Patterns of Collaboration: Towards Learning Mathematics in the Era of the Semantic Web
With current digital technologies there are a number of networked computer-based tools that provide ways for users, be they learners or teachers, to collaborate in tackling visual representations of mathematics, both algebraic and geometric. For learners, there are various ways of collaborating that can occur while the learners are tackling mathematical problems. In this chapter we use selected outcomes from recent innovative research on this aspect of learning and teaching mathematics with digital technologies to review the patterns of collaboration that can occur in terms of teacher and learner experience. Given that such patterns of collaboration are via current digital technologies, this chapter goes on to offer a view on the likely impact on the cyberlearning of mathematics of progress towards the next generation of Web technologies that seeks to make use of ideas related to the web of data and the semantic web. Such impact is likely to be in terms of enhancing the learning applications of digital technologies, improving ways of administrating the educational programmes that they support, and potentially enabling teachers to maintain involvement in technological development and use over the longer-term.
KeywordsArgumentation Algebra Collaborative learning Semantic web Web 3.0
- Anderson, P. (2007, February). What is Web 2.0? Ideas, technologies and implications for education. JISC Technology and Standards Watch. Available online at: http://www.jisc.ac.uk/media/documents/techwatch/tsw0701b.pdf. Last Accessed 23 Aug 2011.
- Bittencourt, I. I., Isotani, S., Costa, E., & Mizoguchi, R. (2008). Research directions on semantic web and education. Journal Scientia: Interdisciplinary Studies in Computer Science, 19(1), 59–66.Google Scholar
- Cohen, E. G., & Lotan, R. A. (1995). Producing equal-status interaction in the heterogeneous classroom. American Educational Research Journal, 32(1), 99–120.Google Scholar
- Devedzic, V. (2006). Semantic web and education. New York: Springer.Google Scholar
- DiNucci, D. (1999). Fragmented future: Web development faces a process of mitosis, mutation, and natural selection. Print, 53(4), 32–35.Google Scholar
- diSessa, A. A. (2000). Changing minds: Computers, learning, and literacy. Cambridge, MA: MIT Press.Google Scholar
- Dragon, T., McLaren, B. M., Mavrikis, M., & Geraniou, E. (2011). Scaffolding collaborative learning opportunities: Integrating microworld use and argumentation. In: A. Paramythis, L. Lau, S. Demetriadis, M. Tzagarakis, & S. Kleanthous (Eds.), Proceedings of the International Workshop on Adaptive Support for Team Collaboration (ASTC-2011), held in conjunction with the International Conference on User Modeling, Adaptation, and Personalization (UMAP2011) (pp. 27–35). CEUR Workshop Proceedings. http://ceur-ws.org/Vol-743/
- EU Education, Audiovisual and Culture Executive Agency. (2011). Key data on learning and innovation through ICT at school in Europe 2011. Brussels, Belgium: EU Education, Audiovisual and Culture Executive Agency.Google Scholar
- Geraniou, E., Mavrikis, M., Kahn, K., Hoyles, C., & Noss, R. (2009). Developing a microworld to support mathematical generalisation. In Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 49–56), Thessalonik, Greece.Google Scholar
- Geraniou, G., Mavrikis, M., Hoyles, C., & Noss, R. (2011). Students’ justification strategies on equivalence of quasi-algebraic expressions. In Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 393--400), Ankara, Turkey.Google Scholar
- Gutierrez-Santos, S., Geraniou, E., Pearce-Lazard, D., & Poulovassilis, A. (2012). The design of teacher assistance tools in an exploratory learning environment for algebraic generalisation. IEEE Transactions in Learning Technologies. http://doi.ieeecomputersociety.org/10.1109/TLT.2012.19
- Gutierrez-Santos, S., Mavrikis, M., & Magoulas, G. (2010). Layered development and evaluation for intelligent support in exploratory environments: The case of microworlds. In Proceedings of Intelligent Tutoring Systems Conference (ITS 2010) (Vol. 6094, pp. 105–114). Lecture Notes in Computer Science. Springer: Pittsburgh, USA.Google Scholar
- Hoyles, C. (1993). Microworlds/schoolworlds: The transformation of an innovation. In C. Keitel, & K. Ruthven (Eds.), Learning from computers: Mathematics education and technology (pp. 1–17). NATO ASI Series. Series F, Computer and Systems Sciences (121). Berlin, Germany/New York: Springer.Google Scholar
- Jones, K. (2011). The value of learning geometry with ICT: Lessons from innovative educational research. In A. Oldknow & C. Knights (Eds.), Mathematics education with digital technology (pp. 39–45). London: Continuum.Google Scholar
- Laningham, S. (Ed.). (2006). Tim Berners-Lee. Podcast, developerWorks Interviews, 22nd August, IBM website. Available online at: http://www.ibm.com/developerworks/podcast/dwi/cm-int082206txt.html. Last Accessed 23 Aug 2011.
- Lavicza, Z., Hohenwarter, M., Jones, K., Lu, A., & Dawes, M. (2010). Establishing a professional development network around dynamic mathematics software in England. International Journal for Technology in Mathematics Education, 17(4), 177–182.Google Scholar
- Law, N., Pelgrum, W. J., & Plomp, T. (Eds.). (2008). Pedagogy and ICT use in schools around the world: Findings from the IEA SITES 2006 Study. Hong Kong/Dordrecht, the Netherlands: CERC/Springer.Google Scholar
- Leonard, J. (2001). How group composition influenced the achievement of sixth-grade mathematics students. Mathematical Thinking and Learning, 3(2–3), 175–200.Google Scholar
- Loll, F., Pinkwart, N., Scheuer, O., & McLaren, B. M. (2009). Towards a flexible intelligent tutoring system for argumentation. In I. Adeo, N. Chen, Kinshuk, D. Sampson, & L. Zaitseva (Eds.), Proceedings of the 9th IEEE International Conference on Advanced Learning Technologies (ICALT 2009) (pp. 647–648). Los Alamitos, CA.Google Scholar
- Lou, Y., Abrami, P. C., Spence, J. C., Poulsen, C., Chambers, B., & d’Apollonia, S. (1996). Within-class grouping: A meta-analysis. Review of Educational Research, 66, 423–458.Google Scholar
- Maudsley, D. B. (1979). A theory of meta-learning and principles of facilitation: An organismic perspective. University of Toronto, 1979 (40, 8, 4354-4355-A).Google Scholar
- Mavrikis, M., Noss, R., Hoyles, C., & Geraniou, E. (2012). Sowing the seeds of algebraic generalisation: Designing epistemic affordances for an intelligent microworld. Journal of Computer Assisted Learning. doi:10.1111/j.1365-2729.2011.00469.x.
- McLoughlin, C., & Lee, M. J. W. (2007). Social software and participatory learning: Pedagogical choices with technology affordances in the Web 2.0 era. In ICT: Providing choices for learners and learning. Proceedings ascilite Singapore 2007. Available online at: http://www.ascilite.org.au/conferences/singapore07/procs/mcloughlin.pdf. Last Accessed 23 Aug 2011.
- Papert, S. (1980). Computer-based microworlds as incubators for powerful ideas. In R. Taylor (Ed.), The computer in the school: Tutor, tool, tutee (pp. 203–210). New York: Teacher’s College Press.Google Scholar
- Pearce-Lazard, D., Poulovassilis, A., & Geraniou, E. (2010). The design of teacher assistance tools in an exploratory learning environment for mathematics generalisation. In: Proceedings of the 5th European Conference on Technology Enhanced Learning (EC-TEL) (Lecture notes in computer science, Vol. 6383, pp. 260–275). Barcelona, Spain: Springer.Google Scholar
- Rollett, H., Lux, M., Strohmaler, M., Dosinger, G., & Tochtermann, K. (2007). The Web 2.0 way of learning with technologies. International Journal of Learning Technology, 3(1), 87--107.Google Scholar
- Scheuer, O., McLaren, B. M., Loll, F., & Pinkwart, N. (2009). An analysis and feedback infrastructure for argumentation learning systems. In V. Dimitrova, R. Mizoguchi, B. du Boulay, & A. Graesser (Eds.), Proceedings of the 14th International Conference on Artificial Intelligence in Education (AIED-09) (pp. 629–631). IOS Press: Brighton, UK.Google Scholar
- Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.Google Scholar
- Shadbolt, N., O’Hara, K., Salvadores, M., & Alani, H. (2011). eGovernment. In J. Domingue, D. Fensel, & J. A. Hendler (Eds.), Handbook of semantic web technologies (pp. 839–900). Berlin, Germany: Springer.Google Scholar
- Shaffer, D. W. (2007). How computer games help children learn. New York: Palgrave.Google Scholar
- Stahl, G. (2006). Group cognition: Computer support for building collaborative knowledge. Cambridge, MA: MIT Press.Google Scholar
- Stahl, G., Zhou, N., Cakir, M. P., & Sarmiento-Klapper, J. W. (2011). Seeing what we mean: Co-experiencing a shared virtual world. In Proceedings of the International Conference on Computer Support for Collaborative Learning (CSCL 2011) (pp. 534–541). Hong Kong, China.Google Scholar
- Thompson, P. (1987). Mathematical microworlds and intelligent computer-assisted instruction. In Artificial intelligence and instruction: Applications and methods (pp. 83–109). Boston: Addison-Wesley Longman.Google Scholar
- Tiropanis, T., Davis, H., Millard, D., & Weal, M. (2009a). Semantic technologies for learning and teaching in the Web 2.0 era: A survey. In WebSci'09: society on-line, Athens, Greece, 18–20 March 2009. Available online at: http://eprints.ecs.soton.ac.uk/18429/. Last Accessed 23 Aug 2011.