AN INVESTIGATION OF THE RELATIONSHIP BETWEEN LOGICAL THINKING STRUCTURES AND THE ABILITY TO CONSTRUCT AND INTERPRET LINE GRAPHS

This study investigates the relationship between logical thinking stru ctures and the ability to construct and interpret line graphs. Seventy -two subjects in 7th, 9th, and 11th grades were administered individua l Piagetian tasks to assess five specific mental structures: (Euclidea n spatial structures) (a) Placement and Displacement of Objects (maint aining horizontal and vertical reference frames) and (b) One-One Multi plication of Placement and Displacement Relations (coordinate systems) ; (c) Multiplicative Measurement; (d) Multiplicative Seriation; and (e ) Proportional Reasoning. Graphing abilities were assessed by having t he subjects construct and interpret numerous graphs of varying content and difficulty. To minimize the researcher's guesses about interpreta tion, each subject's answers and reasons were subsequently explored du ring a clinical interview. The results indicate significant relationsh ips of logical thinking to graphing ability. Multiplicative seriation, multiplicative measurement, and Euclidean spatial structures positive ly influenced graphing abilities. Subjects who showed evidence of prop ortional reasoning did significantly better on many graphing situation s including choosing the part of the graph with the greatest ''rate of change.'' Locating points on a graph without a grid was significantly related to horizontal/vertical frames of reference. Students who did not possess the logical thinking structures were more likely to be dep endent upon, and influenced by, perceptual cues and less able to inter pret or construct graphs correctly.