Category Archives: Math stuff

Think like a test writer II

It is a bit harder to write your own good quantitative question stems (trust me, I once wrote a big chunk of a test bank for my old university’s quantitative methods subject — it took forever!) but there is still some useful thinking like a test writer to do for your normal multiple-choice problem solving questions on the GMAT, GRE or SAT.  In particular, if you are a test writer, you want various percentages of people to pick the wrong answer over the right answer.  So how do you get them to do that?

Well, harder problems are harder (generally) because they require more steps.  Many non-TestSmashing test takers will forget where they are heading on a question and just kind of stop when they feel they have taken enough steps — or stop when they have a number that matches an answer choice.  So how do you gull these poor souls into choosing a wrong answer?  Make sure that each step’s answer appears in the answer choices!  You, of course, are going to remember what the test really tests, and make sure you actually answer the question being asked, right?

And, while it breaks my heart to say it, waaaay too many people who feel helpless on a question will just randomly combine the numbers in a question.  (Are you one of those people?  For the love of God and all that is good, resolve to STOP TODAY and never, ever do that again!)  Fill in the remaining wrong answer slots with such random combinations.

If you want active practice thinking like a test writer for problem solving questions, pick up an algebra text book (or search the internet) and find some open-ended word problems.  Solve them, and note along the way the intermediate steps.  Come up with 5 answer choices.  Post in comments if you want!

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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.