Pedagogic Mediation of Dynamic Geometry in Teachers' Mathematical Activities

Muteb M. Alqahtani; Arthur Belford Powell

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Conference: 2016 ASEE Annual Conference & Exposition
Location: New Orleans, Louisiana
Publication Date: June 26, 2016
Start Date: June 26, 2016
End Date: June 29, 2016
ISBN: 978-0-692-68565-5
ISSN: 2153-5965
Conference Session: Mathematics Division Technical Session 2
Tagged Division: Mathematics
Page Count: 6
DOI: 10.18260/p.25863
Permanent URL: https://peer.asee.org/25863
Download Count: 531

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Paper Authors

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Muteb M. Alqahtani Rutgers University

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I am a doctoral candidate in mathematics education in the Ph.D. program at the Graduate School of Education, Rutgers University-New Brunswick, and I teach in the Department of Urban Education at Rutgers University-Newark.

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Arthur Belford Powell Rutgers University

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Abstract

Technologies developed for teaching and learning mathematics are powerful and potentially useful. One significant factor of successful integration of technology in mathematics classrooms is understanding how technology influences teachers and students’ social interactions and shapes their mathematical knowledge. Vygotsky (1978) emphasized the role of tools and signs for cognitive development. He argued that intellectual development occurs through engagement in tool-mediated activities that allow for social interactions. Some researchers used this perspective to explain the mediation of technological tools in mathematical. However, for mathematics teachers’ to use technological tools in their classrooms effectively, they need to learn how to use the tools. This creates a need for investigating how teachers learn to use mathematical tools and the mediations of these tools in teachers’ activities.

Several researchers theorized how technological tools mediate learners’ activity. For example, Rabardel and Beguin’s (2005) describe two mediation roles of tools in users’ activity: epistemic (focuses on understanding the properties of the object) and pragmatic (concerned with transferring the object to a desirable form). In this paper, we report on a third mediation role that teachers used while working on geometrical tasks in a collaborative dynamic geometry environment. We analyzed the interactions of four middle and high school teachers and identified the third mediation role of the environment.

The four mathematics teachers participated in a 15-week professional development course. They interacted in an online, collaborative, dynamic geometry environment called Virtual Math Teams with GeoGebra (VMTwG), which allows for synchronous interactions among users through a multiuser interface of GeoGebra and a chat feature. VMTwG records users’ actions in GeoGebra as well as their chat massages. The teachers met synchronously in VMTwG for two hours every week to work on open-ended geometrical problems. We analyzed teachers’ weekly sessions by reading their discussions and viewing their GeoGebra actions to understand how the environment mediated their activities. Our analysis of their interactions allowed us to categorize how VMTwG mediated teachers’ activities as they discussed and solved geometrical tasks. We were able to identify a pedagogic mediation, in which teachers concerned themselves with how to teach with this environment. They used it to teach each other and convey their ideas in a didactic manner as well as to discuss how VMTwG could be used to teach certain school topics. In these pedagogic meditative moments, the environment is used as a mediator not particularly to make transformations on the objects or explore objects’ properties and relations, but to help others understand these transformations, properties, and relations.

Pedagogic mediation adds to our understanding of how teachers interact with mathematical tools. It informs professional development design and implementation and informs task design in dynamic geometry environments for teachers and students.

References Rabardel, P., & Beguin, P. (2005). Instrument mediated activity: from subject development to anthropocentric design. Theoretical Issues in Ergonomics Science, 6(5), 429-461. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes (M. Cole, V. John-Steiner, S. Scribner, & E. Souberman, Trans.). Cambridge, MA: Harvard.

Citation
Format

Alqahtani, M. M., & Powell, A. B. (2016, June), Pedagogic Mediation of Dynamic Geometry in Teachers' Mathematical Activities Paper presented at 2016 ASEE Annual Conference & Exposition, New Orleans, Louisiana. 10.18260/p.25863

TY - CPAPER
AB - Technologies developed for teaching and learning mathematics are powerful and potentially useful. One significant factor of successful integration of technology in mathematics classrooms is understanding how technology influences teachers and students’ social interactions and shapes their mathematical knowledge. Vygotsky (1978) emphasized the role of tools and signs for cognitive development. He argued that intellectual development occurs through engagement in tool-mediated activities that allow for social interactions. Some researchers used this perspective to explain the mediation of technological tools in mathematical. However, for mathematics teachers’ to use technological tools in their classrooms effectively, they need to learn how to use the tools. This creates a need for investigating how teachers learn to use mathematical tools and the mediations of these tools in teachers’ activities.

Several researchers theorized how technological tools mediate learners’ activity. For example, Rabardel and Beguin’s (2005) describe two mediation roles of tools in users’ activity: epistemic (focuses on understanding the properties of the object) and pragmatic (concerned with transferring the object to a desirable form). In this paper, we report on a third mediation role that teachers used while working on geometrical tasks in a collaborative dynamic geometry environment. We analyzed the interactions of four middle and high school teachers and identified the third mediation role of the environment.

The four mathematics teachers participated in a 15-week professional development course. They interacted in an online, collaborative, dynamic geometry environment called Virtual Math Teams with GeoGebra (VMTwG), which allows for synchronous interactions among users through a multiuser interface of GeoGebra and a chat feature. VMTwG records users’ actions in GeoGebra as well as their chat massages. The teachers met synchronously in VMTwG for two hours every week to work on open-ended geometrical problems. We analyzed teachers’ weekly sessions by reading their discussions and viewing their GeoGebra actions to understand how the environment mediated their activities. Our analysis of their interactions allowed us to categorize how VMTwG mediated teachers’ activities as they discussed and solved geometrical tasks. We were able to identify a pedagogic mediation, in which teachers concerned themselves with how to teach with this environment. They used it to teach each other and convey their ideas in a didactic manner as well as to discuss how VMTwG could be used to teach certain school topics. In these pedagogic meditative moments, the environment is used as a mediator not particularly to make transformations on the objects or explore objects’ properties and relations, but to help others understand these transformations, properties, and relations.

Pedagogic mediation adds to our understanding of how teachers interact with mathematical tools. It informs professional development design and implementation and informs task design in dynamic geometry environments for teachers and students.

References
Rabardel, P., &amp; Beguin, P. (2005). Instrument mediated activity: from subject development to anthropocentric design. Theoretical Issues in Ergonomics Science, 6(5), 429-461.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes (M. Cole, V. John-Steiner, S. Scribner, &amp; E. Souberman, Trans.). Cambridge, MA: Harvard.

AU - Muteb M. Alqahtani
AU - Arthur Belford Powell
CY - New Orleans, Louisiana
DA - 2016/06/26
PB - ASEE Conferences
TI - Pedagogic Mediation of Dynamic Geometry in Teachers' Mathematical Activities
UR - https://peer.asee.org/25863
DO - 10.18260/p.25863
ER -