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.