Okay, that’s not depressing at all.
Still and all, I’m not sure that’s a fair test: we already know that people will do ridiculous things if they think an authority figure wants them to do the ridiculous things. This test doesn’t control for that. People might be a lot more willing to cal this a nonsense problem if, for example, they’re prompted with the idea that the authority wants nonsense problems to be pointed out when they show up.
Which of these countries do you believe have a lower percentage of children attending High School? (These are all countries that beat the US in all three categories)
Australia
Belgium
Canada
China
Estonia
Finland
France
Germany
Ireland
Japan
Korea
Liechtenstein
Luxembourg
Netherlands
New Zealand
Norway
Poland
Singapore
Switzerland
UK
Just for kicks I did the work for you. I wanted a single source for the data so I used the 2011 Unicef state of The World’s Children Report.
From the above list of countries who scored better than the US in all 3 categories the following countries also had a higher enrollment rate of eligible children in secondary school.
For males:
France
Japan
Finland
Norway
Canada
Poland
UK
New Zealand
Belgium
Estonia (equal)
Netherlands(equal)
For Females:
France
Japan
Finland
Norway
Poland
UK
Canada
New Zealand
Estonia
Netherlands (equal)
Australia (equal)
And not included because numbers were unavailable for them in this report:
China
Germany
Korea
Singapore
Of those with lower enrollment percentages the difference is usually 3 percentage points or less with a couple of exceptions. Luxembourg boys and Lichtenstein and Swiss girls apparently don’t like going to school. They were the three outliers at 85, 81 and 83 percent enrolled respectively.
The US numbers were 88 for boys and 89 for girls.
Same here, even though my math skills have deteriorated a lot since high school. The device is divided into thirds, and, to prevent air leaks, you need walls that will cover that entire length. You need one for each side of the doorway, which leaves a third left, which must be divided into two doorways.
This test is also really bad in that you could get that answer also just from the illustration, and the requirements for the answer do not seem to penalize you for doing that. If any of the countries have a tradition of always having accurate illustrations, that gives them a distinct advantage.
Well, so did I, but since this was given as an applied problem, my teachers would have required me to also give an approximate answer, not just the exact answer. I just don’t consider that as being part of “solving” the problem. I counted myself as having the solution at the point I figured out it was 1/6 the circumference.
Though, back in high school, I was pretty anal and might have given the answer as 100 cm, though not because I was approximating pi=3. No, it would be because of significant figures. We were only given one. If they wanted me to round to the nearest centimeter, they should have given the diameter as 2.00 m (200. cm). Sig figs were just preached too much in every science class. And I would be looking for this to be a trick of some sort.
I probably would have given the answer as stated on my calculator as well, though, and then put an approximately equals sign pointing to the 100cm. So, in a way, I would have given both answers.
And, yes, I assume calculators were allowed, since this test was about reasoning. Not that the math would take long otherwise: 3.14 is obviously precise enough, and 314/3 doesn’t take but a few seconds–I just did it to make sure.
As for the average high schooler: I’d expect a correct answer out of anyone who had at least taken trigonometry. This is not because of trig itself, but becasue I wouldn’t necessarily expect it out of those who took the remedial math courses, which would be about a third of the classes. I also would not expect it out of many sophomores and mostly only juniors in the advanced track. I also would expect that, as such a test would not be a part of your grade*, a lot of kids who could answer it if they thought about it would not bother.
*Assessment tests never were. It’s probably partly a practicality thing, as you were never assured of getting the results back in a timely enough manner to affect your grade, but I also think there was this idea that people would do worse on tests if they felt any pressure. I think we went too far that way. You need some motivation, even if too much will make some people choke.
On the “how old is the shepherd” problem, I once saw an answer given of “25, because in problems like this you add, subtract, multiply, or divide, and none of the other answers make sense for a shepherd’s age”. Which is an interesting middle ground: The student clearly does not have any idea how to set up the problem, but is checking to make sure that the answer makes sense.
I didn’t realize that this difficulty continued as far as 8th grade, though. The case studies I’ve seen with it have all involved 3rd and 4th graders. I’ll have to try it on my nieces and nephew next time I see them…
how are students chosen for the tests? is it voluntary? chosen at random? or only the best students? hopefully, i think BigT’s conclusion is probably on the mark - that the students taking these tests in the US simply didn’t bother.
i can opine that parents in Singapore, and a safe guess Shanghai, would be a strong motivator for the students to take these tests seriously. whether such a marked majority of US student’s nonchalant attitude towards tests is of a concern or not, i don’t know. looking through some of the sample PISA tests online, i see that they weigh more heavily on comprehension and application than technical ability. tests which therefore, can be taken by a 12-year-old student preparing for their PSLE.
if a student’s english is not up to par, the non-standard tests would be daunting; especially with the time limit, the large number of questions and the amount of parsing you’ll need to do. in our thread alone, there is at least one who misunderstood the question and a few who also didn’t bother. i can see students of the tl;dr generation not bothering to try their best on a 2 hour test which does not affect their grades.
FWIW, I tutor a couple of third graders, and last time I tutored, just for my own amusement I gave them each this problem individually. They both started off by saying, “I’m confused, I don’t get it,” but when I went into my Socratic mode (“Why are you confused? Why is this difficult to solve?”) they both started trying to answer it with division.
I really think that the desire to please the teacher is a major confounding factor in such a question.
another reason is that it takes a greater amount of confidence in the subject matter to oppose a topic. take a question printed in error, you have to be pretty well-versed in the subject matter to declare the question as unsolvable, otherwise you’ll simply be wondering if you missed something.
or take the question “which is heavier - a 1kg iron bar or 1kg of pillows”. those not confident enough to declare them equally heavy would simply follow the cue that one of them is heavier.
Don’t feel too bad. Though the answer came to me quickly, I started thinking, “How would my students be most likely to miss this question?” I teach high school physics and even before I saw your post I decided the most common mistake would be to give the answer as 1/3 of the circumference, rather than 1/6, by determining, as you did, the total open length. And, unfortunately, many of them would make this mistake–even among the honors kids. (This wrong answer could also result from misusing the diameter as the radius in calculating the lengths, and this is also likely a common mistake on this question.)
This is a question that’s not really about mathematical knowledge so much as reading comprehension and attention to detail.