Insightful Solution of a Geometry Problem with Instructional Cues: I. Group Experiments
The purpose was (1) to determine empirically the extent of insight exhibited by 429 high school and college students in solving a geometry problem directly solvable by insight without mathematical computations and (2) to study the effects of instructional cues and educational status. Educational status ranged from high school through college freshmen to upper-division students. Insightful solutions were achieved by about 4% of the participants under Condition I with no cues as a control, about 3% under Condition II where an unsolvable Pythagorean equation with two unknown sides was given, about 13% under Condition III giving a solvable Pythagorean equation with two sides of known lengths, and about 16% under Condition IV with an instructional cue that diagonals of a rectangle are equal. The last condition and the combined results suggest insightful solution increases with educational status. Two types of noninsightful responses were noted: empty or no answer and wrong response or incorrect approach through computations. The first type tends to increase, while the second to decrease from high school to college status probably due to a growing cautious deliberation with maturity and higher education. A training program on “the formation of insight sets” is proposed.