Advertisement

Designing Assessment Tasks in a Dynamic Geometry Environment

  • Marta VenturiniEmail author
  • Nathalie Sinclair
Chapter
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 8)

Abstract

Despite the widespread use of Dynamic Geometry Environments (DGEs) in mathematics classrooms, they feature very little in most teachers’ assessment practices. Indeed, many researchers have acknowledged the lack of research on how DGEs can and should be used in the context of assessment, and on how the learning that is developed through the use of DGEs in mathematics can be evaluated. Digital technologies include a range of mathematical and technological competencies that are not assessed in a paper-and-pencil environment. Moreover, the feedback provided by DGEs involves a whole new dynamic of action/interaction during assessment. This paper draws on previous work on task design in DGEs to provide a framework for identifying and designing different types of assessment tasks according to the specific goals of the teacher. These types of tasks will be exemplified using tasks designed by the first author for the iPad-based, multi-touch Sketchpad Explorer.

Keywords

Dynamic geometry Digital technologies Formative assessment Feedback Circle geometry Task design 

References

  1. Ainley, J, & Margolinas, C. (2013). Introduction to theme B: Accounting for student perspectives in task design. In C. Margolinas (Ed.), Task design in mathematics education: The 22nd ICMI study. Google Scholar
  2. Anthony, C. M. O. (2013) Designing tasks to foster operative apprehension for visualization and reasoning in dynamic geometry environment. In C. Margolinas (Ed.), Task design in mathematics education: The 22nd ICMI study. Google Scholar
  3. Caron, F., & Steinke, T. (2005). Learning in the presence of technology: Report of the CMEF working group. In Proceedings of the 2005 Canadian Mathematics Education Forum, Québec, Canada.Google Scholar
  4. Drijvers, P., Mariotti, M. A., Olive, J., & Sacristán, A. I. (2010). Introduction to section 2. In C. Hoyles & J.-B. Lagrange (Eds.), Mathematics education and technology—rethinking the terrain: The 17th ICMI study. Google Scholar
  5. Job, P., & Schneider, M. (2013). On what epistemological thinking brings (or does not bring) to the analysis of tasks in terms of potentialities for mathematical learning. In C. Margolinas (Ed.), Task design in mathematics education: The 22nd ICMI study. Google Scholar
  6. Joubert, M. (2013). A framework for examining student learning of mathematics: Tasks using technology. In Eighth Congress of European Research in Mathematics Education (CERME 8).Google Scholar
  7. Laborde, C. (2001). Integration of technology in the design of geometry tasks with cabri-geometry. International Journal of Computers for Mathematical Learning, 6(3), 283–317.CrossRefGoogle Scholar
  8. 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).Google Scholar
  9. Madison, B. L. (2006). Tensions and tethers: Assessing learning in undergraduate mathematics. In L. A. Steen (Ed.), Supporting assessment in undergraduate mathematics (pp. 3–10). Washington, DC: The Mathematical Association of America.Google Scholar
  10. Mariotti, M. A. (2006). Proof and proving in mathematics education. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education (pp. 173–204). Rotterdam: Sense Publishers.Google Scholar
  11. Ng, O., & Sinclair, N. (2015). “Area without numbers”: Using Touchscreen dynamic geometry to reason about shape. Canadian Journal of Science, Mathematics and Technology Education, 15(1), 84–101.CrossRefGoogle Scholar
  12. Olive, J., Makar, K., Hoyos, V., Kor, L. K., Kosheleva, O., & Sträßer, R. (2010). Mathematical knowledge and practices resulting from access to digital technologies. In: Proceedings of the 17th ICMI Study (Vol. 8, pp. 133–177).Google Scholar
  13. Sangwin, C., Cazes, C., Lee. A., & Wong K. L. (2010). Micro-level automatic assessment supported by digital technologies, Chap. 10. In The 17th ICMI study.Google Scholar
  14. Savard, A., Polotskaia, E., Freiman, V., Gervais, C. (2013). Tasks to promote holistic flexible reasoning about simple additive structures. In C. Margolinas (Ed.), Task design in mathematics education: The 22nd ICMI study. Google Scholar
  15. Sinclair, M. P. (2003). Some implications of the results of a case study for the design of pre-constructed, dynamic geometry sketches and accompanying materials. Educational Studies in Mathematics, 52, 289–317.CrossRefGoogle Scholar
  16. Sinclair, N., & Jackiw, N. (2010). Learning through teaching, when teaching machines. In R. Leikin & R. Zazkis (Eds.), Learning through teaching. Dordrecht: Springer.Google Scholar
  17. Taras, M. (2010). Assessment for learning: assessing the theory and evidence. Procedia—Social and Behavioral Sciences, 2(2), 3015–3022.Google Scholar
  18. Thomas, M. O. J., & Lin, C. (2013). Designing tasks for use with digital technology. In C. Margolinas (Ed.), Task design in mathematics education: The 22nd ICMI study. Google Scholar
  19. Trouche, L. (2005). Calculators in mathematics education: A rapid evolution of tools, with differential effects. In D. Guin, et al. (Eds.), The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument (pp. 9–40). Dordrecht, The Netherlands: Kluwer Academic Publishers.CrossRefGoogle Scholar
  20. Venturini, M. (2015). How teachers think about the role of digital technologies in student assessment in mathematics (Ph.D. thesis). Simon Fraser University, Canada and University of Bologna, Italy.Google Scholar
  21. Wilson, P. (2008). Teacher education: Technology’s conduit to the classroom. In K. Heid & G. Blume (Eds.), Research on technology in the learning and teaching of mathematics, volume 2: Cases and perspectives. Charlotte, NC: National Council of Teachers of Mathematics/Information Age Publishing.Google Scholar
  22. Zazkis, R., Sinclair, N., & Liljedahl, P. (2013). Lesson play in mathematics education. New York: Springer.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Simon Fraser UniversityBurnabyCanada

Personalised recommendations