Calculus instructors’ perspectives on effective instructional approaches in the teaching of related rates problems

Abstract

Much research has reported on students’ difficulties with solving related rates problems in calculus. In an effort to generate a resource that could potentially address some of these difficulties from a teaching standpoint, a questionnaire about effective instructional approaches related to the teaching of related rates problems, among other things, was administered to 14 veteran calculus instructors. Analysis of the responses provided by the instructors revealed that all the instructors considered the use of diagrams to be helpful when solving related rates problems. Furthermore, a majority of these instructors noted that introducing a set of steps (i.e., a guideline), during classroom instruction, that students could follow when solving related rates problems is helpful for students when working with this type of problems. These instructors further identified strengths and weaknesses in the way related rates problems are typically presented in calculus textbooks. Implications for instruction are included.

Best practices for teaching the concept of the derivative: Lessons from experienced calculus instructors

“…Motivated by the scarcity of research that specifically addresses effective instructional approaches related to the concept of the derivative, the current study reports on veteran calculus instructors' perspectives on effective instructional approaches and educational technologies related to the teaching of the concept of the derivative in calculus. On a related note, a recent study (Mkhatshwa, 2023b) investigated experts' views regarding effective teaching approaches in the context of related rates problems in calculus. This study found that using diagrams during classroom instruction could be helpful in supporting students' reasoning about rate quantities that could be represented by derivatives when working with this type of problems.…”