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Flawed Thinking Problem
I used the Flawed Thinking problem to teach about the concept of metacognition, and to test how well students apply previously learned ideas about learning to this new situation. Students were asked to explain the basis for each of the episodes and also explain the phenomenon common to all five episodes.
ADDITION. A 5th grade student worked at the blackboard on the following problem 354 + 249. After some time he solved it correctly. The teacher then gave him another problem, 354 + 250. He immediately set about doing it, and eventually solved it. Then the teacher gave him a third problem, 354 + 250. Again, the student burrowed in and eventually after considerable time solved the problem.
THE CARD GAME. A study with elementary school students asked children of varying ages to evaluate the directions to a "new card game" and point out any problems in the directions. The directions were:
We each put out cards in a pile. We both turn over the top card in out pile. We look at the cards to see who has the special card. Then we turn over the next card in our pile to see who has the special card this time. In the end the person with the most cards wins the game.
Younger children needed many prompts before they realized the gaps in the instructions.
DO YOU REMEMBER? A study of memory development used several groups of children. Each was given 15 cards with pictures of common objects on them. The children were instructed to study the cards until they could remember all of them, and then tell the adult experimenter they were ready to be tested on them. The results indicated that the older children studied the cards and then remembered the entire set. Younger children studied the cards, indicated they were ready, but then were able to remember only a few cards.
THE SIGNATURE. Harvard psychologist Ellen Langer reports the following experience
Once in a department store I handed the cashier a new credit card. Noticing that I hadn't signed it, she handed it back to me to sign. Then she took my card, passed it through her machine, handed me the resulting form, and asked me to sign it. I did as I was told. The cashier then held the form next to the newly signed card to see if the signatures matched.
HOW MANY BUSES? In a national test with 45,000 students, 13-year-olds were given the following problem.
"An army bus holds 36 soldiers. If 1,128 soldiers are being bused to their training site, how many buses are needed?"
70% of the students performed the division correctly but 29% wrote that the number of buses was 31, remainder 12, and another 18% wrote that the number of buses was 31. Only 23% gave the correct answer.
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