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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.
If the question has no answer and is supposed to foster critical or creative thinking, how did the teachers grade the answers?
What were the actual answers? As it stands, this is bullshit "news" cause the important part of the whole incident wasn't reported. Why am I not surprised that it's "news" from Jeff Bezos' Blog?
Did the pupils get full credit when they pointed out how the question is unanswerable? Did they get credit for the lower bound of 18? Did they get no credit for things like the 42 answer which is simply a lame old joke?
I beg to differ... SOME questions have many answers with no single answer being more correct than another and sometimes there are questions for which there are no answers at all.
Expecting all questions to be solvable from the information given is a commonly misunderstood issue. Critical thinking involves realizing that you may not be given all the relevant data and may need to find additional information to get a good answer. In other words, good problem solving involves thinking about the unknown, both the known unknowns and the unknown unknowns.
Have an issue with Known unknowns vrs unknown unknowns? Let me illustrate what I mean. Known unknowns is understanding that you will have a calculable number of software bugs during a specific sized software project. You don't know what they will be, but you know they will happen and you can guess what it will take to fix them from experience, a known unknown. Unknown unknowns are things you simply cannot foresee, like your office being hit by a tornado in the middle of the project.
"File to fit, pound to insert, paint to match" - Aircraft Maintenance 101
But I see a lot of people didn't get it. Oh well.
What have I got in my pocket?
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
I'm going to assume you're being incredibly sarcastic here because life is full of problems for which there is insufficient data to determine a correct answer. There are a great many that do already have good answers, but at one point there was insufficient data to answer them.
If you wanted to make this exercise more useful, I'd rephrase the question (to something that's not immediately obvious) and once they've figured out that they lack sufficient data, ask them what information they would need to produce an answer. Knowing that you have insufficient data to answer a question is one thing, but understanding what is missing and how to go about getting it is a highly valuable critical thinking exercise.
Mod up please. This is exactly the kind of quality information that makes me read the comments before the article. The entire discussion makes no sense without knowing this. Shame on The Washington Post for publishing making this sound like some controversial idiotic thing, without providing the basic background!
Perhaps I could help explain with a math problem. Seems fitting.
Since hype and bullshit are proven revenue streams, how many clicks and likes does it take to dismiss journalistic integrity and relevant information?
if it's really as intended. But it's probably a typo that didn't get caught. They happen. Feynman has a story in one of his books about finding a math problem like
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.
I looked at the original article which Feynman wrote and your summary, while extremely condensed and accurate enough for here, just assumes that the reader will get the point of Feynman's dislike of the question. I bet most here will miss it. The reason that Feynman objected to the question in the textbook is that in real life there is no reason at all to add the temperatures of stars, not that the question had a horrible mistake in it. That's very different from the question in the parent article, which is to test critical thinking.
You don't need to memorize the material, but it is an extremely important lesson to learn that such material exists, and it's even relevant to advanced mathematics.
I don't remember most of my calculus days, but I do remember that most of my work consisted of trying random arbitrary approaches, and seeing which one advanced the problem toward the solution. Whether L'Hopital's rule, integration by parts, or other tactics I no longer remember, it's not always obvious how to proceed. Developing the skill to match a problem to a solution approach is vital.
In the real world, the same skill is necessary for a lot of everyday analysis, perhaps best demonstrated by Randall Munroe's "What if?" series. The questions posed are often absurd, but the approach to answering them typically relies on making connections to apparently-unrelated (but similar) phenomena, allowing for some rough estimation of the original problem. More practically, these kinds of questions appear every day, in less obvious forms such as "How much more will it cost if we double the scale of this whole project?" or "If we add a Widget to the Wotsit, will the Frobozz still function?", usually accompanied by an impatient boss with very little technical skill...
Getting back to the subject at hand, I expect the purpose of the question was not to seek any particular answer, but to gauge whether the students are able to consider non-obvious paths to a solution. Knowing the rules for boating licenses is one viable route. Random guessing is another. Giving up and complaining that the teacher didn't spoon-feed you enough information is not.
Sneaky little Hobbitses. Wicked. Tricksy. False.
This problem is not sufficiently bounded to solve from a mathematical perspective.
(That's the actual answer... You don't need to be over 18 if you are piloting the boat illegally and there may not even be a captain.)