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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.
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?
I'm sorry to hear that. As an instructor, I always encouraged my students to show their work for an entirely different reason.
As I would explain: if you do the problem correctly, you will get full credit. If you get the problem wrong, I will go through the work you've shown and try to give you as much partial credit as I can justify. If you don't show much work, I can't give you any partial credit and so you'll get zero points on the question.
This is the only fair way to do it. Students that get 90% of a problem right should get 9/10 possible points. But to do that, you really do have to encourage them to show their work in sufficient granularity for the instructor to grade it.
I don't know what mental shortcuts you use, but I can prove that mine are valid.
Why would I write down 162 + 199 and add it up, when I can just mentally add 161 + 200?
Why would I do long multiplication of 50*49, when I can do (50*50)-50 in my head?
I once watched a class mate add zero to a number on his calculator. Can we accept that there are some mental shortcuts that are valid?
"Show your work" is shorthand for "prove you didn't cheat".
That's part of it. "Show your work" also gives you partial marks if you had the correct reasoning but made a mistake somewhere along the way. It also reveals to the teacher if a large proportion of the class doesn't understand the same thing, so the teacher can concentrate on this.
But most of all, "show your work" is what real mathematicians do for a living. If you write a paper which says "the Goldbach conjecture is true, and I know because I proved it in my head", it will not get published because you need to show your work.
sub f{($f)=@_;print"$f(q{$f});";}f(q{sub f{($f)=@_;print"$f(q{$f});";}f});