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This Chinese Math Problem Has No Answer. Perhaps, It Has a Lot of Them. (washingtonpost.com)
Fifth-graders in China's Shunqing district were recently asked to answer this question: "If a ship had 26 sheep and 10 goats on board, how old is the ship's captain?" The Washington Post: The apparently unsolvable question sparked a debate over the merits of the Chinese education system and the value it places on the memorization of information over the importance of developing critical thinking skills. "Some surveys show that primary school students in our country lack a sense of critical awareness in regard to mathematics," a statement by the Shunqing Education Department posted Jan. 26 reportedly said. One student offered a pragmatic law-abiding answer: "The captain is at least 18 because he has to be an adult to drive the ship." Meanwhile on Twitter, some have gone with 42, a reference to the science fiction novel "A Hitchhiker's Guide to the Galaxy," by Douglas Adams, in which 42 is the "Answer to the Ultimate Question of Life, The Universe, and Everything." BBC: "If a school had 26 teachers, 10 of which weren't thinking, how old is the principal?" another asked. Some however, defended the school -- which has not been named -- saying the question promoted critical thinking. "The whole point of it is to make the students think. It's done that," one person commented. "This question forces children to explain their thinking and gives them space to be creative. We should have more questions like this," another said.
The Washington Post article links to a BBC article containing the following:
And of course, there's always that one person that has all the answers.
The total weight of 26 sheep and 10 goat is 7,700kg, based on the average weight of each animal," said one Weibo commenter.
In China, if you're driving a ship that has more than 5,000kg of cargo you need to have possessed a boat license for five years. The minimum age for getting a boat's license is 23, so he's at least 28.
Johnny observes three stars through his telescope. The stars' temperatures are X, Y, and Z kelvin. What is the total temperature observed?
when he was asked to evaluate science textbooks for the school board in Pasadena.
In one of Richard Feynman's books, he told about his experiences at a university in Brazil. He was horrified to realize that the students were ritually memorizing the course material with very little actual understanding.
When he asked questions in a way that echoed the textbook, students were able to recite an answer straight out of the book. But when he made up a "word problem" they were totally unable to answer.
A student was quizzed on physics, asked to compute what happens when light passes through a diamagnetic substance, and he recited the answer correctly and then calculated the correct result given the index and thickness of the substance. Immediately afterward, Feynman talked to that same student; Feynman held up a book and asked what would happen if the book was made of glass and he looked at something through the book. The student didn't realize that glass is a diamagnetic substance, and gave a very incorrect answer.
Richard Feynman on education in Brazil
In the domain of math questions, I saw an example: if a person has 4 boards of length 2.5 metres each, and cuts them with a saw, how many 1-metre boards can that person make? Obviously the correct answer is 8 (two per board, with 4 left-over pieces of length 0.5 metres minus the width of two saw cuts). If you were just playing with the numbers abstractly you might think that since 4 * 2.5 == 10 that you could produce ten 1-metre board segments. You can't actually glue together 4 boards to make a single board, and you can't actually make zero-width cuts.
I can't speak for others, but I enjoy word problems more than abstract problems. (Good ones, anyway... you can take a simple problem and write an annoying and confusing word problem, and nobody likes those.)
lf(1): it's like ls(1) but sorts filenames by extension, tersely
I dislike teachers like you. Why? I show my work. You can see the lines on my face, the callouses on my hands, and the holes in my boots. But when I gave the landlord 9/10 of the rent, he still threw me out.
The problem is that that if a kid gets the correct answer, points are TAKEN AWAY for not "showing your work".
Be sure to tell your reviewers that next time you submit a paper to an academic journal which is just a conclusion with no evidence for it. Maybe you'll get the lesson in the scientific method that your American school didn't give you.
BTW, you may have missed the word "also" in the sentence that you replied to.
sub f{($f)=@_;print"$f(q{$f});";}f(q{sub f{($f)=@_;print"$f(q{$f});";}f});
"Trying hard" is no excuse for wrong answers.
He didn't say it was. The issue is, why was the answer wrong?
Teachers like you are why America is falling behind.
Teachers like him are trying to teach the concepts and measure the success of the student based on concepts and not trivial errors.
Which is more important? Knowing the equations behind equilibrium concentrations and the concept that an equilibrium exists, or the ability to poke numbers into a calculator and get a number that is close enough to be right?
As a TA in college, I graded lots of papers. If a student just wrote down a number and it was wrong, maybe because he made a mistake entering something in his calculator, I had to mark the problem completely wrong. No credit. He demonstrated neither an understanding of the problem nor the solution. He might have been an Einstein in chemistry, but without showing the work his wrong answer didn't show his mastery.
But, if the student showed his work, I could see that he did understand the problem. Maybe his solution was incorrect because he entered the exponent incorrectly and got the wrong number. Maybe he understood half the problem but not the other half. He could get credit for what he did know.
I used chemical equilibria as an example on purpose. Solving concentrations in a weak acid or base solution requires solving a quadratic equation for the full, complete answer. But there is a shortcut that gives "close enough"* answers when the numbers meet a certain criterion (low enough disassociation constant that the concentration of unionized chemical does not change significantly). If a student uses the shortcut when it does not apply, gets the wrong answer, but shows his work, I can properly critique and evaluate his answer, giving him partial credit. If he just has a number, it gets marked wrong.
I learned this the hard way, personal experience. I was taking the class I later TA'd and solved one problem using the full method. I decided it was easy enough to always use the full method so I did. I didn't show my work. The TA marked the answer wrong. What!? At the next discussion session I asked why it was wrong, and showed him step by step why it was right. Woopsies. He had created the answer key using the shortcut and it did not apply for that problem. His mistake. Had I shown my work, it would have saved his embarassment and everyone's time because he could have seen why his answer was wrong and corrected his key before anyone knew he made a mistake.
Is it better to grade "all or nothing" on a problem, or allow for human error in pressing buttons on a calculator and grant credit for what was shown?
* by "close enough" I mean "within the precision of the problem as stated", or "based on the number of significant digits". If you have a starting concentration that is valid to three digits, then an answer that is off in the fourth digit is "close enough".
I wouldn't complain about that exam for any snowflake reasons, I'd complain about it because it's completely ignoring the last 60 years of exam theory research if given as stated. The most obvious problems with it:
The question difficulty needs calibrating. There are well-known tools (facility and omit rates) for doing this, but you need a very large population of exam sitters to properly calibrate an exam where every question is optional. This means that if candidate 1 answers questions 2, 3, 4, and 5 all correctly, but candidate 2 answers questions 6, 7, 8, and 9 all correctly then you almost certainly don't have enough information to be able to compare them at all, unless either you have a few tens of thousands of students sitting the exam, or you have a bank of questions that you're reusing and are doing pre-testing to calibrate them.
The ordering with respect to cohort means that your reliability is low. A single outlier at the top end will move everyone's marks down a lot. The lack of such an outlier will move everyone's grade up a lot. If your exam is meant to actually measure anything useful and not just be a dick-waving contest, then you'll need to do some normalisation and not use the scheme that you've proposed.
Your discrimination is likely to be all over the place. Most exams are intended to have high discrimination at specific places. For example, in admissions testing you have deselection tests that have high discrimination somewhere in the bottom half and selection tests that have high discrimination nearer the top. The first means that there's a big jump between the definite-reject and the possible-accept candidates, the second means that there's a big jump between the definite-accept and possible-accept students. For most graded exams, you want high discrimination between grade boundaries: if someone gets a B, you want to be confident that they're definitely worse than students who get an A and better than ones that get a C, but you don't care much about their ordering with respect to other students that get a B. This structure makes it almost impossible to design an exam for high discrimination.
If you want a snowflake reason, then your exam structure is likely to penalise women if it is being administered to teenage or undergraduate-age students, because they tend to be more negatively affected by time pressure than boys of the same age (this effect reduces with age).
TL;DR: It sounds like you like exams that don't measure anything useful, because you do well in them.
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