Bob Speiser

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.

How does building arguments relate to the development of understanding?: A response to the last three papers

Abstract In mathematics, for professionals, the most compelling way to back a statement is to prove it. This could even be true, as recent research indicates, for 9-year-olds (or for even younger learners), given appropriate conditions in the early grades. In this article, based on data drawn from the three preceding papers, I explore some ways in which the building of an argument can emerge in step with the development of understanding.

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.