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Publications and Presentations

Research articles using the VideoPaper format are to be published in forthcoming CD-ROM issues of the Journal of Research in Mathematics Education and Educational Studies in Mathematics. Authors in the U.K, Italy, Israel, Brazil, and the U.S. have contributed to these volumes. Researchers have also used the format to present their work at several conferences.

On Forms of Knowing: The Role of Bodily Activity and Tools in Mathematical Learning

Chris Rasmussen, San Diego State University
Ricardo Nemirovsky, TERC
Jennifer Olszewski, Kevin Dost, and James L. Johnson, Purdue University Calumet

We analyze three undergraduate students' evolving ways of knowing ideas associated with system dynamics in a series of open-ended interviews as they work with a tool we call the “water wheel.” We characterize how bodily activity and emerging tool fluency combine in mathematical learning and how this combination suggests an alternative view on the nature of knowing. In particular we develop the idea of knowing-with, which characterizes aspects of meaning making as it relates to developing expertise with tools. We propose that the idea of knowing-with is not a different type of knowing to be contrasted with the well-known distinction between knowing-how and knowing-that, but rather a distinction independent of these other forms of knowing. Our analysis suggests that knowing-with a tool (1) engages multiple and different combinations of dwelling in the tool, (2) invokes the emergence of insights and feelings that are unlikely to be fully experienced in other ways, and (3) is situated in the moment.

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Approaching Functions through Motion Experiments

Ferdinando Arzarello, Ornella Robutti
Dipartimento di Matematica, Universitˆ di Torino

The paper describes an approach to Calculus in secondary schools within technological environments. It illustrates a case study, where the concept of function is introduced in the 9th grade using a motion sensor connected to a calculator. Pupils can move and see the Cartesian representation of their movement produced by the calculator in real time, on a space-time graph. The paper analyses some protocols from working groups and class discussion. Within a general Vygotskian frame, the authors use different complementary tools to analyse the situation: the embodied cognition by Lakoff and Nuñez, the instrumental approach by Rabardel, the cultural-semiotic approach by Radford. In particular the role of the perceptuo-motor activity in the conceptualization of mathematics is stressed. In the end, some problems and lines of investigations are pointed out.

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