Interesting article in the Jan. 20 The Atlantic Magazine concerning the problems with the new SAT (which once was called the Scholastic Aptitude Test).

One problem is that the problems are wordy as all get out and are mostly testing the students’ ability to decipher highly abstract text, not their ability to do math. For example, I present two questions that were cited in the article.

First problem, which you may click on to enlarge:

Not having studied the bones of the hand since junior high school, I didn’t recall what the “First Metacarpal Bone” was;I wrongly guessed it was one of those little tiny bones that allow you to bend your wrist. Only when I looked at how long thse bones are ( 4 to 5 cm) and looked it up online did I find that this is the long bone at the base of your thumb, as you see here in red.

Of course, this fact was was not explained anywhere in the text; and if your first language isn’t English then you are going to have a very hard time with this question. I suspect that the reading level of this problem is very, very high.

Having studied and taught some statistics, I know that the slope of the line of best fit for this graph shows how an increase or decrease of 1 cm in the length of that thumb-bone will predict an increase or decrease in the height of those people.

Now, here is a graph of a very similar correlation (hand length and height) from * a real study* (and for which a line of best fit would be a whole lot more realistic!):

Why does David Coleman feel the need to make everything so obscure? Oh! I remember! * He’s never taught students, ever*!

Oh, and by the way, this question is considered by Mr Coleman to be “easy”.

As is this one, which I am also taking from the Atlantic article:

I will recommend that you read the Atlantic article, since that author has much more patience than I do to explain all of this stuff. The basic idea is that when you sample more items in a population of things or people, then your margin of error gets smaller, which is highly counterintuitive! So asking more people will give you better results, hence a smaller margin of error. Which is not really taught outside of statistics classes. (Assuming that these students generally read for pretty close to an hour and a half a day and feel like telling the truth, OR that they know that they are supposed to say something near 90 minutes a a day…)

In any case, the readability of this question is pretty high, according to the Fry and Lexile algorithms that I used.

Recall, this is supposed to be an EASY question!

And PS: I defy my readers to * solve this question*: (p,.111)

An international bank issues its Traveler credit cards worldwide. When a customer makes a purchase using a Traveler card in a currency different from the customer’s home currency, the bank converts the purchase price at the daily foreign exchange rate and then charges a 4% fee on the converted cost. Sara lives in the United States, but is on vacation in India. She used her Traveler card for a purchase that cost 602 rupees (Indian currency). The bank posted a charge of $9.88 to her account that included the 4% fee.

part 1

What foreign exchange rate, in Indian rupees per one U.S. dollar, did the bank use for Sara’s charge? Round your answer to the nearest whole number.

part 2

A bank in India sells a prepaid credit card worth 7,500 rupees. Sara can buy the prepaid card using dollars at the daily exchange rate with no fee, but she will lose any money left unspent on the prepaid card. What is the least number of the 7,500 rupees on the prepaid card Sara must spend for the prepaid card to be cheaper than charging all her purchases on the Traveler card? Round your answer to the nearest whole number of rupees.

You exhibit a fundamental misunderstanding of what The SAT test tests. If you would like guidance, let me know.

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Oh, please, dear wise one, please do give us all some guidance. We await.

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In the first question, none of the offered answers is an interpretation of the best fit line. At best they are descriptions of the best fit line. An interpretation would be: as humans grow, the rate of growth of the bones in the hand grow at rates that relate to the rate of growth of the height of the individual.

The second question requires only arithmetic but couldn’t be worded in a more complicated way. mathematics students have struggled with “word problems” for many generations, It looks like these people have solved the way to teach them, which so many mathematicians failed to do. (Yes, I am being sarcastic.)

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It occurs to me that your answer to the last question very much will depend on how you round stuff off. Apparently the ‘correct’ answer is 7,212 rupees, but my result was 7,211 rupees, a difference of about one and a half cents. Would 7,211 be considered ‘wrong’ and only 7,212 ‘correct”?

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Educational Testing Service spent decades perfecting a test whose purpose was to help colleges predict which applicants would be successful. They accumulated data and experience in doing this. Then came Mr. Coleman who mandated that the company now create a test that measures what students have learned in high school. It’s a totally different purpose, and one that I suspect will take ETS many years to get right. I’m fairly certain that these new tests will provide plenty of odder for anyone who wants to ridicule the SAT.

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