## Date of Award

12-1-1991

## Document Type

Dissertation - NSU Access Only

## Degree Name

Doctor of Education

## Department

Center for the Advancement of Education

## Abstract

The purpose of this Major Applied Research Project was to investigate the weaknesses in post-secondary mathematics problem solving and to develop an instructional design that would help mathematics majors become better problem solvers. A case study was conducted including an extensive literary search to determine which strategies were needed to enhance problem solving. Three basic research restrictions were examined: 1. Why do Brescia mathematics majors fail to develop correct cognitive strategy selection during their normal course of study. 2. How can an appropriate course of study be designed to teach proper cognitive strategy selection? 3. How can an appropriate course of study be implemented into the Brescia mathematics curriculum? Each Brescia mathematics course was carefully studied to determine which cognitive strategies were covered in the curriculum. Tests were given to Brescia College mathematics majors and interviews conducted to determine which strategies were used in problem solving. Upper level mathematics courses were carefully studied to determine which additional strategies were needed in those courses and how they could be learned. An appropriate instructional design including a model textbook was created to eliminate the problem-solving deficiencies of Brescia College mathematics majors. In addition an implementation plan was developed for extending the problem solving techniques to other courses and programs. Four conclusions were reached as a result of the study. First, Brescia College mathematics majors failed to develop correct cognitive strategy selection during their normal course of study because the existing curriculum was not designed to teach cognitive strategies. The second conclusion was that an effective course of study for teaching cognitive and metacognitive strategies would benefit Brescia College mathematics majors by preparing them for upper level courses. The third conclusion was that an effective course of study must clearly present those strategies in a holistic way similar to the Harvard Case Study Method. Students who participated only in the traditional lecture-recitation method of problem solving did not develop the appropriate cognitive strategies. The fourth conclusion was that a course of study that would teach the necessary strategies could be implemented into the Brescia College mathematics curriculum students sophomore year. Recommendations derived from the study were that: (1) The proposed course of study shall be implemented into the curriculum during the spring of 1991. (2) Formative evaluations should be conducted during the course as well as during future Brescia College mathematics courses to determine if the students participating in the strategy course were more successful ln problem solving during. higher level classes. (3) A similar study should be undertaken to determine if the method of strategy instruction can be implemented into other Brescia College mathematics or science classes. The final product was the development of an instructional design and text to teach a three credit hour course in problem solving during the spring semester of 1991. The model text included a chapter on the process of developing mathematical strategies and the background material that the students needed to use those strategies.. Additional problems were added to help the students mesh those strategies into higher order skills. The instructional manual included a clear and detailed plan for presentation of each of the strategies and how the strategies are to be used in mere advanced classes and real life situations. Sample tests and other measures were included to be used ln the formative evaluation. It is with the authors great expectation that this instructional design will lead to new ways of presenting mathematics in the classroom at all levels of instruction. The improvement of strategy selection among mathematics students at Brescia College will result in a new and more able generation of future problem solvers.