In a classic study in the area of problem solving, Katona (1940) compared the effectiveness of two methods of instruction. One group of participants was shown the exact, step-by-step procedure for solving a problem and was required to memorize the solution. Participants in a second group were encouraged to study the problem and find the solution on their own. They were given helpful hints and clues, but the exact solution was never explained. The study included the problem in the following figure showing a pattern of five squares made of matchsticks. The problem is to change the pattern into exactly four squares by moving only three matches. (All matches must be used, none can be removed, and all the squares must be the same size.) After three weeks, both groups returned to be tested again. The two groups did equally well on the matchstick problem they had learned earlier. But when they were given new problems (similar to the matchstick problem), the memorization group had much lower scores than the group who explored and found the solution on their own. The following data demonstrate this result.

Memorize Solution	Explore to Find Solution
n = 8 M = 10.50 SS = 108	n = 8 M = 6.16 SS = 116

Is there a significant difference in performance on new problems for these two groups? Use a two-tailed test with = .05.

t-critical	=
t	=

Reject the null hypothesis; there is a significant difference.

Fail to reject the null hypothesis; there is no significant difference.

Fail to reject the null hypothesis; there is a significant difference.

Reject the null hypothesis; there is no significant difference.

t Distribution

Degrees of Freedom =21

-3.0-2.0-1.00.01.02.03.0t

Construct a 90% confidence interval to estimate the size of the mean difference.

0.818 to 7.862

0.340 to 8.340

2.579 to 6.101

2.340 to 6.340