Investigation of students' application of critical thinking to solving related rates problems

Abstract

This study aims to explore students' critical thinking novel to the related rates problem. Students are having hard time to understand the concepts mainly because they are not understanding the meaning while they solve relates rates problem. Facione, Peter A suggested important critical thinking skills and subskills are essential for success in each endeavor. I leveraged these skills to inform the design of task-based questions that I used when I interviewed with students to understand how their reflective thinking makes the problem progress or how wrong reasoning made them incorrect answer. The result of my study indicates that failing to engage in critical thinking skills such as Interpretation, Analysis, Evaluation, Inference, Explanation, and Self Correction will demonstrate wrong conceptualize meaning of related rates and derivatives. Also, the result suggest that students did not understand the meaning of implicit differentiation and the rates and showing difficulty of solving tasks. Thus, Instructors should develop conceptual understanding of related rates to encourage them to engage in critical thinking while they solve problems and provide them variety of problems to improve the skills.