Instructional Design in the Formation of Mental Images and the Genetic Decomposition of a Concept

Abstract

This paper reports on the instructional design used in an APOS (Actions, Processes, Objects and Schema) approach to difficulties experienced by first year engineering students at a University of Technology in constructing the concept of the chain rule. Instructional treatment followed the activities, classroom discussions and exercises (ACE) model as specified by a proposed genetic decomposition of the chain rule concept in differential calculus. This paper in particular presents instructional design used on three sequential lessons that were video recorded during class time in slots of one hour duration whilst introducing the chain rule to a class of about 197 first year students. Those lessons followed immediately after the students had done an introduction to calculus, differentiation using the product and quotient rules. Here I discuss in brief the techniques used in those lessons, instructional strategy used and the interactions between the researcher and the students, students to student collaborations in the classrooms. This was a qualitative study where the results revealed to a greater extent the effect of instructional design to an object understanding of the chain rule concept. The students’ interactions indicated that the instructional pedagogy should accommodate presentation of tasks that evoke rigorous deductive reasoning enabling the students to write and reflect on how they construct various mental images. A wide range of interactions between students themselves and between students and the researcher revealed that most students preferred the straight form technique and barely ever used Leibniz technique when differentiating loaded trigonometric functions.

DOI: 10.5901/jesr.2014.v4n3p139