Communicating Experience of 3D Space: Mathematical and Everyday Discourse

Abstract

In this article we consider data arising from student-teacher-researcher interactions taking place in the context of an experimental teaching program making use of multiple modes of communication and representation to explore three-dimensional (3D) shape. As teachers/researchers attempted to support student use of a logo-like formal language for constructing 3D trajectories and figures in a computer microworld, a system of gestures emerged. Observations of multimodal classroom communication suggest that teachers/researchers and students used similar words and gestures to represent different types of movement. We discuss possible sources of these differences, contrasting formal mathematical and everyday systems of representation of 3D space. More generally, we argue that understanding the structures of everyday discourse and their relationships to the structures of specialized mathematical discourse can provide insight into student interactions.

ACKNOWLEDGMENTS

We wish to thank the school, teachers, and students who allowed us to work with them on the ReMath project. In particular, we appreciate the collaboration of GD in planning and teaching and her permission to use her image to illustrate this article.

Notes

This research was carried out as part of the ReMath project (Representing Mathematics with Digital Technology), funded by the European Commission Framework 6 Programme IST4–26751.

¹The ReMath project (Representing Mathematics with Digital Technology), was funded by the European Commission Framework 6 Programme IST4–26751

²This “necessity” is, of course, open to challenge and resistance. The forms of scientific and mathematical writing have evolved over time, just as the nature of scientific and mathematical activity has changed. Even in the relatively narrow field of academic research papers in mathematics, there is considerable variation in the language used (Burton & Morgan, 2000).

³We use register in Halliday's (1974) sense:a set of meanings that is appropriate to a particular function of language … [thus we] can refer to a “mathematics register,” in the sense of the meanings that belongs to the language of mathematics (the mathematical use of natural language, that is: not mathematics itself), and that a language must express if it used for mathematical purposes. (p. 65) This is different from Duval's (2006) use of register to denote a specialized mode of representation (e.g., algebraic notation or Cartesian graphs).

⁴The pedagogic plans used in the ReMath project may be found at http://remath.itd.cnr.it/index.php.

⁵“Programmable constructions in 3D geometrical space (familiar)” http://remath.itd.cnr.it/index.php?cmd=view.

⁶See McNeill's (2005) development of his characterization of gestures, recognizing iconic and deictic as dimensions rather than categories of gesture.

⁷In fact, two axes is the minimum required to define any rotation, but using only this minimum can result in more complex sequences of turns. For example, any pitch can be achieved by a combination of rolls and turns. In the simplest case, a pitch up 90° can be substituted by the sequence roll right 90°, turn left 90°, roll left 90°.

⁸An exercise I (CM) remember being set (and enjoying) at primary school involved being required to substitute other verbs for go or get in a pageful of such sentences.

⁹The online dictionary Dictionary.com (http://dictionary.reference.com/browse/go) shows 98 distinct uses for go and 63 for get.