Media outlets around the world went crazy over a 5th grade math exam question in China. But they all missed the real story! The problem actually dates back to French researchers in 1979. In this video I present the real story to the viral “Chinese” captain’s age question.

Update thanks to comment from Markus Schüt: the origin dates back to 1841 in a letter Flaubert wrote! See:

https://en.wikipedia.org/wiki/Age_of_the_captain

My blog post for this video:

https://wp.me/p6aMk-5rE

Captain’s age question

“If a ship had 26 sheep and 10 goats onboard, how old is the ship’s captain?”

South China Morning Post

http://www.scmp.com/news/china/society/article/2130892/26-sheep-10-goats-lot-flak-over-chinese-primary-school-maths-exam

The Portal (Chinese)

http://www.thepaper.cn/newsDetail_forward_1971117

RT

https://www.rt.com/news/417231-china-math-problem-sheep-goats/

BBC

http://www.bbc.com/news/world-asia-china-42857864

Washington Post

https://www.washingtonpost.com/news/worldviews/wp/2018/01/31/this-chinese-math-problem-has-no-answer-actually-it-has-a-lot-of-them/

Newsweek

http://www.newsweek.com/can-you-solve-it-bizarre-math-exam-question-leaves-students-scratching-their-796005

Official response (Chinese).

http://news.sina.com.cn/s/wh/2018-01-27/doc-ifyqzcxh0729685.shtml

Sherlock Holmes’ deduction in The Hound of the Baskervilles

https://www.quora.com/What-are-some-of-the-best-deductions-by-Sherlock-Holmes

Novotná, Jarmila, and Bernard Sarrazy. “Model of a professor’s didactical action in mathematics education: professor’s variability and students’ algorithmic flexibility in solving arithmetical problems.” The Fourth Congress of the European Society in Mathematics Education. 2005.

http://www.erme.tu-dortmund.de/~erme/CERME4/CERME4_WG6.pdf#page=68

de Corte, Eric, Brian Greer, and Lieven Verschaffel, eds. Making Sense of Word Problems. CRC Press, 2000. Pages 3-5.

https://books.google.com/books?id=OOyHRpWsI7sC&lpg=PR7&ots=oRk2XlgRGu&dq=%2226%20sheep%22%20%2210%20goats%22%20boat&lr&pg=PA4#v=onepage&q=%2226%20sheep%22%20%2210%20goats%22%20boat&f=false

Reusser, Kurt. “Problem solving beyond the logic of things: Contextual effects on understanding and solving word problems.” Instructional Science. 17.4 (1988): 309-338.

https://files.eric.ed.gov/fulltext/ED270327.pdf

Benjamin Dickman Twitter and tweet

https://twitter.com/benjamindickman

https://twitter.com/benjamindickman/status/960304080462798851

Benjamin Dickman answer on Math Educators Stack Exchange about the shepherd problem

https://matheducators.stackexchange.com/questions/11543/does-the-how-old-is-the-shepherd-phenomenon-occur-for-more-relatable-word-prob/11546#11546

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The entire worldwide media missed the actual history of this problem! Please tweet this at any news organization that posted a story so they can share the real story dating back to French researchers in 1979.

Update comment from Markus Schütz (also noted in tweet by Benjamin Dickman): "Actually the origin goes back to 1841: https://en.wikipedia.org/wiki/Age_of_the_captain. In french speaking areas "… and what's the captain's age?" is a very popular saying when someone tells you a story with many unrelated details, or poses a problem in a very complicated wording, or gives you an unsolvable problem. And everyone knows that the correct answer is always "42" ;-)"

Also, some minor clarifications/corrections and one elaboration:

3:06 – A more accurate description is: Benjamin Dickman, who has a Ph.D. in Mathematics Education from Teachers College, Columbia University, and currently teaches math at The Hewitt School, an all girls day school in New York City. Benjamin believes such problems are well-known to math education researchers, specifically those with interests in sense-making, problem solving, and problem posing.

5:02 – the blog "has other posts, too"

Gene Wirchenko suggested elaborating the ending of the video with this point:

"Mathematical tools have requirements for their use. For example, if one has two of voltage, current, and resistance for some types of electrical circuits, one can compute the third using the formula E=IR. BUT you must have two of the values. If you only have one of them, you do not have enough information.

"In a real world problem, you may have to hunt down the missing information. Sometimes, you can compute a missing value from other information given in the problem.

"For example, in the problem 'Albert has 25 marbles more than Carl does. Beth has 45 marbles. Carl has 15 fewer marbles than Beth. How many marbles does Albert have?', Albert has c + 25 marbles. We do not know the value of c, but we do know that c = b – 15. That still is not enough, but since we know b = 45, we can substitute 45 for b to get c = 45 – 15 = 30 and then for c in a = c + 25 to get a = 30 + 25 = 55. Thus, Albert has 55 marbles."

IAM sorry but this can be a question of general aptitude but not mathematics.

Because to guess an answer the student should be aware of something which is beyond the scope of mathematics and that is the regional law on boat cargo .

I just thing of being deaf as those animals can be loud as hell.

There is really another layer to this story because the question that has not been answered here is

whyso many students tried to solve the problem by manipulating the numbers. It points to a flaw in human reasoning that is actually very common and affects us all in often very subtle ways. When faced with difficult problems or those that involve a lot of uncertainty the human brain has a tendency to look for easier problems and solve them instead. The problem here has no simple solution (although it does have a better solution than the one given if you consider probability and population distributions) and involves a lot of uncertainty so the brain looks for a solution it can easily solve – adding two numbers. This was studied by Kahneman & Tversky and Kahneman talks about it in his book 'Thinking, Fast and Slow', a really good read by the way.Nowhere in that problem does it say that the ship/boat even HAS a captain 😛

I agree this is a valuable lesson, but you should teach critical thinking during a LESSON not during an exam. I find this pretty unfair to those that wasted valuable time on trying to find a solution. They may have lacked critical thinking but might have been brilliant at finding solutions to the other problems.

That's because students are told, over and over, under duress, in many different wordings and situations, YOU WILL SOLVE THIS! IF YOU CAN'T, THEN YOU'LL NEVER FIND A JOB AND YOU'LL FLUNK OUT AND STARVE AND NOBODY WILL LIKE YOU. Given this kind of punitive-based conditioning, no one DARES to say "this problem isn't solvable", even if they really do think that it isn't.

It may have something to do with the conception that in a test students are expecting their to be a logical straight answer in mathematics and not open ended,

So even if they are unsure as to why, they’ll do anything with the information given to come to a reasonable value even if the logic that number of animals has 0 relation to age of people

Simply because ‘it’s in my maths tests, it must have an obtainable answer using these values’

Heinlein did something similar in one of his novels.

A recruit was given a series of aptitude/skill testing activities to do. One was a game with a set of confusing and contradictory rules.

The ACTUAL test was to see how long it took you to figure out that it was impossible to score.

It was either "Space Cadet" or "Starship Troopers" – can't remember now.

the big question i want the answer to is: is the problem that we are not teaching them critical thinking or is the problem that we sometimes teach kids that even if they dont know an answer they must solve it, so they end up thinking there must be a way to know the captains age.

The captain is 1 year old

the shepherd is actually 625 sheepdog years old.

Surprisingly, student's don't expect that their teachers will give them ridiculous problems, and try to go to great lengths just to get any answer.

"Iceland is in the North Atlantic. Its capital city is Reykjavik…"

I'm taking your commentary about the need to challenge the question, by challenging your commentary. Haha.

We know that the students, overwhelmingly, provided a numerical answer to the question. I gathered that the conclusion that most resonated with you was "We still need to improve the critical thinking skills of students in math class.". This is a possible conclusion, but it's not the only one.

I've thought of 3 possible conclusions to the study, one of which lines up with yours.

In response to this question: Why do kids provide and a numerical answer to the question instead of identifying that there is insufficient information

The first one (which lines up with yours) is that they do so because they've never been taught to challenge or assess the question. We spend most of our time answering questions, rather than assessing them. It would need to be explicitly taught as part of the curriculum, otherwise, they'd probably never do it.

The second one is that they've been trained not to question authority. As a teacher myself, I can say that schools, on some level (depending on the school), all have a bit of 'Do as I say' and 'Teachers don't make mistakes' in the learning environment.

The third one, and the one I'm most in favor of, is that their brains (either instinctually, due to limited processing power, or due to habits of not bothering with the words) only mentally hold onto the numbers, and therefore can't assess how they're really correlated. While one kid did use the 'age' part of the question to choose 125/5 as the most probably answer, his failure to mention the animals again could signal his brain dumped that information early on.

My point is not to assert that any of these are the correct conclusion – mentioning my favorite one doesn't mean I think it's any more correct than another one. Rather, I just think we must be careful to avoid implying the conclusion, when one wasn't made available.

Now, to be fair, maybe the researchers did find out the reason, and the reason is what you said. But only in response to what you put in your video (meaning, I chose not to read about it outside the video, because lots of people only watch one video and never look into it further), I think that educational content needs to be sure that conclusions that are not explicit or provable from the source material should not be tossed on the end as a button to finish the video.

I'm going through a binge watch of your videos, because they're great and I'll keep watching!!