Type of Document Dissertation Author Nancarrow, Michael URN etd-04022004-160144 Title Exploration of Metacognition and Non-Routine Problem Based Mathematics Instruction on Undergraduate Student Problem Solving Success Degree Doctor of Philosophy Department Middle and Secondary Education, Department of Advisory Committee
Advisor Name Title Elizabeth Jakubowski Committee Chair Leslie Aspinwall Committee Member Maria L. Fernandez Committee Member Sande Milton Committee Member Keywords
- Executive Control
- Problem Solving
- Metacognitive Control
- Non-Routine Problems
- Mathematical Resources
Date of Defense 2004-03-18 Availability unrestricted AbstractThe purpose of this research was to examine and attempt to influence the problem solving processes used by typical undergraduate mathematics students. A structured problem solving methodology designed to foster a heuristic way of reasoning was introduced and a study of how this treatment affected the participants' non-routine problem solving styles and abilities was performed.
An approximately equal mix of male and female student participants self-selected into three sections of precalculus algebra at a private southeastern institution. Each section consisted of approximately 15 students. The researcher and one other professor instructed the three sections. All sections were instructed using the same set of notes, were given the same assignments, and covered the same mathematical topics in the same order.
The research model consisted of the following elements.
1. Testing students in treatment and control sections for routine algebra skills necessary to successfully find solutions to specific non-routine problems.
2. Testing students in treatment and control sections for ability to solve non-routine problems that can be handled using the routine algebra skills on which they had previously been tested.
3. Providing metacognive control practice and instruction in the treatment section using a combination of weekly homework and in-class assignments.
4. Conducting pre- and post-treatment videotaped interviews of four treatment section students engaged in non-routine problem solving.
5. Analyzing interview records in an attempt to determine if any changes in metacognitive control occurred.
6. Examining statistical evidence gathered from the pre- and post-treatment examinations.
Results of the study were mixed. A significant increase in the statistical correlation between resources (mathematical facts and procedures) and non-routine problem solving success indicated that students may have benefited from the treatment by improving their metacognitive control of resources. However, analysis of the videotaped interviews did not reveal any significant change in the way students approached non-routine problems. Group statistical evidence comparing treatment to control sections seemed to substantiate most of what was observed during the interviews
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