Cognitive Economy in Physics Reasoning: Implications for Designing Instructional Materials

Abstract

In this chapter we discuss observations arising from our work with think­ aloud protocols of novices' attempts at kinematics problems. We report on some general observations made on their problem-solving techniques and examine one key issue in detail, namely whether multiple representations are a help or hindrance to problem solving. Modeling the successful and unsuccessful problem-solving behavior of pairs of students has led us to formulate the hypothesis of cognitive economy. Novices solving a physics problem can more easily achieve success when they restrict themselves to using only one representation of the problem. The cognitive economy hypothesis has consequences for the design of intelligent tutoring systems (ITS). In particular it implies that imposing constraints on the learning environment, rather than being a wholesale limitation of conventional intelligent tutors, is a positively helpful act. The chapter is divided into four main sections. The first section describes our motivation for studying the domain of physics and introduces a prin­ ciple-cognitive economy-that we believe is essential in accounting for the various apparently strange behaviors students exhibit while solving problems. The first section also describes various approaches to teaching problem solving and gives a brief review of the cognitive science/artificial intelligence literature in this area. The second section deals with data col­ lection. We are convinced that the accumulation of good-quality data on individuals' attempts to solve problems is a prerequisite for work in this area. We describe our data-collection methods, the type of problems we use, and two studies involving data from individuals and pairs. The third section of the chapter discusses a key experiment that we have recently conducted. Pairs of students were presented with a problem that forced them to shift from one representation to another. We analyze these data and discuss a production rule framework that we used to construct models to account for the observed behavior. The last section discusses the results,