This study investigated the quantitative and qualitative aspects of the sequence of steps taken in a solution path for solving conic sections (parabola, ellipse and hyperbola) problems. It identified critical behaviors or incidents, habits or mannerisms of students during problem-solving to determine the relation of these to the understanding of the concept of conics. The think-aloud interview technique was used in conjunction with an interpretive method of case study observation. The data came

more »

... from sixteen (16) case studies of first-year students in the Bachelor of Science in Agricultural/Civil Engineering programs, also referred as General Engineering. The result of the Prior Knowledge Test on Conics was the basis in selecting the subjects. Starting with the highest score, the 8 top-scoring students were classified as the Top-8 Group, and the 8 lowest scoring students were classified as the Bottom-8 Group. The subjects were asked to solve six problems in conic sections, two problems each (one routine and the other an application problem) on parabola, ellipse and hyperbola. Their verbalizations were tape-recorded, and their behavioral characteristics were observed as they individually solved the problems. The quantitative and qualitative data obtained showed that the unsuccessful problem solvers had difficulty in solving the conic problem because of: a) Insufficient knowledge and recall of the standard equations for conics for specific conditions or situations; b) Incomplete use or non-use of the properties for graphing the curve ; c) Poor understanding of the concept of asymptotes ; d) Lack of mastery of skills in algebraic manipulations; not carrying out the operations accurately; confusion in using coordinates of points; e) Poor understanding of the English language; f) Failure to make illustrations using information about the task; inability to explore real-world application problems; not representing the variables correctly, and failure to develop an algorithmic procedur [...]