Geometric error analysis in applied calculus problem solving

The paper investigates geometric errors students made as they tried to use their basic geometric knowledge in the solution of the Applied Calculus Optimization Problem (ACOP). Inaccuracies related to the drawing of geometric diagrams (visualization skills) and those associated with the application of basic differentiation concepts into ACOP solution were reported. A test instrument was used to collect quantitative data, while qualitative data were generated using follow- up interviews (stimulated recall). The targeted samples were freshmen students who registered for Calculus I in the department of Mathematics at a University in south eastern region of the United States of America, USA. The study indicated that students had achieved a very low success rate on the ACOP solution process, immediately after receiving/completing instruction on the optimization in their calculus I class. In general, they failed to integrate basic geometric competences required in the ACOP solution. Qualitative evidence from students’ test performance indicated that failure to visualize geometric diagrams from word problems tended to preclude them getting the required formula. The overall finding of the research was that students face structural and procedural setbacks that ultimately led to a worsening of the ACOP solution process.