That kind of thing.  Unless you like to think about numbers, and be curious about them, this stuff is actually kind of hard to learn — it isn’t really a part of the math curriculum.  You just sort of have to notice it as you go along.  Basic function manipulation — the mechanics of algebra — are also super important.  Can you solve for x?  And not just, do you know how to if you sit down and think about it, but do you automatically start rearranging equations in your head — accurately — every time you see an x?

It also doesn’t hurt to know a few things about triangles.  And the GMAT has a pretty substantial emphasis on combinatorics and probability in the hard questions.  But if math makes you queasy, don’t sweat this stuff.  Focus on estimation, number sense, and function manipulation.  Once you’ve mastered them, then you can start to pick up the less central stuff.

The stuff you don’t need to know

Notation and jargon.  Avoid explanations or manuals that use a lot of either.  It is cognitively taxing and pays no benefits whatsoever on the tests.  (And very little in life, though it can be fun to throw a string of jargon into someone’s face if they aren’t taking you seriously enough.)

How to learn it

The very best self-study guide for learning and cementing the skills you need is Forgotten Algebra by Barbara Lee Bleau.  Units 1-15 are pure gold and on target.  Polynomials are almost never on the tests, so Units 16-22 are not so useful, but Units 23, 25-28, 31 will also help.  The book is great because it breaks everything down into micro-steps, gives lots of examples, has clear explanations and plenty of practice problems.  It is also great in its focus on number sense.  If you do one unit a day, you will be good to go in 2-3 weeks.

If you have found another book that you like, please let me know in the comments section!

How to love it

If you are mathphobic, the problem isn’t so much that you are incapable of learning the mechanical steps in Forgotten Algebra.  It’s that you have blocked your ability through boredom or trauma.  This is common and tragic, and there are books out there that could inspire you past the block.  The very first thing I would do is go read A Mathematician’s Lament.  It won’t take long.  It might make you angry, but the second half of the book, in particular, will pique your brain in a way it may not have been since you were a toddler learning to stand.   Hold on to this sense of joy, excitement.  This is the key to TestSmashing.

I’ll also re-iterate my recommendation of The Myth of Ability: Nurturing Mathematical Talent in Every Child.  It implements Paul Lockhart’s vision, and re-iterates through counter-example how very badly we teach math.  Some of the specific teaching tools he describes are also useful to get you to think about numbers differently, and in a way that will be rewarded by your test.

I know this is a lot of reading, but I think that this is actually time better spent that cranking through GMAT questions if you are mathphobic.  Once you have found the joy, the cranking through GMAT questions will actually be fun and even exciting.

Advertisements

Don’t just take my word for it

I wrote a while ago about how intelligence is not really the issue when taking these tests.  Guess what?  I was right!  The entire concept of intelligence as this immutable, etched-in-stone thing is totally, completely bullshit.  It turns out that studying for the LSAT makes you smarter.  You, dear test smasher, have within your power the option to exercise your brain more, and literally change its structure.  Woohoo!

My favorite quote from the article:

“A lot of people still believe that you are either smart or you are not, and sure, you can practice for a test, but you are not fundamentally changing your brain,” said senior author Silvia Bunge, associate professor in the UC Berkeley Department of Psychology and the Helen Wills Neuroscience Institute. “Our research provides a more positive message. How you perform on one of these tests is not necessarily predictive of your future success, it merely reflects your prior history of cognitive engagement, and potentially how prepared you are at this time to enter a graduate program or a law school, as opposed to how prepared you could ever be.

(My bolding.)  This is really great news for you.  This means that the test you are taking is not a measurement of your sum as a human being for ever and for all.  Instead, it is merely a snapshot of where you are on a particular set of skills at the moment.  This is really great news.

Except.  Now you have to act on it.  If you are performing poorly on your favorite test — or just performing more poorly than you like — you can’t just shake your fist at the sky and go about your life like you always have.  Instead, you have a choice.  You can change how you spend your time, and how you approach problems, and then see your score go up and your view of the world change.  Or, you can stay the same.  Your choice.  Change is really hard, and there is no harm, no foul, if you choose to not change. Life can be rich, wild, and wonderful for people with all levels of cognitive engagement.

But you gotta change your approach if you want to change your score.

I’m a low scorer. Can I TestSmash too?

Absolutely.

Indeed, you are going to have to do some TestSmashing.  If you are already in the upper percentiles of whichever test, TestSmashing is just a little nudge, activating a perspective on the tests you are probably halfway to figuring out yourself already.  If you are a low scorer, TestSmashing is going to be hard.  Really, really hard, but not in the way you might expect.  Instead, it’s hard because you have to change how you think about yourself, the test, and how to solve problems.

I’m starting to develop a program for low scorers to turn themselves around and dramatically improve their scores.  If anyone wants to be a beta tester for this program, contact me and I will give you a pretty steep discount for a 4-session package to lay the foundation for a more successful experience with the test that is between you and your dreams.  This isn’t test prep, its prep-for-test-prep stuff that will, I think, save you tons of time, money and agony in the long run if you take some risks and about three weeks up front.

In the meantime, some rules of the road for a low scorer:

  1. Be realistic and set your goals carefully.  Dramatically increasing your score (say by at least 150 or 15 points, depending on the test, particularly if you are starting below the 50th percentile) is going to take time.  It isn’t going to happen in a few weeks.  If you’ve already signed up to take the test in less than 2 months, I would cancel.  Even if it means delaying your applications by a year.  Painful, I know, but you need to
  2. …be patient.  This kind of change won’t happen overnight.
  3. You MUST find a way to transition from the self-concept “I am bad at tests” or, god forbid, “I am not smart enough to do well” to “I happen to have performed badly on some tests in the past, but I am working hard and will master the mistakes I used to make.”
  4. You MUST be prepared to acknowledge that you don’t know what you are doing, and that the approach you have taken so far isn’t working.
  5. Find a way to protect your ego through this process.  Do something joyful, creative and fun on a regular basis during this Test Smashing period of your life.
  6. Be sure this is what you want.  If it isn’t, it is an awfully time-intensive, ego-bruising activity to embark on if you don’t actually want to go to graduate school (or college).

Managing your study time

Time management is another hurdle that can trip up the aspiring test smasher.  It’s also a life skill that is well worth attaining.  Fortunately, I can outsource a lot of my recommendations for how to manage your study time to the Pomodoro Technique, which has a great, free .pdf version of the book on the website.  There are also free apps for those of you who want to manage your studying on your phone or tablet.

The essence of the pomodoro technique is working in disciplined, timed chunks.  I use it in the rest of my life to do my academic writing, and it has transformed my productivity.  The basic time unit, a “pomodoro,” is 25 minutes, but if you are going to use this for test preparation, you need to make one modification to the technique: your time unit while studying will be the length of the section on your test. This way, you will get used to the pace of your test — a section unit of time will be a very known quantity, you’ll learn an accurate sense of where you are in the unit, and you will know exactly where in the block of time your attention flags, etc.

For GMAT takers, use a 35 minute pomodoro.  Your GMAT sections will be 2 pomodori: 70 minutes of intense focus, plus 5 minutes of mental rest/slippage.  For GRE takers, the sections are annoyingly of different length.  You should pick the length of the type of section that gives you the most trouble, so your pomodoro will be 35 minutes if you are weakest on the verbal sections, and 40 minutes if your real difficulty is math.  SAT takers should use 25 minute pomodori, and LSAT takers 35 minutes.

Another great aspect of the Pomodoro Technique is that it helps you make great use of relatively short periods of time.  You can always find a way to squeeze a 25-35 minute block out of your day, right?  If nothing else, setting your alarm that much earlier is not an outrageous idea.  Which leads to the next point:

Study every day and never more than 4 pomodori (unless you are taking a practice test). 

Really.  You can’t learn the kinds of practices you need to absorb into your bones without frequent repetition, and your brain can’t take a huge amount of the intense focus you will be applying during your study periods.  So six hours on the weekend isn’t going to cut it.  It is a waste of your time!  Both too much time at once, and not enough time over the week.  Now, I also don’t really recommend you study for all four pomodori every day of the week, unless you are trying to do this all in 2-3 weeks (not recommended).

Instead, I would take your first pomodoro of the week and spend that time looking at your calendar for the week.  What do you need to accomplish this week?  Let’s say it is mastering Reading Comprehension, and you are studying for the LSAT.  Then plan your week:

Sunday: 1 planning pomodoro for the week.  1 RC diagnostic pomodoro, where you take an entire RC section in the time it would take on the test just to see where you are.  1 pomodoro going through your answers, and annotating the questions you got wrong and the questions you got lucky on.  Also figure out if you need to speed up to answer all the questions or if you can afford to slow down.  1 pomodoro reviewing my recommendations on RC and slowly working through a maximum of one passage’s questions, taking as long as it takes to prove which answer is the correct one.  Check your answers, diagnose the nature of your mistakes.

Monday: Set the alarm earlier than normal and do 2 pomodori before your day starts.  Spend both doing the slow, agonizing practice of proper RC, always proving your answer is correct and closely analyzing and recording the nature of any mistakes you make.

Tuesday: You have time in the morning for one pomodoro, and another in the evening after dinner.  For the morning, spend the pomodoro doing a practice game and a handful of arguments, just to remind yourself of what those questions are like.  As you work, consider whether the RC practice is helping you with the other question types.  Check your answers and note why you made any mistakes you made.  In the evening, spend your pomodoro reviewing the notes you have taken so far this week.  Are there common themes among the questions you get wrong?  Are you trying to fight a battle with ETS over whether unacceptably clunky answer choices could possibly be correct?  Are you giving in to temptation to read the entire passage?  Whatever the result of this reflection, you must prioritize changing your approach for your next practice session.  After this evening pomodoro, go take a walk, even if it is just around the block.  Smell the air, stretch you limbs, enjoy life, think about how you are excited to change your methods.

Wednesday:  You have time for four pomodoros in the middle of the day today, so start out with another diagnostic pom where you do an entire section in the right time length (try to stay focused on the changes you need to make in your approach).  Then spend a pomodoro checking your answers, and journaling about where you are still getting answers incorrect and about how you are managing your time.  If you are starting to see big changes in your accuracy rate, do one pomodoro of RC practice, maybe trying to see how little of the passage you can get away with reading, then one pomodoro of the other question types.  If you are not seeing big changes yet, you need to slow way down and spend a pomodoro where you write down every thought you have about each answer choice and what disqualifies the four wrong answers.  Do this for as many questions as you can in a pomodoro, but don’t be upset if it is just one or two.  Then do it again for the last pomodoro of the day.

Thursday: Today is a busy day, so you can’t spend much time studying.  All you do is set your alarm early, and do one pomodoro of RC questions the very first thing of the day (a fantastic time for learning).  Be sure to leave 5-10 minutes at the end of the pom to review your answers carefully and take notes on your mistakes.

Friday: Another busy day, so you do a diagnostic pomodoro first thing, and nothing else.  You don’t even check your answers, but you are getting to the point where you know you are getting almost every question correct, and are pretty sure which answers are the most likely to be wrong, if any.

Saturday: You’ll do 4 pomodori today, but in two groups.  In the morning, the first pom you use to check your answers from yesterday — are there any surprises?  Also review your notebook from the week.  How many bad habits have you smashed?  Are you still struggling with accuracy or is all there is left to do is learn to increase the pace?  Can you move on to another question type?  Spend the second morning pomodoro doing a focused practice on the issues you are struggling with.  For example, maybe you can find a way to shave a couple of seconds off of each question by having a clearer process that you always follow?  Are you really only reading what you need to read?  Once you have proven a correct answer, have you moved on or do you waste precious seconds in self-doubt or unnecessary double-checking?  Go about your afternoon activities, then when you come back to your last two pomodori of the day, spend the first on another full section and the second checking your answers and planning what more needs to be done on RC to have it smashed.  You should always plan on maintenance, but maybe you still have a lot of bad habits to get past….

Throughout the week, you should be exercising, enjoying friends, limiting alcohol and sleeping lots.  These will all help you keep your ego healthy, your mind sharp, and you ability to self-reflect wide open.

Also, note how much time is spent assessing and planning.  Mindless imprecise practice is only going to waste precious practice questions and your time.  If you are very focused and very reflective, you won’t need a whole lot of questions to make dramatic strides in smashing the test.

RC: Working an example II

The previous example covers your most typical question types.  But one question per passage usually looks at the passage as a whole.  I’ll show you how I handle those kinds of questions using the same passage as in the last post.  The question is framed here as “Which one of the following most accurately states the main idea of the passage?”

For this question, I start out by reading (some of) the first sentences of each paragraph.  I don’t need to read the whole sentence, necessarily, just enough to get the structure of the passage.  There are four paragraphs:

  1. “Intellectual authority is defined as the authority of arguments….”
  2. “In contrast, some critics maintain that whatever authority judicial pronouncements have is exclusively institutional.”
  3. “But, the critics might respond, intellectual authority is only recognized as such because of institutional consensus.”
  4. “The analogous legal concept is the doctrine of precedent, i.e., a judge’s merely deciding a case a certain way becoming a basis for deciding later cases the same way — a pure example of institutional authority.”

This passage is interesting because we get a lot of what the critics say, and not so much what the main argument is (though we can infer it is a pro-intellectual authority argument).

When I go to the answer choices, I notice something interesting: they all start out one of two ways

Although some argue that the authority of the legal system is purely intellectual/institutional….

While it is clear that either one is literally true, since there is disagreement over a dichotomy, we have to consider the point of view of the author.  Which side is the “some argue” on?  Well, it is the critics, of course!  And they are big believers in institutional authority.  See that?  Once we decide that, we can eliminate A/C/E without further consideration.

Then we have to pick between the final two choices, and here, because we got so much of the critics view to begin with, it is helpful to read the very last sentence:

The conflict between intellectual and institutional authority in legal systems is thus played out in the reconsideration of decisions, leading one to draw the conclusion that legal systems contain a significant degree of intellectual authority even if the thrust of their power is predominantly institutional.

Adding that sentence to our arsenal makes the choice between the last two answers clear:

Although some argue that the authority of the legal system is purely institutional, these systems possess a degree of intellectual authority due to their ability to reconsider badly reasoned or socially inappropriate judicial decisions.

It’s all about the “reconsideration of decisions,” baby!

RC: Working an example I

To give you an example of how to work a smashed reading comprehension question, I’m going to show you how to prove your answer is correct using question 13 from section 3 of the LSAT PrepTest 38 (2002).

  1. I do not read the passage.  I do allow my eye to stray over the first few words of the passage “Intellectual authority is defined…” and am very very glad I do not have to read or comprehend the passage.
  2. I read the question stem carefully.  “The author discusses the example from musicology primarily in order to.”  Okay, it is pretty clear that I’m going to skim for the word “musicology.”
  3. A quick roll of the eyes over the passage makes it clear that the word “musicologist” shows up in the third paragraph and only once.
  4. The sentence that contains the word: “For example, if a musicologist were to claim that an alleged musical genius who, after several decades, had not gained respect and recognition for his or her compositions is probably not a genius…” Okay, running out of steam here!  I don’t want to waste a ton of time on the verbiage.  Let me focus on the question stem again: what am I being asked?  The key is “discusses the example primarily to.”  Where does the sign post in the passage to the right answer point?  “For example,…” points to the sentence before!  That sentence reads “But, the critics might respond, intellectual authority is only recognized as such because of institutional consensus.”  This is the important bit: my answer choice must match this sentence.
  5. The correct answer choice reads: “illustrate the claim that assessing intellectual authority requires an appeal to institutional authority.”
  • illustrate: well, that is what examples do.
  • the claim: “critics might respond” with a claim
  • assessing intellectual authority requires an appeal to institutional authority: intellectual authority is only recognized as such because of institutional consensus: yup, both indicate intellectual authority being fundamentally derived from institutions.
  • QED

This one wasn’t even that infelicitous.

I must confess, though, there was an answer choice that called out to me!  It was “distinguish the notion of institutional authority from that of intellectual authority.”  The reason it called to me was that, in all honesty, I read the entire sentence that contained the “musicologist.”  The end of that sentence reads “the critics might say that basing a judgment on a unit of time…is an institutional rather than an intellectual construct.”  That sounds a whole lot like the answer choice, right?  The “For example” sign post, however, says that you need to base your answer to the question “discusses…primarily to” on what the “for example” is referencing.  Also, is it really distinguishing the notion or just an instance?

So, to recap:

  1. I followed directions by answering the question asked.  This helped me zero in on the “for example” cue.
  2. I paid attention to detail by proving my answer choice word-for-word and by noticing the sketchy “the notion” in the answer choice that called to me.
  3. I organized the information given to me carefully, by focusing on only the part of the passage that could contain my answer.  I then carefully matched that information with the information in the answer choices.

Barriers to Smashing this question type:

  1. It is hard to trust not reading the passage.
  2. It is going to take a lot of practice.
  3. You might see a dip in your accuracy rate.

Methods to overcome:

  1. Trust it anyway
  2. Practice, practice, practice.  Hundreds of passages.  Until you are getting them 100% correct.
  3. You will develop a sense for the tricks and traps they place for you if you practice enough, now that your attention isn’t cluttered with passages.

Reading Comprehension

‘Nough with the throat clearing.  Let’s talk question types.

I’m going to start with Reading Comprehension.  It tends to get short shrift in people’s study time, since they think “I know how to read!” but it is the one question type that is universal to all of the major tests.  It also isn’t measuring your ability to read.  Or comprehend.  And it is completely breakable.

There are two ways the test writers like to trip you up.  First, they want you to get the wrong answer.  Second, if you are going to get the question right, they’d like it to take a long time.  Don’t feed the test writers!  Refuse to follow their lures.

The cardinal rules of Reading Comprehension:

  1. Do NOT, under any circumstance, read the fucking passage.  It is a time sink put there to bore you to death and a low score.
  2. Read the question stem carefully instead.  Figure out what words or phrases you are going to skim for.
  3. Skim for said word/phrase.
  4. Read just the section that contains the word/phrase.
  5. Now consider your answer choices: you must prove your answer choice.  Every fucking word in the answer choice MUST be in the passage.  You must point it out to yourself.
  6. The correct answer is usually infelicitous.  It will usually be phrased in a way that you would never consider phrasing the answer.  It might even be written in a way that you have a hard time understanding.  But every fucking word will match what is in the text.
  7. There will be a wrong answer, which is clearly written, that almost matches the text.  There will be some slight deviation, though.  IT IS THE WRONG ANSWER.  Do NOT choose it.  It will sing to you, call you out.  Plug your ears and pick the ugly answer.

Once you learn to do that EVERY TIME, you will have smashed RC to smithereens.  No more wrong answers.  Yay!

What do you do when it is a question along the lines of “The primary purpose of this passage is to:”?  If it is an overview question, read the first sentence of each paragraph, and, possibly, the last sentence of the entire passage.  Each paragraph must be addressed in the correct answer.  There will be a wrong answer that beautifully describes the most important/interesting paragraph in the passage.  Don’t choose it.  It is the wrong answer.

Lots of students hate not reading the passage.  It makes them really nervous.  They might miss something.  They are right: they are going to miss most of the traps the test writers have carefully placed for them!  They are going to miss the lost time that reading the passage extracts from their lives!  Do.  Not.  Read.  The.  Passage.

My recommendation will be hard at first.  I don’t care.  Get over it.  Keep following the rules, and you will smash this question type.  You may already be scoring pretty well on RC, relative to some of the other question types, so it might be tempting to just keep up with your current practice.  DON’T!  Unless you are getting them 100% correct all the time and creating time to spend on the harder question types, you need to keep practicing reading comprehension.  This is one of the easiest question types to smash, so get out your hammer and free yourself once and for all from boring passages!