Screencasting as a Tool to Capture Moments of Authentic Creativity
In the context of working with preservice secondary mathematics teachers (PSMTs) in a course on mathematical problem solving with technology, we tested the potential of technology to both inspire and capture moments of authentic creativity in the mathematics classroom. In a case study of two PSMTs working in partnership to solve a task using Interactive Geometry Software (IGS), we documented a rich narrative based on four episodes of creativity. These four episodes can be characterized as moments of creative insight because they represent moments that inspired either the development of new solutions or strategies (Problem Solving Insights) or spurred new questions (Problem Posing Insights). At the heart of the case is a task that requires constant negotiation and discussion in a digital workspace. Capturing an authentic narrative can be challenging with verbalized thinking alone, as the articulation of insight is not always possible. Screencasts are a tool that captures verbalized thinking as well as on-screen activity. This case study illustrates the power that this tool has in preserving the authenticity of those moments, but also in creating a record of practice to which both students and teachers might refer when making learning processes explicit.
KeywordsPreservice teacher education Problem solving Interactive geometry software Screencasting Modeling
- Beatty, R., & Geiger, V. (2010). Technology, communication, and collaboration: Re-thinking communities of inquiry, learning and practice. In C. Hoyles & J.-B. Lagrange (Eds.), Mathematics education and technology-rethinking the Terrain: The 17th ICMI study (pp. 251–284). New York, NY: Springer.Google Scholar
- Chamberlin, S. A., & Moon, S. M. (2005). Model-eliciting activities as a tool to develop and identify creatively gifted mathematicians. Journal of Advanced Academics, 17(1), 37–47.Google Scholar
- Cox, D. C., & Harper, S. R. (2016). Documenting a developing vision of teaching mathematics with technology. In M. L. Niess, S. Driskell, & K. Hollebrands (Eds.), Handbook of research on transforming mathematics teacher education in the digital age (pp. 166–189). Hershey, PA: IGI Global.CrossRefGoogle Scholar
- Dreyfus, T., & Eisenberg, T. (1996). On different facets of mathematical thinking. In R. J. Sternberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 253–284). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
- Ginsburg, H. P. (1996). Toby’s math. In R. J. Sternberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 175–282). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
- Graf, K.-D., & Hodgson, B. R. (1990). Popularizing geometrical concepts: The case of the kaleidoscope. For the Learning of Mathematics, 10(3), 42–49.Google Scholar
- Kaplan, G., Gross, R., & McComas, K. K. (1996). Mathematics through the lens of a kaleidoscope: A student centered approach to building bridges between mathematics and art. In K. Delp, C. S. Kaplan, D. McKenna, & R. Sarhangi (Eds.), Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (pp. 573–580). Phoenix, AZ: Tessellations Publishing.Google Scholar
- Laborde, C., Kynigos, C., Hollebrands, K., & Strässer, R. (2006). Teaching and learning geometry with technology. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 275–304). Rotterdam, The Netherlands: Sense Publishers.Google Scholar
- Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art. ZDM, 45(2), 159–166.Google Scholar
- Lewis, T. (2006). Creativity: A framework for the design/problem solving discourse in technology education. Journal of Technology Education, 17(1), 36–53.Google Scholar
- Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For the Learning of Mathematics, 26(1), 17–19.Google Scholar
- Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Newbury Park, CA: Sage Publications.Google Scholar
- National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.Google Scholar
- National Governors Association Center for Best Practices and Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Authors.Google Scholar
- Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257–315). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
- Tharp, M. L., Fitzsimmons, J. A., & Ayers, R. L. B. (1997). Negotiating a technological shift: Teacher perceptions of the implementation of graphing calculators. Journal of Computers in Mathematics and Science Teaching, 16(4), 551–575.Google Scholar
- Torrance, E. P. (1966). Torrance test on creative thinking: Norms-technical manual, Research Edition. Lexington, MA: Personal Press.Google Scholar
- Udell, J. (2005, November 16). What is screencasting? O’Reilly Media archive. Retrieved from http://archive.oreilly.com/pub/a/oreilly/digitalmedia/2005/11/16/what-is-screencasting.html.
- Wert, T. (2011). Creating a kaleidoscope with geometer’s sketchpad. [Video file]. Retrieved from https://www.youtube.com/watch?v=Wgxyd0Iveu4.