Chuck Walter

Representing motion: an experiment in learning

Abstract In this paper we concentrate on how students make sense of motion. To understand the challenges the students actually faced, we focus on how learners work with models, representations, and their personal experience. The student subjects are participants in the Kenilworth longitudinal study by the third author. They work on a task, based on a set of 24 time-lapse photographs, to determine how a cat was moving as it progressed from walking to running. We document how learners work with a wide range of graphic presentations, including inscriptions, calculator-generated plots, drawings, and photographs. Analysis centers on how students reason, based on these representations, to make sense of the cat’s motion.

Modeling Perspectives in Math Education Research

Too often powerful and beautiful mathematical ideas are learned (and taught) in a procedural manner, thus depriving students of an experience in which they create and refine ideas for themselves. As a first step toward improving the current undesirable situation in undergraduate mathematics education, this chapter describes several different modeling perspectives and their implications for teaching and learning.

Models as Tools, Especially for Making Sense of Problems

For us, a model is a tool to solve a problem. Our research concentrates on what learners actually do when they solve problems that demand fresh insight. We want learners to build ideas and understanding they can use to solve new problems. In relation to this goal, the ways specific models help make sense of novel situations can become important subjects for investigation. We anchor our discussion to concrete examples drawn from elementary arithmetic.