Take This Test (Please), writes John Merrow on Taking Note. He lists five test questions that “may explain why American students score lower than their counterparts in most other advanced nations.”

From the University of Wisconsin/Oshkosh [1] for high school students:

Jack shot a deer that weighted (sic) 321 pounds. Tom shot a deer that weighed 289 pounds.  How much more did Jack’s deer weigh then (sic) Tom’s deer?

From TeacherVision, part of Pearson :

Linda is paddling upstream in a canoe. She can travel 2 miles upstream in 45 minutes. After this strenuous exercise she must rest for 15 minutes. While she is resting, the canoe floats downstream ½ mile. How long will it take Linda to travel 8 miles upstream in this manner?

Merrow wonders whether students will be “distracted by Linda’s cluelessness,” asking “how long it will take her to figure out that she should grab hold of a branch while she’s resting in order to keep from floating back down the river.”

From a high school math test in Oregon:

There are 6 snakes in a certain valley.  The population doubles every year. In how many years will there be 96 snakes?

a. 2
b. 3
c. 4
d. 8

The new Common Core standards expect students to do more than subtract and count on their fingers by high school, notes Merrow.

From New York state’s sample tests for eighth graders:

Triangle ABC was rotated 90° clockwise. Then it underwent a dilation centered at the origin with a scale factor of 4. Triangle A’B’C’ is the resulting image.  What parts of A’B’C’ are congruent to the corresponding parts of the original triangle?  Explain your reasoning.

No illustration is provided, says Merrow.

From PISA (for Programme in International Student Assessment), here’s a question for 15-year-olds around the world:

Mount Fuji is a famous dormant volcano in Japan.  The Gotemba walking trail up Mount Fuji is about 9 kilometres (km) long. Walkers need to return from the 18 km walk by 8 pm.

Toshi estimates that he can walk up the mountain at 1.5 kilometres per hour on average, and down at twice that speed. These speeds take into account meal breaks and rest times.

Using Toshi’s estimated speeds, what is the latest time he can begin his walk so that he can return by 8 pm?

The correct answer (11 am) was provided by 55 percent of 15-year-olds in Shanghai and only 9 percent of U.S. students.

American kids score highest in “confidence in mathematical ability,” despite underperforming their peers in most other countries, PISA reports.  “Is their misplaced confidence the result of problems like ‘Snakes’ and others of that ilk?” asks Merrow.

1. Jerry Doctor says:

I’ve heard of fuzzy math but in the case of the “Linda” problem I believe the issue is fuzzy question writing. I would maintain the answer is 3 hours and 45 minutes. I’m sure that is not what the authors intended.

My reasoning: At the end of one hour Linda has traveled 2 miles upstream. She has also drifted one-half mile downstream. At the end of three hours she has traveled 6 miles upstream, although also drifting 1.5 miles down. Another 45 minutes and she has traveled 8 miles upstream.

Of course she is only 6.5 miles upstream from where she started but I wasn’t asked how long it would take her to get to a point 8 miles from the start.

If you intend to write “clever” little questions you cannot assume the student will “know what you meant.”

• Mark Roulo says:

I am quite certain that the authors intended to ask: “How long before Linda is 8 miles upstream from where she started.”

So I think the answer they want is “5 hours.”

But, yes, the question is poorly phrased.

Actually, if they want “How long before Linda is 8 miles upstream from start”, then I think the answer is 4:45. After 1 hr, she’s up 1.5; after 2, up 3; …; after 4, up 6. The next 45 minute row takes her to the 8-mile mark.

This is just a rewriting of the old worm-climbing-out-of-a-hole chestnut that is at least 50 years old.

• Jerry Doctor says:

For a half dozen years I served on the American Chemical Society’s High School test committee. It took us two years to write an 80 question multiple choice exam. One year was spent writing questions and the second year pretesting and doing a statistical analysis of the pretest results.

When we were done we had a pretty good exam that produced reliable stats after being put in general use but it sure was a lot of work. And if the committee members hadn’t been volunteers the cost would have been enormous.

• Jerry Doctor says:

Oops! Meant as a reply to Mr. Lopez.

2. Michael E. Lopez says:

Some of these are terrible. The Canoe question for instance… is she *IN THE BOAT* when it floats downstream? Or does she get out to rest and have to walk down to get the damn canoe? Because the first time I read it that’s what I was picturing.

The painful truth is that most people in the education business, and by that I mean in the testing business, don’t really know how to write a good multiple choice question. (I can prove this by the fact that most multiple choice questions are terrible, including nearly every reading comprehension question I’ve ever seen in my entire life — which is a LOT of freakin’ reading comprehension questions.)

(For more on my thoughts on this issue, please see: http://higheredintel.blogspot.com/2012/01/horrible-multiple-choice-questions.html)

3. Bill says:

While the wording in some of these questions is atrocious, if a high school student preparing to go to college cannot handle this stuff (when properly worded), they shouldn’t be admitted at all.

I’d say the level of math at best is stuff that I got in middle school (of course, it’s the dreaded word problem issue as well)…

heh

4. Gray Hat says:

The “weighted deer” question is a joke [Were calculators allowed? Inquiring minds want to know]. The canoe problem is ambiguous, as other commenters have pointed out. But the Triangle problem, which sounds sophisticated, is very easy — with dilation, there cannot be congruence. The PISA question is also very easy — easier, in fact, than the canoe problem, though comparison is made difficult by the fact that it is also better written. Conceptually the Snakes problem is the hardest of the lot, though the numbers are small enough that the student can “walk through” it without knowing anything about exponential growth. So I’d hesitate to draw conclusions from these examples.

Just my two cents’ worth.

5. I’m not sure what’s supposed to be wrong with the triangle dilation problem. It seems appropriate for good students in the eighth grade.

Merrow’s comment about there not being an illustration is just daft; the whole point of the exercise is that you can’t draw a diagram (because you don’t know where the origin is) but you still know what the congruences are.

• Jerry Doctor says:

Jeff,

I haven’t taught geometry since the 70’s so maybe I’m missing something here. Am I right that the original triangle was simply rotated and then enlarged? If that is correct, the angles are still all the same size so they’re congruent (although we’d more commonly say they are equal). If that’s it, all the rest is just obfuscation.