Insightful Solution of a Geometry Problem with Instructional Cues: II. Individual Studies

Abstract

As a sequel to a group experiment, this paper reports a study of the effects of instructional cues on individuals' insightful solutions to a problem in geometry. 96 college freshmen, 28 men and 68 women, were selected from hundreds of volunteers, carefully matched for mathematical background and divided into four equal groups who were given varying graded amounts of suggestive instructional cues. Group I, a control without cues, yielded the lowest percentage of insightful solutions but consumed the longest time; Group II, with an unworkable equation, gave more solutions in shorter time upon stratified analysis, but seemed to show some detrimental effect of the misleading cue on the whole group's gross mean time; Group III, with a solvable equation, produced still better scores both in amount and speed as well as four correct answers by computation; Group IV, with a direct cue that diagonals of a rectangle are equal, achieved the best performance. By manipulating the variables of sampling and procedure, the pooled mean score has been raised from the less than 9% obtained earlier in a group experiment to 50% insightful solutions.