Factors influencing the problem solving of college students solving a mathematics problem in a small group
Crawford, Linda Bailey
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This study investigated the problem solving of college students as they worked together in a small group to solve a mathematics problem. Eight students participated in the study and were divided into two groups of four. All eight students completed a semester of precalculus mathematics (MATH 1113) the spring semester of 2002. The researcher was the teacher for the two precalculus classes from which the participants were selected. The students were asked to participate in the study after the MATH 1113 class was completed. Data collection for the study occurred between May 15, 2002 and August 14, 2002. Data for the study included individual interviews, observations and videotapes of problem-solving sessions, and written reflections. The final interviews used video clips from the problem sessions to stimulate participant recall. Group 1 required four sessions of approximately one hour each to complete the problem whereas Group 2 solved the problem in one session of about one hour. The approaches used by the two groups were different and the dynamics within the two groups were different. The study identified the factors influencing the group problem solving and described how these factors influenced the problem solving. Schoenfeld’s (1992) definition of problem solving as learning to think mathematically was the definition of problem solving used in the study. The factors influencing collaborative problem solving identified by Watson and Chick (2001) were used as starting points to identify the factors influencing the problem solving in the two groups. Social, cognitive, and external factors were identified and found to interact. Social factors influencing the problem solving included leadership factors, egocentrism, and social collaboration. Cognitive factors included cognitive ability, prior experience, a sense-making perspective, communication factors, the big picture, and goal focus. External factors included task factors, outsider, and logistical factors. The processes the groups used to solve the problem were described through the identification of these influencing factors. The problem solving in the two groups differed as a result of how the participants allowed these factors to influence them personally. A significant observation from the study was the number and type of misconceptions the students possessed.