Among several things, these days, I have been doing some (serious) reading of literature on psychology, cognitive development, learning, linguistics, philosophy and a few other subjects. Well, the ones I just named happen to be parts of interdisciplinary areas, which are precisely the ones I am interested in. Of course, on many levels those parts also have a lot to do with mathematics, especially mathematical education. Ok, that was just a little background I wanted to provide for the content of today’s post.
I need to do a small (online) experiment in order to test a hypothesis, which will be the subject of my next post. Let me not reveal too much for now. The experiment is in the form of two puzzles that I ask readers (you!) to solve. They are both “multiple choice” puzzles with exactly two correct answers to each. Please bear in mind that this is NOT an IQ test. It is also not meant to test how good you are at solving puzzles individually. I am really interested in “aggregate” results. That is, for testing my hypothesis, I am only interested in what the majority thinks are the right answers. What is more, you won’t be graded, and no one (not even me) will ever know if you got the right answers. Please submit answers to both the puzzles.
Lastly, please don’t cheat or try to look for answers offline or online. As I said, this is NOT a test!
Let us now look at the puzzles.
Puzzle 1:
There are four cards, labelled either X or Y on one side and either 3 or 7 on the other. They are laid out in a row with their top (visible) sides shown like this: X Y 3 7. A rule states: “If X is on one side then there must be a 3 on the other.” Which two cards do you need to turn over to find out if this rule is true?
1) X
2) Y
3) 3
4) 7
Puzzle 2:
As you walk into a bar, you see a large sign that reads, “To drink alcohol here you must be over 18.” There are four people in the bar. You know the ages of two of them, and can see what the other two are drinking. The situation is: Alisa is drinking beer; Dymphna is drinking Coke; Maureen is 30 years old; Lauren is 16 years old. Which two people would you need to talk to in order to check that the “over 18 rule” for drinking alcohol is being followed?
1) Alisa
2) Dymphna
3) Maureen
4) Lauren
If you think you have the answers to those puzzles, then please click here Puzzles to submit your answers. (I couldn’t use PollDaddy to embed the above puzzles in this post because I am not allowed more than 160 characters in a single question. What a pain!) So, please go ahead and click the above link to submit yours answers.
Note: I will keep this “poll” open for a week to collect as much data as possible. Thanks!
Update: It seems many readers weren’t aware of the short duration of the “poll” and that they would have very much liked to participate. So, I am extending the poll till Jan 7, 2010 for them. (Doing so would also help me in collecting more data.)
12 comments
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December 12, 2009 at 10:53 pm
ot
Could you give some advice on good readings about the subjects you mentioned?
Thanks!
ot (another mathematician who recently got interested in psychology, learning, linguistics, etc..)
December 13, 2009 at 12:21 am
jim
I think in puzzle 1 you either meant “if x is on the visible side…” or you forgot to mention that each symbol occurs 2 times.
December 13, 2009 at 1:04 am
John Armstrong
@jim no, he’s stated it perfectly well. I also see the point of the two questions, and what Vishal is really asking, but I won’t say it yet lest I give anything away.
December 13, 2009 at 1:39 am
Adam Glesser
A wonderful little experiment; I was just reading about it in Willingham’s new book. It should be interesting to see how it works out with this audience.
December 13, 2009 at 2:04 am
Theo
Having seen this type of cogpsych stuff before, I’ll say this: even though I got both “right” (I think), definitely 2 was easier than 1, which I’m guessing is the hypothesis you’re going for.
Of course, the better test is to do this in a laboratory, where you can measure reaction times. And then you can also randomize the order of the two questions: having thought about 1 made 2 much easier.
December 14, 2009 at 10:19 am
Andrew Wyld
A couple of points: firstly, all your readers are probably quite mathematically literate, so this is not exactly a randomized study!
Secondly, thinking about this (and the way you phrased the question) made me wonder if there was a complementary solution, that is, two ways of finding out the same answer by asking a different question. I did this for question 1 but not 2. The equivalent logical condition for 1 is “if 7 is on one side, Y must be on the other”. The test is exactly the same. I decided not to bother for question 2 🙂
December 14, 2009 at 1:59 pm
Roger Witte
I agree with Andrew Wyld. There may be other meanings of ‘if’ … ‘then’ … in English besides material implication (otherwise people wouldn’t, for example, use conter-factual hypotheses … ‘If I were President then I would have sorted out health care quickly’). However, in the absence of context indicating otherwise, Mathemeticians, Logicians, and computer Scientists will always opt for material implication as their default interpretation.
December 30, 2009 at 11:52 am
Américo Tavares
Vishal and Todd,
Carry on your good job. Happy New Year!
PS. My vote went with the majority.
April 12, 2010 at 6:09 am
Kaz Maslanka
Very interesting
and 2 seemed easier than 1 to me as well.
Cheers,
K
May 16, 2010 at 2:22 pm
palibacsi
I stumbled over this post about 10 days ago. I posed the above questions to some high school students who are about 15 to 17 years old. I posed the bar version first, the abstract one a week later. Nevertheless, the abstract one took much longer and students gave incorrect answers more often. If you are interested, I can continue posing the questions and give a more quantitative report to you.
May 16, 2010 at 3:44 pm
Vishal Lama
palibacsi,
That would be wonderful indeed! A quantitative report would be a nice thing to have. Thanks. Our email is topological[dot]musings[At]gmail[dot]com.
February 1, 2012 at 3:16 pm
david pinto
um where are the results, since the poll is closed..?