I have spent hundreds of hours working with dozens of students in preparation for standardized exams. One of the most interesting phenomena I have observed is that a student can plateau – and sometimes even reduce – his or her score on a standardized test, even though he or she has spent dozens of hours practicing and gaining more knowledge. This seems counterintuitive, but thanks to the experience of working with many students, I have identified a common fallacy in this method of preparing for standardized tests.
I am going to focus on the Math section specifically to explain the pattern, although this is applicable to all sections. The problem is as follows: Let’s take a student named Jeff, for example. Jeff began with a Math score of 23 on his diagnostic examination [the ACT is scored out of 36 even though the math section has 60 questions]. The Math section gets tougher with increasing question numbers (i.e. question 40 is usually tougher than question 20). He answered approximately 48 questions and guessed on about 12. He was not convinced he could answer many of the last 15 questions. Fast forward to today and Jeff has worked with a test-prep instructor. He now has the self-confidence to tackle some of the tougher questions in the last quarter of the test. However, he now begins to rush through the first 30 questions, making small mistakes because he is not fully focused. He is already thinking about the last 15 questions, which he never worried about before because he didn't believe he could answer any of them correctly.
This is what I call “learned panic.” Jeff now answers three difficult questions correctly that he was unable to answer correctly before, which is great. However, his overall math score has dropped by one mark. Remember, college applications simply contain the final scores (e.g. 31 Composite, 29 Math) and all questions possess the same amount of marks. Your university does not know which of the questions were easy or tough, nor do they care. What good has all this effort (both time-wise and fiscal) been if Jeff is actually now in a worse position overall with his math score? The proposed solution -- one I have found works well with my students -- begins by writing what I call a “summary sheet.” The steps are simple to follow and easy to implement. After you complete a practice test, section, or other means of practicing, mark it. Go through the incorrect answers. Record a bullet point of the question and ascertain how you got it wrong. This usually falls into one of the following brackets:
You need to focus on points 1 and 2 by yourself and 3 and 4 with a mentor/textbook. The more summary sheets you have, the more data points you have collected and you (or you and your mentor) can identify the errors that you usually make. More importantly, you can implement safety mechanisms to protect yourself from your own mistakes. A good mathematical example of this involves inequalities. I have worked with many students who have made the incorrect logical follow-through when facing a negative sign in an inequality. They go from -x < -3 to x < 3, which is incorrect. You should flip the inequality when dividing by a negative to correctly get x > 3.
When I identify this with a student, he or she explains to me that “Ahhh, this is a silly mistake, Niall. This won’t happen again.” This is exactly where most people are wrong. Students often do not make the appropriate connection that there may be a trend in their mistakes because their egos get in the way of them taking this point seriously. What then happens? In a different test, they make the same mistake. They have forgotten the previous situation and explain to me again that “Ahhh, I can’t believe I made that mistake...”, and the cycle continues. Data recording is imperative.
The question you miss is a mark that you should never have lost. What is the point of putting in all this hard work to answer question 57 correct if you answer question 5 wrong? The way to overcome this is to record the point on your summary sheet as point 1 or 2. Then, once you have a bank of summary sheets (a minimum of 5 is my recommendation), you can easily identify trends. The next step is important. Create a personalized “cheat sheet” (not literally for cheating) of your common errors and write down your safety mechanism when that type of question comes up. You will then know what questions lend themselves to these kinds of mistakes, and you’ll know how to handle them next time.
Let’s take the inequality problem we discussed earlier. I would urge my students to simply write “FLIP” every single time they see an inequality sign. This is the best two-second investment you can make in your examination, as not only will it remind you how to solve the question correctly, but it will put you on alert to pay better attention to this specific question and not fall prey to any common pitfalls. It provides peace of mind, as you do not have to look at the inequality question and think, “I always get this wrong.” Instead, you can look at it and say, “I am prepared for this and have the appropriate systems in place to tackle this. Let's do this.” Standardized tests are about compounding mini wins, and having these systems in place affords you the mental bandwidth to focus on the tougher questions rather than wasting energy worrying about making mistakes on simple questions.
I am convinced that reducing the questions you make silly mistakes on is more important than answering those tougher questions correctly. This ties into another part of standardized testing: solving a question versus answering a question correctly. We will discuss that in a later blog post. The questions you do not understand are the questions you need to research yourself, discuss with friends, consult in a textbook, or go over with your academic mentor to ascertain the required knowledge. This will make your time spent practicing more productive and enjoyable for both you and your mentor, as you do not have to be ineffective with your use of time during a lesson by going over silly mistakes. Rather, you and your mentor can focus on the tougher questions. Parents, I would ask your student's instructor to follow this method if he or she does not do so already, as you will get a better return on your investment. Fortunately, my students usually do well, but this is something I wish I knew at the beginning of my career in test prep. Students, this is not a guaranteed fix without the time and due diligence required on your part. But it will help you be in the best possible mindset come standardized examination time, and it will help you smash through those plateaus. I wish you the best of luck.
