I first came across Wason’s Selection Task while reading Dan Willingham‘s Why Don’t Students Like School. I’ll use the wording of the problem that Willingham uses in the article entitled “Inflexible Knowledge” that appeared in American Educator.

Example 1

Consider this classic example (Wason, 1968). Each of the four figures below represents a card. There is always a letter on one side of the card and a number on the other side. Your job is to verify whether or not the following rule is true: If there is a vowel on one side of the card, then there must be an even number on the other side. What is the minimum number of cards you must turn over to test the truth of the rule [and what are they]?

If you’ve never seen this question. I want you to think about it for a moment and write down your answer.

Read on when ready.

The answer is that you must turn over the A card and the 3 card. Most people choose the A card, but most fail to select the 3. You must choose the 3 because if there is a vowel on the other side, then the rule has been violated. Something like 20 percent of college undergraduates get this problem right. The percentage goes up very little even when subjects have just completed a one-semester course in logic that includes learning the logical form Modus Tollens, on which this problem is based (Cheng et al., 1986).

Example 2

Now consider another version. You are an officer at the border of a country. Each of the four cards that follow represents a traveler. One side of the card lists whether the person is entering the country or is in transit (just passing through). The other side of the card shows what vaccinations the person has received. You must make sure that any person who is entering the country is vaccinated against cholera (Cheng & Holyoak, 1985).

About which travelers do you need more information? You need to check the “entering” person (to ensure that he has the cholera vaccination), and you need to check the “flu mumps” person (to ensure that he is in transit).

The lesson here is that:

This question has exactly the same formal structure (Modus Tollens) as the previous problem, but people are much more likely to get it right. Why? Because this problem has a concrete structure that makes sense–it doesn’t use letters and numbers–and the rule about disease and entry is sensible, not arbitrary. The idea that the human mind prefers to consider novel concepts in concrete ways should ring true to every teacher. When presented with a new abstract idea or formula, students clamor for examples.

There is an alternate rewording of the Four Card Task from Willingham’s book.

Example 3

You are to imagine that you are a bouncer in a bar. Each card represents a patron, with the person’s age on one side and their drink on the other. You are to enforce this rule: If you’re drinking beer, then you must be twenty-one or over. Your job is to verify whether this rule is met for this set of four people. You should turn over the minimum number of cards necessary to do so. Which cards would you turn over?

If you’re like most people, this problem is relatively easy: you flip the beer card (to be sure this patron is over twenty-one) and you flip the 17 card (to be sure this kid isn’t drinking beer). Yet logically the 17 card has the same role in the problem that the 3 card did in the previous version, and it was the 3 card that everyone missed.

This one is even more familiar to students since high school teenagers are very aware of when it is legal for them to do things (like drinking, smoking, and driving) on their own.

I encountered these questions in the following order: Example 1, Example 3, and Example 2.

For me, Example 3 was the quickest and easiest. It should be for anyone who grew up familiar with a legal system that sets restrictions on purchase and/or consumption of alcoholic beverages. That would be just about anyone who might come across this blog. I can imagine this to be difficult question for someone from a culture without this kind of restriction. There’s something to be said about how real world experiences can help students learn abstract principles, but that’s for another post.

Example 1 took a little longer to come up with the right answer. It might be due to the fact that it was the first problem of its kind that I encountered. The first thing that popped into my mind was contrapositive. I don’t know why that happened, but I guess all that practice done in Geometry in high school didn’t go to waste.

Interestingly, of the 3 questions, Example 2 took me the longest to solve. It took me a while before I understood what they meant by “Entering” and “Transit” and then I was stuck for a while on the word mumps. I’m familiar with the words cholera, flu, and typhoid but not so much so for mumps. I was also distracted by the presence of mumps in 2 cards. I was being cautious about potential tricky situation, but worried for naught in this case.

I’ll follow up on the wording of the question angle, but for now I’m thinking about whether this could be a good teaching tool or maybe a good example to start discussion in class.

For the following scenarios:

• What is the least number of cards you need to turn over to verify the statement is true?
• What cards are they?

One common example is “If it rains, then the ground is wet.”

A colleague uses “If an animal is a dog, then it’s a mammal.”

More generally “If P then Q.”

Maybe instead of asking about “If P then Q” we could ask about “If not Q then not P.” Would that tip off the students? If we did that then we’d have “If you’re not twenty-one or over then you’re not drinking beer” instead.

I don’t teach a Geometry class this year. Maybe this will be useful to someone. So what do you think? Good idea? Bad idea? Worth the time? Waste of instructional time in a math class? Do you have a different way of using this idea?

NOTE: Peter Wason was a cognitive psychologist. There’s also an entry about him under Confirmation Bias.

UPDATE: Dropped the “Contrapositive” from an earlier title of this post of “Wason’s Selection Task and the Contrapositive.” That could be a spoiler for people who haven’t seen this question before.
UPDATE2: The tables were replaced with pictures. Custom CSS don’t show up properly in Google Reader.
UPDATE3: I goofed example 3′s thumbnail. It’s fixed now.