Tag Archives: math

Your Performance on the SAT and GRE Depend on Your Attitude


Think you’re smart?  Then you’re also right.  At least that’s what’s indicated by the psychological research on a concept called stereotype threat .

The short version?  People tend to do worse on standardized tests when they’ve been primed to think they will do worse.  In one example, African American students at Stanford did worse on the GRE when subtly reminded of the stereotypical preconceptions about African Americans’ lower performance on such tests (see study).  In another study , when it was suggested to a group of golfers that golf was an intelligence game, white golfers’ performance increased and black golfers’ performance decreased.  When it was suggested that golf was a game of innate physical skill the results were reversed!  Similar studies have shown that stereotypes concerning women’s mathematical abilities affect their test performances on math-related tests.  Indeed, there are more than a hundred of these studies (see http://www.reducingstereotypethreat.org/ for more info).

This effect, however, is not limited to stereotyped groups.  Everyone is affected by this under some circumstances … especially on exams and standardized tests!  There is a simple method to counteract this effect, and to actually make it work FOR you. [hidepost]

Anyone can sink themselves by thinking negative thoughts and boost their performance by thinking more helpful thoughts.  This effect is well supported by research and practice (see cognitive behavioral therapy, and Learned Optimism , by Seligman, for examples.)  Obviously, it doesn’t matter how good your attitude is if you didn’t learn the material.  But, eliminating unhelpful thinking can allow you to maximize your possible performance.

So what to do?  How do I convince my brain that I’m actually brilliant?  Here’s an easy technique that I teach my students.  Take a minute to think of someone that really makes you feel good about your ability to perform … could be a coach, a parent, a significant other … whoever.  Now imagine that person coming with you to the test.  Before each test section or whenever you feel anxious, imagine that person giving you a pep talk to encourage you; “Don’t worry.  You can do this!  You spent all that time preparing.  Knock ’em dead!”  Try to imagine them as clearly as possible.  Let yourself feel better.  Give it a try!  It absolutely works.[/hidepost]

Math for Neanderthals


“Locksmith?  Please come as soon as you can!  It’s about to rain and I’ve locked my keys in my convertible with the top down!”  Ouch.  Most of us have done things just as painfully stupid … or, is it just me.  What’s going on?  How is it that we can sometimes behave like total neanderthals?  (I apologize if you, your relatives, or your significant other is a neanderthal.)*

The screw-up comes because we’ve bypassed our brains [hidepost]in favor of a standard response to the problem in front of us.  We are so focused on the way we usually do it–in this case, unlocking the car door with a key–that we overlook the obvious and simple solution.

Enter the GRE and SAT quantitative sections.  The “right way” to do any given math problem was drilled into our heads in junior high and high school math classes.  We did that particular problem type over and over again.  We showed our work.  We lost points if we didn’t follow the method step-by-mind-numbing-step.  Now, whenever we see a familiar problem on the SAT or GRE, we start following the steps, showing our work as we go.

News flash: the testmakers left the top down on the convertible!  If you are looking for the key you learned in high school, you are wasting time.  Since the GRE and SAT are timed tests, you are not expected to do much in the way of long calculations.  If you find yourself doing a ton of calculating, you missed a short cut somewhere.

Example:  Which quantity is greater?    1/16 + 1/4 + 1/7    OR    1/6 + 1/16 + 1/4

If you started looking for a common denominator, tell the locksmith, “nevermind,” and put away your phone.  Just eliminate the fractions both have in common; 1/4 and 1/16 are common to both sequences, so eliminate them.  You’re really just comparing 1/6 to 1/7.  1/6 is the larger fraction, so that’s your answer; no math necessary.

As you work practice problems in preparation for the test, STOP … DROP … and ROLL (hmmm … seems like I’ve heard that somewhere before).  StopDrop your pencil.  And … errr … Roll your eyes over the problem looking for that shortcut.  You KNOW it’s gotta be there. when you find yourself starting on a long series of calculations.

WARNING: this takes practice.  So break out those practice problems and begin searching for shortcuts.

*No neanderthals were harmed in the writing of this post.[/hidepost]

Calculators are way too slow


[hidepost]Awright SAT and GRE preppers; dust off those old synapses.  Do you know your multiplication tables as well as you should?  “As well as you should,” means instantly!  You shouldn’t have to stop and think about the product of 7×9 or 8×6; it should just pop into your head.  Being able to do that will really speed you up on the test!  Here’s a great site to help you get up to speed.  Five minutes of practice a day for a couple of weeks could mean big gains on your test scores![/hidepost]