Numerous students in the Mathematics Education Ph.D program have expressed a deep interest in learning about technology and the affordances of different technologies in mathematics education. During the Spring of 2013, a series of three lectures was offered at the Kaput Center by the Director, Dr. Stephen Hegedus.
The lectures incorporated a mixture of theory, design and applications in the classroom. Many aspects were touched on including curriculum and activity design, implementation, as well as history and representation theory. The first lecture focused on dynamic geometry, the second on multimodality, and the third on representation and communication infrastructures. Detailed information regarding each lecture can be found on their respective pages listed below.
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Lecture 1 – Dynamic Media
Abstract:
This lecture opens up the trilogy lecture series by outlining some basic assumptions I make in my work that focuses on the development, role and use of software and hardware in mathematics education. I outline a historical perspective on how media has evolved from static to dynamic forms over 1000’s of years and how such media has been integrated into mathematics learning. I problematize how such development has impacted communication and expression in the classroom. I focus on dynamic geometry offering many examples from various mathematical topics and discuss the mathematical affordances for both teaching and learning.
Resources:
- Moreno-Armella, L., Hegedus, S. J., & Kaput, J. J. (2008). From static to dynamic mathematics: Historical and representational perspectives. Educational Studies in Mathematics, 68(2), 99-111.
Multimodality: Touching and Feeling Mathematics
Abstract:
I build on my first lecture in focusing on how latest technological advances can enable mathematical affordances in terms of creating access for all students. I will present historical advances in multimodal technologies and research from a wide variety of disciplines in how such advances can benefit learning. I attend to a critical question: How Should Young Children be Doing Mathematical Problem-Solving in the Future? This question purposely focuses on how children should be working versus what they should be learning. I will continue to substantiate my arguments with applications to the classroom and recent research in local schools.
Resources:
- Gucler, B., Hegedus, S., Robidoux, R., & Jackiw, N. (2013). Investigating the mathematical discourse of younger learners involved in multi-modal mathematical investigations: The case of haptic technologies. In D. Martinovic, V. Freiman, & Z. Karadag (Eds.), Visual Mathematics and Cyber Learning (pp. 97-118). Springer.
- Hegedus, S. J. & Moreno-Armella, L. (2010). Accommodating the instrumental genesis framework within dynamic technology environments. For the Learning of Mathematics, 30(1), 26-31.
- Hegedus, S. J. (2013). Young children investigating advanced mathematical concepts with haptic technologies: Future design perspectives. The Mathematics Enthusiast, 10(1 & 2), 87-108.
Please contact us if you have problems obtaining any resource.
Representation and Communication Infrastructures
Abstract:
When you take the latest advances in representationally-rich software and wireless communications new forms of expressivity can occur. I present, from an infrastructural perspective, the profound potential of combining such technologies and the resulting impact on learning and participation in the classroom. I present examples and data from the SimCalc project which involve students working within a dynamic, interactive environment using executable simulations to investigate concepts related to slope as rate, proportional reasoning, families of functions and the fundamental theorem of Calculus. Participation is discussed from a discourse perspective which includes both verbal utterances and gestures. Results from a recent randomized control trial in MA are also presented. I conclude by outlining a set of recently published ‘future design principles’ for researchers and developers who wish to build on such work outlined in the trilogy lectures.
Resources:
- Moreno-Armella, L. & Hegedus, S. J. (2009). Co-action with digital technologies. ZDM Mathematics Education 41, 505-519.
- Hegedus, S. J. & Moreno-Armella, L. (2009). Intersecting representation and communication infrastructures. ZDM Mathematics Education, 41, 399-412.
- Hegedus, S. J. & Penuel, W. R. (2008). Studying new forms of participation and identity in mathematics classrooms with integrated communication and representational infrastructures. Educational Studies in Mathematics, 68(2), 171-183.
Please contact us if you have problems obtaining any resource.