kitchen table math, the sequel: pop quiz, part 5

## Friday, June 10, 2011

### pop quiz, part 5

How many people do you think answer this question from the Wason test correctly:
[Four] cards are placed on a table to show 3, 8, red and brown....The rule is: “If a card shows an even number on one side, then it is red on the other.” Which cards do you need to turn over to tell if the rule has been broken?
And how many people would you expect to get the answer right on this one:
“If you borrow the car, then you have to fill the tank with petrol.” Once again, you are shown four cards, one side of which says who did or did not borrow the car and the other whether or not that person filled the tank:

Dave did not borrow the car
Helen borrowed the car
Brianne filled up the tank with petrol
Kirk did not fill up the tank with petrol

Does learning math make you more likely to know the answer?

Or, alternatively, does being able to answer these questions make it easier for you to learn math?

I'll put the percent-correct in the comments.

Here is Language Log on the Wason test. (Haven't read yet.)

Catherine Johnson said...

“If a card shows an even number on one side, then it is red on the other.” Which cards do you need to turn over to tell if the rule has been broken?

[snip]

In terms of formal logic, the problems are the same. But most people have an easier time answering the second one than the first. (In both cases it is cards number two and four that need to be turned.)

20% get the first question right
70% get the second question right

Socially challenging
Economist
November 11, 2010

For problems cast as social contracts...non-psychopaths got it right about 70% of the time. Psychopaths scored much less—around 40%—and those in the middle of the psychopathy scale scored midway between the two.

Text Savvy said...

Hainish said...

I say it's B: being able to do the first version of the task correctly indicates a high ability to reason abstractly, making it easier to do math.

Then again, maybe having done enough math increases one's ability to reason abstractly.

Allison said...

People understand what B means, and life teaches them that by adulthood--what conditions must I check? Few recognize the relationship between the 2nd version (car and gas) and the first. That's been shown by research over and over.

Nearly all teens get this question right if phrased as "if you want to drink, you must have an ID that says you're 21 or over." I'm drinking beer; you're not; he's 17 and drinking something dark; she's 35 and drinking something in light. Who/what must you check to make sure everyone is behaving legally?" They know the beer drinker needs to be checked for ID, and that the 17 yr old's drink needs checking for no alcohol.

That's because these conditions are pre programmed in their head, not because they see the truth values of if-then relationships to their inverse,converse, or contrapositive.

Knowing more math doesn't make you more likely to get B right. It makes you more likely that you'll know how to do A, even if you STILL don't see the connection to B. (because you have explicitly learned that a - > b is equivalent to its contrapositive not b -> not a)

The point is that even math-literate people don't get the connection between the two questions.

Catherine Johnson said...

I say it's B: being able to do the first version of the task correctly indicates a high ability to reason abstractly, making it easier to do math.

That's the answer I was fishing for!

Catherine Johnson said...

fyi: the article was about an ingenious study of psychopathy. The authors reasoned that psychopaths, who do know moral rules, use 'reasoning' as opposed to 'emotion' to make moral judgments. (I'm using quotes because I don't remember how they put it, exactly.)

If that's true, then psychopaths ought to have as much difficulty doing the borrow car/put gas in the tank problem as the abstract problem.

Sure enough, prisoners who tested high on psychopathy had significantly more trouble than normal people handling the car/petrol question.

Catherine Johnson said...

Another interesting element: I think I read at Language Log that if you substituted something like "California," "Nevada," "patient," and "impatient" and gave the rule as "People who live in California are patient," the test is very difficult to do. In other words, although "Californians are patient" is a great deal less abstract than even-odd and color, the greater degree of concreteness doesn't make the problem appreciably easier.

People do well **specifically** on 'social contract' and 'risk' questions.

Am I a psychopath if I found the number/color version much easier to see the answer to immediately than the car/petrol one?

Allison said...

it's not the degree of concreteness that matters. It's the specific social rule you must learn to follow. Neurotypical humans know how to ascertain social rules from their surroundings, even when they are not made explicit. That's why nearly every teenager gets the drinking age rule right, but still might not get the "he didn't put gas in the car" side of the rule right--because that's NOT a universal social contract to them.

Few people jump contextual boundaries and see the similarities. That's because the contextual boundaries tell us to whom we're loyal, or when we feel pride, or when we can dissemble. The if-then ness of a card game just doesn't affect our species' survival the way telling the loyal group member from the sociopath does.