TASKS AND META-TASKS TO PROMOTE PRODUCTIVE MATHEMATICAL DISCOURSE IN COLLABORATIVE DIGITAL ENVIRONMENTS

Year 2015, Volume: 2 , 254 - 263, 01.09.2015

Arthur B. Powell Muteb M. Alqahtanı

Abstract

Rich tasks can be vehicles for productive mathematical
discussions. How to support such discourse in collaborative digital
environments is the focus of our theorization and empirical examination of task
design that emerges from a larger research project. We present the theoretical
foundations of our task design principles that developed through an iterative
research design for a project that involves secondary teachers in online
courses to learn discursively dynamic geometry by collaborating on construction
and problem-solving tasks in a cyberlearning environment. In this study, we
discuss a task and the collaborative work of a team of teachers to illustrate
relationships between the task design, productive mathematical discourse, and the
development of new mathematics knowledge for the teachers. Implications of this
work suggest further investigations into interactions between characteristics
of task design and learners mathematical activity.

Keywords

Collaboration, dynamic geometry, mathematical discourse, task design, technology

References

• Christiansen, B., & Walther, G. (1986). Task and activity. In B. Christiansen, A. G. Howson & M. Otte (Eds.), Perspectives in mathematics education: Papers submitted by members of the Bacomet group (pp. 243-307). Dordrecht: Reidel. Common Core State Standards Initiative. (2010). Common core state standards for mathematics Retrieved from http://www.corestandards.org/assets/CCSSI_Math Standards.pdf Euclid. (300 BCE/2002). Euclid's elements (T. L. Heath, Trans.). Santa Fe, NM: Green Lion. Gattegno, C. (1987). The science of education: Part 1: Theoretical considerations. New York: Educational Solutions. Grisi-Dicker, L., Powell, A. B., Silverman, J., & Fetter, A. (2012). Addressing transitional challenges to teaching with dynamic geometry in a collaborative online environment. In L. R. Van Zoest, J.-J. Lo & J. L. Kratky (Eds.), Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1024-1027). Kalamazoo, MI: Western Michigan University. Hegedus, S. J., & Moreno-Armella, L. (2010). Accommodating the instrumental genesis framework within dynamic technological environments. For the Learning of Mathematics, 30(1), 26-31. Hewitt, D. (1999). Arbitrary and necessary: Part 1 A way of viewing the mathematics curriculum. For the Learning of Mathematics, 19(3), 2-9. Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students' learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393-425. Margolinas, C. (2013). Tasks design in mathematics education. Proceedings of ICMI Study 22. Oxford, UK. McGraw, R., & Grant, M. (2005). Investigating mathematics with technology: Lesson structures that encourage a range of methods and solutions. In W. J. Masalski & P. C. Elliott (Eds.), Technology-supported mathematics learning environments (Vol. Sixty-Seventh Yearbook, pp. 303-317). Reston, VA: National Council of Teachers of Mathematics. Mercer, N., & Sams, C. (2006). Teaching children how to use language to solve maths problems. Language and Education, 20(6), 507-528. Mishra, P., & Koehler, M. J. (2006). Technological Pedagogical Content Knowledge: A Framework for Teacher Knowledge. Teachers College Record, 108(6), 1017-1054. Pirie, S., & Schwarzenberger, R. (1988). Mathematical discussion and mathematical understanding. Educational Studies in Mathematics, 19(4), 459-470. Powell, A. B., Borge, I. C., Floriti, G. I., Kondratieva, M., Koublanova, E., & Sukthankar, N. (2009). Challenging tasks and mathematics learning. In E. J. Barbeau & P. J. Taylor (Eds.), Challenging mathematics in and beyond the classroom: The 16th ICMI study (pp. 133-170). New York: Springer. Powell, A. B., Grisi-Dicker, L., & Alqahtani, M. (2013). Letramento matemático: Desenvolvendo as práticas colaborativas, matemáticas, e discursivas com tecnologia [Mathematical literacy: Development of collaborative, mathematical and discusive practices with technology] XI Encontro Nacional de Educação Matemática, Educação Matemática: Retrospectivas e Perspectivas [XI National Conference of Mathematics Education, Mathematics Education: Retrospectives and Perspectives. Curitiba, Paraná. Rabardel, P., & Beguin, P. (2005). Instrument mediated activity: from subject development to anthropocentric design. Theoretical Issues in Ergonomics Science, 6(5), 429-461. Ray, M. (2013). Noticing and wondering Powerful problem solving: Activities for sense making with the mathematical practices (pp. 42-55): Heinemann. Resnick, L. B., Michaels, S., & O’Connor, C. (2010). How (well-structured) talk builds the mind. Innovations in educational psychology: Perspectives on learning, teaching and human development, 163-194. Rowe, K., & Bicknell, B. (2004). Structured peer interactions to enhance learning in mathematics. Paper presented at the Proceedings of 27th Annual Conference of the Mathematics Education Research Group of Australasia-Mathematics Education for the Third Millennium, Towards 2010. , Townsville, Australia. Sierpinska, A. (2004). Research in mathematics education through a keyhole: Task problematization. For the Learning of Mathematics, 24(2), 7-15. Stahl, G. (2008). Social practices of group cognition in virtual math teams. In S. Ludvigsen, A. Lund & R. Säljö (Eds.), Learning in social practices: ICT and new artifacts—transformation of social and cultural practices: Pergamon. Stahl, G. (2013). Translating Euclid: Designing a human-centered mathematics. San Rafael, CA: Morgan & Claypool. Stahl, G. (2015). Constructing dynamic triangles together: The development of mathematical group cognition. Cambridge, UK: Cambridge. Stahl, G. (Ed.). (2009). Studying virtual math teams. New York: Springer. Stylianides, G. J., & Stylianides, A. J. (2005). Validation of solutions of construction problems in dynamic geometry environments. International Journal of Computers for Mathematical Learning, 10(1), 31–47.