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Mar
1
2013

In a recent online class, I asked my students, “How would you feel if the test makers added 15 extra minutes to each section?”

The chat lit up with excitement. I was expecting a positive response, but there was so much enthusiasm that I was taken aback. One student called it “a blessing.” Many others agreed that if they had 15 extra minutes per section, it would be just about the greatest thing that’s ever happened to them: they’d be less stressed, get more problems right, have a higher score; the sun would shine brighter and longer and warmer; a cavalcade of parachuting puppies would rain down from the sky and deliver every child in the world a cupcake made of love and hope; a cadre of unicorns would …

“HANG ON, HANG ON!” I said. “If you had more time to work on each section … what else would happen?”

And then there was silence. For a moment, the class was confused. Nobody saw what I was getting at. I prodded a little more, and finally one student said, “… other people would have more time too?”

Another student caught on. “And the scoring scale would be harder.”

Right. If you had 15 extra minutes per section, that would be terrible! Your competition would get the same bonus you would, so it’d be exactly as hard to get any particular score as it is now, except the test would be 75 minutes longer. Because every student’s score depends entirely on her performance relative to everyone else, a feature that benefits everyone actually benefits no one.

Don’t rail against the strict time limits of the GRE. Don’t fume, saying, “This is stupid. If I had infinite time, I could get all these questions right!” The thing is, if you had infinite time, so would your competition, and you wouldn’t be any better off. Learn to love the clock — it’s an opportunity for you to succeed where others fail.

Aug
8
2012

One of the new Verbal question types on the revised GRE is sometimes called Critical Reasoning. These questions mimic very short Reading Comprehension passages, but they differ in that Critical Reasoning problems are a little shorter, and they typically present a flawed argument. Sometimes, you’ll be asked to find the assumption in the argument, while at other times you’ll be asked to strengthen or weaken the argument. The GRE test-makers love coming up with new flawed arguments to present to you on Test Day, but for the most part, we know that there are consistent ways in which the arguments are flawed. One flawed argument concerns the conflation of numbers and rates. This reasoning error is actually a pretty common fallacy in day to day life, and if you keep your eyes and ears peeled, I bet you’ll start noticing this faulty reasoning in the news, in conversations with your friends, and even perhaps in your own arguments.

This flaw is especially prevalent in public policy and politics, where the truth has never gotten in the way of a good argument, and where statistics can be used to support any myriad number of positions. I was reminded of this the other day, when our village hosted a community forum to discuss skateboarding within city limits. I live in a pretty laid-back college town, and our two prevailing ethos were in direct conflict – on the one hand, there is the desire to let college kids act like college kids, and on the other hand, there is the desire to protect college kids from themselves.

The forum was a place to discuss the local police department’s request to make skateboarding on city streets and sidewalks a misdemeanor offense. The police department’s justification centered on the inherent dangers of skateboarding, and the city’s liability in the event of injuries suffered or inflicted by skateboarders. Opponents of the measure presented an interesting case. They pointed to local hospital records that showed the difference in the number of injuries due to skateboarding, and the number of injuries due to jogging. In the last five years, they claimed, the hospital admitted four patients with injuries resulting from skateboarding, while in the same five years, the same hospital admitted twenty-four patients with injuries resulting from jogging. Opponents claimed that these numbers showed that skateboarding was actually much safer than jogging and that if anything, jogging should be outlawed.

Ah, there it is. The old fallacy that conflates numbers and percents. Are you convinced by the opponents’ argument? If not, why not?

First of all, we need to know how many people, in total, are jogging and how many people are skateboarding. If it turned out that every year, an average of 5,000 people went jogging three days a week, then twenty-four injuries over a five year period doesn’t seem that bad. And what about the number of skateboarders in town? Suppose there are only 20 people who routinely skateboard on the streets and sidewalks of my sleepy college town. In that case, four injuries could be considered somewhat alarming. To make the claim that skateboarding is safer, then what we really need to know is the difference in the likelihood of injury between jogging and skateboarding. In other words, what percent of people who go jogging get injured? What percent of people who go skateboarding get injured?

If on the GRE you’re presented with an argument like the one above, stop and evaluate how numbers and percents are being used. Is there a shift in scope from the evidence to the conclusion? If numbers are presented as evidence, with no comparison to the other values in the evidence, then a conclusion that jumps to rates or percents will often be flawed.

On the GRE, be sure to be on the lookout for Critical Reasoning problems where numbers and percents are conflated. In fact, don’t just stop at the test. Be on the lookout for this faulty reasoning everywhere. Allowing your GRE studies to eddy out into your everyday life is one of the best ways to help ensure incremental score improvements over time.