I received an email recently about my advice in the column "Marshmallows, Delayed Gratification, and Test Prep."  In it, the writer asked a very important question:  "How does one truly study one's wrong answers?" He elaborates:

My problem is that I choose a wrong answer and then I look at an explanation and I don't really take much away from it…. I am having trouble taking the next step and making progress to improve from the point where I am. I read the explanation and it makes sense for that question but don't know where to go from there and apply it to the rest of the questions.

This question strikes at the heart of standardized test prep everywhere, and is actually a great way of describing a distinction I made in another column I wrote, "The Fiction that the SAT Isn't Coachable."

In that column, I made an attempt to distinguish good test preparation from bad test preparation.  To rephrase what I said in that article, bad test prep is bad because it makes you think you're learning how to take the test, but in reality you're just learning a bunch of things about the test.  Another fundamental way that bad test prep is bad is that there is no framework, or there is only a faulty framework, behind the different explanations.

Take for example the LSAT SuperPrep book, which contains three practice LSAT's "with explanations."  The Official GMAT Study Guide works the same way.  These two prep books provide an abundance of explanations, but like the letter above clearly articulated, there's no real takeaway from one question to the next.  In the LSAT book, there is no advice given besides general information on study skills and setting up a practice regimen.  In the GMAT book, there is a review of general math principles, but little that explains how to solve hard GMAT questions besides one-off explanations.

To truly learn from your own mistakes is actually much more straightforward than it seems.  To learn from your mistakes, you need to build a framework around them.  Since that answer begs the question, "how do I build a framework?" I would respond in a sort of semi-humorous way: "patiently."  In all seriousness, building a framework for your wrong answers requires peace of mind.  If you're worrying about your score and your grad school acceptance while you're trying to study for the test, you might as well stop right there for the day because you're not going to make any progress.

First, you need to look at your mistakes dispassionately.  Don't see them as errors; see them as opportunities to learn.  I know that sounds unbelievably corny and silly, but that doesn't make it less true.  You have to appreciate the logical process of figuring out the answer just as much as you value a high score.

Second, you need to find the common elements among your mistakes.  Do they all deal with a certain topic?  A certain way of thinking?  I know, for example, that I am weakest on the formal logic questions in the LSAT, and that I impatiently try to diagram them too quickly and often make my diagrams too complex.  More to the point, I also know that I am really good at the non-formal questions, and so I spend too much time and energy trying to solve formal questions non-formally.  What categories do your mistakes fit into?  Most importantly, if your mistakes don't fit into some abstract category that some test prep company has created, make your own category system.  That step takes time and more patience, but it's the best way to learn.

Third, you need to experiment in grouping your errors.  For the LSAT, does classifying them as formal or informal help?  (I am classifying my mistakes as dealing with formal logic for the time being; I actually have some reservations about that classification system.)  What about by topic?  For example, do you have some latent dislike of some topic where you always think the argument is more complicated than it is?  What about by position in the exam?  For example, do you always seem to make a bunch of mistakes between questions 17 and 21 on the arguments section?  Do you fail in the games when they reach a certain level of complexity?  If so, start trying to understand that complexity.  Answers to individual questions are less important at this point than understanding the complexity of the thought process required to find the answer.  That's what you're after, and that's the purpose of this exercise.

Finally, once you have come up with some sort of grouping for your mistakes, you need to take the most important step:  explain them to yourself.  Again, that might sound silly, but the biggest problem that students have is that they go into the test prep process thinking as passive students, not active learners.  They think that as long as they memorize whatever message the test prep company gives them, they can depend on getting a better score.  With each answer, pretend it's your responsibility to explain them to someone with no knowledge of the test.  Find a friend who's studying for the test and practice explaining questions to him/her.  The point is not to know the answer, but to verbalize the answer.  Taking that step forces your brain to organize your thoughts much more logically, and makes a framework easier to discover.

I often tell my students, "I can show you all the methods of problem solving in the world, but this process doesn't work unless the ultimate responsibility of solving the problem falls on you."  In other words, it's my responsibility to explain a problem, but it's a student's responsibility to challenge him/herself to apply that explanation to a similar scenario.  I try to do this by explaining a framework where there are connections between each and every problem.  However, if the student doesn't take the step of actively trying to absorb that framework, and to transfer that framework into new situations, then he or she will never "learn" anything.  Once students train themselves to ignore the scattered shortcuts and focus on building a sustainable, integrated problem solving framework, the test is nowhere near as scary as it once may have seemed.

For the past eight years, Charles Williamson hasn't met a standardized test he didn't like, helping hundreds of students in everything from the SAT and ACT to the SSAT to the GMAT to AP Calculus. A longtime student of the thought process that defines performance on standardized tests, Charles got off to a good start, receiving a perfect score on his SATs in high school. He then graduated from Brown University, earning bachelor's degrees in computer science and history.  He has long been fascinated by the intersection of education and technology, and when not writing about standardized tests and educational policy, he will be happy to speculate rampantly about how the Internet will affect the ways that we learn.  Charles blogs for the Ivey Files about test preparation.