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UBC Theses and Dissertations

The effect of problem context upon the problem solving processes used by field dependent and independent students : a clinical study Blake, Rick N.


It was the purpose of this study to analyze the processes students used in solving mathematical word problems and to determine the effect of problem context on these processes. A concomitant purpose was to determine whether students who differ in their degree of field independence, differ in the processes they use in solving mathematical problems. Forty subjects of both sexes, who were completing a grade eleven academic mathematics program were randomly selected from 14 Algebra II classes. The subjects were of average ability for students on this program (IQ range 115-125). The subjects were tested individually, using Witkin's Embedded Figures Test. They were matched on this variable and randomly assigned to one of two groups. One group was given problems using a real world setting, while the other group was given the same problems using a mathematical setting. The subjects were individually interviewed and asked to think aloud as they solved five mathematical word problems. To analyze the problem solving procedures the subjects' tape recorded protocols of the interviews were coded by means of a system based on a model of mathematical problem solving by MacPherson. The coding system had two parts: a coding matrix used to sequentially code problem solving behavior, and a summary sheet for compiling information obtained from the coding matrix as well as other data related to the subjects' problem solving behavior. The coding system had intercoder reliability of .80 and intracoder reliability of .86. Problem context proved to be unrelated to the heuristics used. Both the total number of heuristics used and the number of different heuristics used were not influenced by problem setting. Subjects working problems in the math world setting had a slightly more difficult time understanding the problems, but performed as well as the other group. Within the IQ range, 115 to 125, field independence had a marked effect on the use of heuristics and on the number of correct solutions obtained. The field independent subjects used a greater variety of heuristics (r = .33) in attacking and solving problems. They were more willing to change their mode of attack (r = .27) and they obtained a greater number of correct solutions (r = .30) than their field dependent counterparts. Both total number of heuristics as well as number of different heuristics, accounted for a significant (P <.0l) amount of the variance in number of correct solutions. In particular, heuristics accounted for an additional 21% of variance not accounted for by core procedures (algorithms, diagramming, equations, and guessing). The heuristics used by the subjects in this study added to their ability to solve problems beyond their mathematical core knowledge. The number of times a subject attempted to solve a problem was found to be unrelated to obtaining a correct solution, while changing one's mode of attack in solving a problem was significantly (P <.0l) related to obtaining a correct solution. When the subjects were grouped by problem context, both groups exhibited the same general pattern of problem solving behavior. The real world students expressed concern for solutions obtained using heuristics while those students in the math world setting expressed none. However, expression of concern for solution was unrelated to the correctness of the solution. When grouped by field independence a difference was observed in the overall pattern of sequential moves in the problem solving process. These differences among the groups were not tested for statistical significance. The field independent student moved more freely across all procedures coded. He was more concerned with his work, and continually checked both the procedures he was using as well as his solution. The field independent student was more willing to check his work, usually by retracing his steps, whereas the field dependent student usually reread the problem.

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