Standardized Test Prep
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The Scarsdale Principle.
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Keith Berman, INCREASE Admissions Guru, on the Scarsdale Principle.
One year we were lucky enough to have the valedictorian of Scarsdale High School as one of our students. And to talk to this kid, this young lady, was quite marvelous. She would talk about advents in biomedical engineering, she had a balanced geopolitical perspective, she read Harold Bloom for fun as a companion to her Shakespeare anthology -- which was not assigned by school -- and for all intents and purposes it was like talking to an award-winning Ph.D. student who was amid their dissertation.
And then she had to take the ACT.
And, considering she had A-pluses at arguably the world’s most competitive public high school, for years, I figured, a test wouldn’t be so hard for her.
And she got a 29 out of 36, which to much of the world would be a quite above average score. But for arguably the smartest 17-year-old I had ever met, I was stunned that her score wasn’t close to perfect. And she, at some level, was stunned that I thought it was going to be perfect. And so we got into a little bit of a dialogue, and it went a little something like this:
I said, “How did you study for the exam?” and she folded her arms with the pride of a valedictorian and she said “Well, every Tuesday and Saturday I take a full length ACT practice exam and I go over what I got right and wrong.”
I kinda shifted in my chair like I’m shifting now and I said, “Is that all you do?” and she looked at me bug-eyed and said “That’s ten hours of studying a week!”
And I started laughing and I said, “How is that studying?” She said “What do you mean?” and I said, “Well, let me take a guess here. You pretty much get questions 1-15 correct every time. You really hate dual passage reading questions. You miss questions that are word problems in the math section and maybe a probability question or two. And the science section, it really depends on the topic.”
And she just sat there stunned, like, “How did you know that?”
And I said, “When you study for a test in school, do you go back and get all the old exams that that teacher gave and start taking them one by one?”
And she said, “No, that would be really inefficient. I just open the textbook and learn the stuff that I don’t know.”
And I said, “Yeah, why don’t you do that instead?”
And she said, “What do you mean?”
I said, “You’re going to continue to get the same questions right and wrong. Why not just study the stuff that you’re getting wrong?”
You could see the light bulbs flashing over her head. And so I called her parents and I said, “Listen, I know you guys are big into studying, and good, well, you should be, but I want to do a social experiment, and unfortunately, you’re the guinea pig.
There are 5 weeks till the next ACT and goodness knows she wants to take it again. She can study one hour a week, but she can never take another problem from the actual exam. She can only study the things that she doesn’t know, and she has to use other resources.”
And they were like “But that’s 10% of the studying she did previously!” You could see where she got it from.
And I said, “I know. I will take the heat if this doesn’t work. But could you enforce her not continuing to take practice exams?” Fine. 5 weeks later she got a 35. And this created something that I have talked about with every private counselee since, and I call it the Scarsdale Principle, after her.
And it goes like this:
Raise your hand when you’ve solved this algebraic equation.
All right, go ahead Chris.
Super. OK. So I assume that….Just in case any of you find the amount of math a high school student needs to know is daunting, that’s like the middle of the first 10 problems.
So there are 2 ways to do this problem, right? One looks like this:
And so I subtracted 7 from both sides, 2x=0, divide by 2, x=0. A.
I like writing it out this way because my favorite personal steps are not only dividing zero by 2 – a real mystery what you’re going to come up with there – but then writing the answer to the question in the lower left corner. Like, “so I’ll remember to bubble in A.” Now it is conceivable that someone would bubble in B after doing this. Zero is probably going to be the first choice. So basically there is a one in a million chance that I forget that zero is the first choice while transferring to the bubble sheet, so why write it?
And generally the Scarsdale Principle is that one in a million things do not happen on the exam. In fact, I have some anecdotal reasons for saying that. When I took the real deal SAT, one student vomited on me during one section. During another section, a student fainted and landed on me. And so I watched as EMTs pulled him off me as his eyes were rolling back in his head. And I still did fine on the exam. I think that’s about as close as a one in a million event occurring on the SAT and they rarely have that much of an effect on the outcome. What you want to do is focus on the primary factors that affect scores.
The way to solve this equation according to the Scarsdale Principle?
Raise your hand if you did it this way.
[all raise hands]
That’s the principle. 2x plus 7 equals 7 – well obviously whatever is before the 7 equals zero. I’ve asked this question to probably a hundred students at this point. The average response time is less than two seconds. And it leads me to the beginning of any discussion on standardized testing.
What does standardized mean? I am going to tell you that standardized does not mean that the knowledge they are testing is considered standard. Standardized is a term in statistics that is used to score the exam.
Does anyone have a working definition of standardized? This is more out of general curiosity… Would anyone know what that word means, that almost every high school kid utters? Here is a working definition:
It’s dimensionless. It has no meaning unto itself.
A standardized test goes through this process before it’s scored, such that on the SAT, if you were to be the only person in the world taking it – it’s a dimensionless quantity – there is no point in answering the questions because you’d get 500 on all 3 sections. Because that is what they are trying to do when they standardize the score. If I could take a lot of questions – People think the idea of standard comes from the idea of educational standards, but it actually comes from the process of normalizing, or standardizing. And this actually has huge implications for how you tutor.
In standardized testing, everything is relative. In other words, “standardized” is a synonym for “competitive”. You are working to compare people in a population.
You’ve got to get more right than other people. And because the amount of time is fixed during the exam, the Scarsdale Principle is go faster.
If we go back to our 2x+7 example, I would say the number of high school students who would answer that correctly is around 98-99%. The ones who miss it, most of it would be due to sloppy error. So you’re not going to win the race there by being more accurate. You’re going to win it by going faster.
Because if you can do things faster, you can check them more. You can go through every problem twice, thereby eliminating any real chance of sloppy error. Those one in a million chances become one in never.
What that student in Scarsdale was doing – and I saw her sample exams at that point – was this.
A question that would take the average high school student three seconds to answer was taking her thirty seconds. This was 27 seconds she didn’t have for a later problem -- because she was writing this out. And believe me you, she was writing out the divide by two and the x=0.
From this point down, at least half of this is absolutely already done in your head before you reach for the pen. It takes longer to flourish the pen than write it. The eyeball test would’ve been the best way. Getting to 0 and clicking A would have been the next best. And I say to myself, she should find enough time to go back through the test.
The Scarsdale Principle might fall into the realm of game theory. I also call students who do this: gamers.
Gamers, tennis players, concert pianists are good at this type of thing. They’re like “Look, it matters what it sounds like. It matters whether I win more points than the other person. IT doesn’t matter whether every stroke or every key press is a thing of beauty.” They think about what it will look like in the end and so they come up with shortcuts. They come up with ways of getting to the end.