Conversations with Materials and Diagrams about some of the Intricacies of Oscillatory Motion
- PDF / 2,690,565 Bytes
- 25 Pages / 439.37 x 666.142 pts Page_size
- 105 Downloads / 176 Views
Conversations with Materials and Diagrams about some of the Intricacies of Oscillatory Motion Ricardo Nemirovsky 1 Matthew Voigt 3
& Giulia
Ferrari 2
& Chris
Rasmussen 3 &
# The Author(s) 2020
Abstract This article relates a case study on how a conversation with materials and diagrams – the actual use of materials and diagrams to think, imagine, explain, collaborate, design and build – featured a certain kind of interplay between material and digital components. The physical components present in this setting included a water wheel, which is a wheel driven by flow of water whose rotational motion is a classic example of chaotic dynamics regulated by Lorenz equations. Digital components allowed for real-time graphical displays corresponding to the turning of the water wheel. We selected for this article a sequence of episodes from an interview with Jake, an undergraduate student majoring in engineering. Through a micro-ethnographic analysis, we reflect on how Jake combined the responsiveness of the digital displays with the tangibility of the water wheel to gain insight into some of the intricacies of oscillatory motion. Keywords Diagrams . Materials . Micro-ethnography . Oscillatory motion . Plural speech .
Polyvalent events . Tool use . Motion sensors . Embodied cognition In this article, we discuss mathematical activities such as using tools and creating diagrams as particular instances of conversations with materials and diagrams. We start by theoretically framing this statement, articulating the seemingly contradictory idea of “conversation” in such contexts. We are particularly interested in highlighting the
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s40751-02000073-5) contains supplementary material, which is available to authorized users.
* Ricardo Nemirovsky [email protected]
1
Manchester Metropolitan University, Manchester UK
2
University of Torino, Turin Italy
3
San Diego State University, San Diego CA USA
Digital Experiences in Mathematics Education
complexity of these conversations, pointing at the irreducible significance of physicality and feelings in the doing of mathematics. To do so, we present and analyze episodes from an interview in which an undergraduate student, Jake, makes sense of a particular device we call the water wheel, and investigates certain graphical configurations expressing its movement. The functioning of the water wheel will be described in the methods section, which also contains an explanation of the kind of graphs that are digitally produced by means of photogate sensors and a software interface. We present six episodes selected from the second interview with Jake, where he investigates some of these motions by using hand-produced diagrams, digitally produced ones and the actual manipulation of the wheel. As he encounters an unexpected diagram, we observe how the conversation with the water wheel and the graphs evolves along the expressive, performative and temporal dimensions of activity with diagrams.
Data Loading...
