Type of Document Dissertation Author Usman, Ahmed Ibrahim Author's Email Address ahmediu22@yahoo.com URN etd-08142008-150737 Title Analysis of Equation and Diagram Construction in Applied Calculus Problem Solving Degree Doctor of Philosophy (Ph.D.) Department Educational Theory, Policy, & Practice Advisory Committee

Advisor Name Title David Kirshner Committee Chair Eugene Kennedy Committee Member James Madden Committee Member Kristin A Gansle Committee Member Tom Ricks Committee Member Qin J Chen Dean's Representative Keywords

- optimization
- Applied Calculus
- visualization
- concept image
- concept definition
- transformation/symbol skills
- algebraic
- geometric
Date of Defense 2008-08-04 Availability unrestricted AbstractThe purpose of this study was to assess algebra and geometric prerequisites skills as incorporated into the Applied Calculus Optimization Problem (ACOP) solution. The difficulties that students encounter in applying algebraic and geometric prerequisites at the early stages of the ACOP solution were identified. The study analyzes errors related to variables and equations (i.e. algebraic symbol/transformation skills), drawing of geometric diagrams (visualization skills) and those associated with application of basic differentiation concepts into ACOP solution process.The study’s goals were addressed as seven specific research questions further subdivided into three main parts: the first four research questions investigated prerequisite algebraic and geometric skills, while question five examined the ability to use some or all of the prerequisite skills to obtain the required ACOP model. Question six is concerned with how some prerequisite (differentiation) skills are use in ACOP solution process. Finally, question seven looked into students’ ability to fully bring into play all the prerequisite skills into ACOP solution process. Furthermore, each of the seven research questions was split into quantitative and qualitative parts. The quantitative data were collected using a test instrument; and a follow up interview was conducted to collect qualitative data. These qualitative data were used to supplement, support and illuminate results from the quantitative components. The target sample is freshmen students taking calculus I in the department of mathematics, Louisiana State University, Baton Rouge.

Overall, the study has revealed that students have achieved a very low success rate on ACOP, immediately following instruction on ACOP solving in their calculus I class. In general, they failed to integrate the basic competences required in ACOP solution. Qualitative evidence from students’ test performance indicated that failure to visualize geometric diagrams from word problems tendered to preclude getting the required formula. More generally, failure in at least one competence lead to collapse in another, and hence the whole breakdown of the ACOP solution process.

The overall finding of the research was that students generally failed in integrating the independent algebraic and geometric competences; in cases where integration occurred, students face structural and procedural setbacks that ultimately led to a weakening of the ACOP solution process.

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