Atlantic Magazine Article on What’s Wrong With the New SAT

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:

predicted metacarpal

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!):

second metacarpal versus height

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:

standard deviation psychology

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.

How Money Talks in Westchester County, New York

If you think it’s only in your school district that wealthy kids do better in school, think again. It’s all over the nation — and it starts when children are quite young and poor ones are often not spoken to or read to nearly as much by their parents, so that kids from poor families actually start preschool with a vocabulary disadvantage.

A recent article by Dave Greene, a teacher, author and activist in Westchester County, NY, puts that into focus by examining a local magazine centerfold that gives average family household income and a bunch of other data about schools so that home-buyers can figure out how “good” the schools are.

The old real-estate saying is that the three most important things about a house are its location, its location, and its location. That’s not quite true: it really should be, the average income of the other folks in the neighborhood (or AIOFN), AIOFN, and AIOFN.

It’s also true with the schools, as the data make clear — and it’s even clearer still if you put the data into a graph, which the original author did not do.

So I did.

Here are two such graphs:

sat and family income westchester co ny

I hadn’t realized that there were poor as well as rich areas in Westchester County, but apparently there are. The line of best fit that Excel calculated shows a very, very strong correlation: r-squared is 0.8819, which means that R itself is about 93.9% — about the strongest correlation you’ll ever see in the social sciences. The two variables here are average household income and average SAT score (these go from 600 to 2400).

The next graph shows average family income versus a composite score of college readiness as measured by the New York State Regents.

family income and college readiness westchester co ny

Once again, an extremely tight correlation between average family income and college readiness score.

Read the original article for the original data and its source. Here is my spreadsheet:

westchester raw data

The Rest of the 2011 Mathematics Baccalaureat exam

As promised, here is the last section (four pages, two long exercises, each one made of subsections and subquestions) of one of the French Mathematics Baccalaureate exams. This version is one for folks who did serious secondary work in mathematics and science. This was a lot of very slow, technical typing, and trying to figure out whether I want to give a literal translation, or whether I should reach for easier understanding by American readers. I tried to opt for the second choice.

Be prepared: this section of the test is rough going, too. If you can’t quite even figure out what they are asking, you are in very good company! Only folks who have been specifically and recently studying or teaching these particular concepts would have a chance of passing.  Even with a score of 45%.

(page 4:)

and page 5:

page 6:

 and finally, page 7:

If you’ve read until here, you might think that the math part of the regular SAT is almost trivial in comparison to this test I translated. But remember this: kids raised in the French tradition and who attend French schools, find that a lot of the content of the American SATs is a mystery to them as well.

Published in: on June 29, 2011 at 11:50 pm  Comments (2)  
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