LINDA BAILEY CRAWFORD
B.S., Georgia College, 1975
M.Ed., Augusta College, 1988
A Dissertation Submitted to the Graduate Faculty of The University of Georgia in Partial
Fulfillment of the Requirements for the Degree
DOCTOR OF PHILOSOPHY
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