AN EXRIMENTAL STUDY OF “DISCOVERY” LEARNING

Purpose: The present, study investigates what instructional procedure facilitates the utilization, retention and transfer of a learned mathematical for-mula.<BR>The hypotheses are as follows:<BR>1) Those who comprehend the principle upon which the formula is derived will be superior in test performance to those who learn the formula by rote.<BR>2) Those who learn the principle by discovery will be superior to those who learn it receptively.<BR>These hypotheses are tested in the situation very similar to school education.<BR>Procedure: Ss are 93 girls in the 2nd grade of a senior high school. They are divided into 4 homogeneous groups with regard to mathematical achievement.<BR>G1: the formula only;<BR>G2: both the formula and the principle;<BR>G3: the formula and a hint to comprehend the principle;<BR>G4: only a hint facilitating the discovery of the formula.<BR>The formula to caluculate the sum of a arithmetic progression is learned.<BR>The instruction procedure consists of an explanation exercise. It lasts 25 minutes.<BR>Post-instruction tests are administered3times; immediately, one week and 8 weeks after the in struction. They include items concerning the retention, utilization and appliciation of the formula.<BR>Results: The main findings are as follows:<BR>1) As for the simple use of the formula and its transfer, no difference was found among the4- groups. But the performance of the G1, which was given no explanation of the reason why the formula was valid, was inferior to the other3groups when they are reqired to handle the formula in a complex way.<BR>2) G2 (a receptive learner) shows a marked decline from the one-week-after to 8-week-after post test, whereas G4 (a learner by discovery) gets high scores in both of these tests with only a slight change. These findings seem to support both of the hypotheses.<BR>Supplementary experiment: A supplementary experiment is conducted to clarify the process through which these differences are brought about. Fifteen 11 graders were taught the same formula individually. They are divided into 5 groups, 4 of which received the similar instructions to those of the main experiment, and the remaining one is the “no-hint” group. Observations of their learning processes suggest the following points:<BR>1) Ss of the G1 can calculate rapidly, but tend to use the formula in a rote manner and indifferent to how the formula is derived.<BR>2) While in Ss G2 cannot incorporate the formula and the principle into their cognitive structure, Ss in the G3 & G4, though they need much time for the use of the formula, tend to treat it in a flexble way.<BR>3) Even the Ss who are left to solve the formula themselves without any hint can calculate correctly but cannot arrive at the solution by a single formula.