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 3 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.

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

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

Incidentally, if you still have not discovered the solution to the matchstick problem, keep trying.
According to Katona’s results, it would be very poor teaching strategy for us to give you the answer. If you still have not discovered the solution, however, check Appendix C at the beginning of the problem solutions for Chapter 10 and we will show you how it is done.

Memorization of the Solution n=8 M = 10.50 SS=108 Find a Solution on Your Own n = 8 M = 6.16 SS=116