1. 2 4 6 Classic Problem What is the Rule? Wason’s 2 -4 - 6 Problem
HYPOTHESIS TESTING: CONFIRMING THE HYPOTHESIS VS. SEEKING DISCONFIRMING EVIDENCE
Classic
Problem
Wason’s Problem
Evidence of Confirmatory Bias
The Numbers:
What is the Rule?
Now, you suggest a set of 3 numbers and write down why you picked them. After each set, I’ll tell you whether they follow the rule.

2. A Typical Subject’s Data Showing Confirmatory Bias
Trial Subjects #’s Hypothesis Feedback Strategy
Increasing by 2s Yes Confirmatory
Increasing by 2s Yes Confirmatory
Increasing by 2s Yes Confirmatory
Increasing by 2s Yes Confirmatory
Increasing by 2s Yes Confirmatory
Increasing by 2s Yes Confirmatory

3. CONTROL OF VARIABLES: THE CANAL PROBLEM
You are asked to determine how canals should be designed to optimize boat speed. Working with an actual canal system and timing the boats from start to finish, you can conduct experiments to identify factors that influence speed. (boats are towed with a string and pulley system)
Variables:
large and small boats
square, circular, and diamond shaped boats
canal can be shallow or deep
you can make a boat heavier by adding a barrel
Counterintuitive: boats are faster in deeper canal, shallow canal due to greater turbulence

4. CONTROL OF VARIABLES: THE CANAL PROBLEM
A typical 11 year old child’s experimentation:
Trial 1: small, circular, light boat in a deep canal
Trial 2: large, square, heavy boat in a shallow canal
After Trial 2, the child concluded that weight makes a difference, but when asked to justify the conclusion, he simple said that if the boat in Trial 2 had been light it would have gone faster.
Trial 3: small, diamond-shaped, light boat in a shallow
canal
Child predicts that the boat in Trial 3 would go faster than the boat in Trial 2 because “it depends on how much edging is on the thing” (a hypothesis about the shape)
Note: child fails to systematically test hypotheses, only notices confirmatory evidence

5. CONTROL OF VARIABLES: THE CANAL PROBLEM
A college student’s experimentation:
After numerous trials the student summarizes what she has accomplished so far.
Well, so far we worked with small boats. First, light, and then we added the weight to each of them, and we found that without the weight they would go faster. We also found out that the diamond shape was the fastest, with the circle being next. And the slowest was the square. Let’s take the bigger boats in the deeper water. We’ll start with the square and go in order.
Student notices the counterintuitive result with depth of canal. She immediately searches for a plausible explanation.
“My God! It does have an effect! It takes longer in shallow water! The only thing I can figure out is that the depth of water would have something to do with the buoyancy. The added water, adds more buoyancy, making the boat sit up higher in the water.

6. EXPERT/NOVICE DIFFERENCES: THE CAR PROBLEM
A car traveling 25 meters per second is brought to rest at a constant rate in 20 seconds by applying the brake. How far did it move after the brake was applied?
Here are some useful equations:
1. distance = average speed x time
2. final speed = initial speed + (acceleration x time)
3. average speed = (initial speed + final speed) / 2
4. distance = (initial speed x time) + 1/2 (acceleration) x time2
5. final speed2 - initial speed2 = 2 (acceleration x distance)

7. EXPERT/NOVICE DIFFERENCES: THE CAR PROBLEM
1) Experts solves these types of problems faster
2) Experts have their formulas integrated into larger units
(knowledge is more interrelated)
In contrast, novices have a list of separate formulas
3) Experts start with givens and work their way toward the
unknown.
In contrast, novices look for a formula with the unknown,
and work from there.

8. EXPERT/NOVICE DIFFERENCES: THE COMPLETE LIST
experts perceive meaningful patterns in their domain
experts are fast; and they make fewer errors
experts show superior short-term and long-term memory for domain-related materials
experts see and represent a problem in their domain at a deeper (more principled level)
experts spend more time analyzing problem qualitatively
experts have strong self-monitoring skills