Using Multiple Representations to Improve Conceptions of Average Speed

Abstract

We evaluated a computer-based learning environment that uses multiple representations to improve students' conception of the average speed of a round trip. The instruction explained that average speed is a weighted average of the component speeds in which the weights reflect the amount of time spent traveling at each speed. Students then improved their estimates of average speed by using visual feedback provided by a simulation. Correct answers and estimates were plotted on a graph to encourage students to discover the principle that average speed cannot be greater than twice the slower speed. A conceptual explanation (average speed as the ratio of total distance to total time) and an algebraic explanation (the limit of a function) helped integrate the multiple representations of the concept. Students' responses during the instruction and to a questionnaire provided useful information for improving the program, which was then reevaluated in a second study. The concluding discussion summarizes how the multiple representations were used in the instruction and examines the different functions of the representations based on Ainsworth's (1999) taxonomy.