Mathematics teachers’ knowledge-sharing on the Internet: pedagogical message in instruction materials

Yvonne Liljekvist

doi:10.7146/nomad.v21i3.148734

Authors

Yvonne Liljekvist

DOI:

https://doi.org/10.7146/nomad.v21i3.148734

Abstract

This article reports on a study of teacher-shared documents containing mathematical tasks published on the Internet. The aim was to identify the goals, methods and pedagogical justifications presented in the documents and what was needed to solve the tasks. Content analysis was used to define their pedagogical message. The results show that the documents mainly involve content goals for younger pupils that are not consistent with the explicit descriptions. The conceptual goals are communicated to a great extent, but are not supported by task features. The reasons for why the tasks given are expected to lead to a certain goal are very often implicit, and, as a result, the content of the documents and the quality of the tasks are somewhat unclear to other teachers.

References

Bartolini-Bussi, M. G. (1990). Learning situations and experimental domains relevant to early childhood mathematics. In L. P. Steffe & T. Woods (Eds.), Transforming children's mathematics education: international perspectives (pp. 304-312). Hillsdale: Lawrence Erlbaum Associates.

Bergqvist, T., Lithner, J. & Sumpter, L. (2008). Upper secondary students' task reasoning. International Journal of Mathematical Education in Science and Technology, 39 (1), 1-12. https://doi.org/10.1080/00207390701464675

Bissessar, C. S. (2014). Facebook as an informal teacher professional development tool. Australian Journal of Teacher Education, 39 (2), 121-135. https://doi.org/10.14221/ajte.2014v39n2.9

Boesen, J., Lithner, J. & Palm, T. (2010). The relation between types of assessment tasks and the mathematical reasoning students use. Educational Studies in Mathematics, 75 (1), 89-105. https://doi.org/10.1007/s10649-010-9242-9

Bommel, J. van (2014). The teaching of mathematical knowledge for teaching: a learning study of primary school teacher education. Nordic Studies in Mathematics Education, 19 (3-4), 185-201.

Bommel, J. van & Liljekvist, Y. (2015). Facebook and mathematics teachers' professional development: informing our community. Paper presented at the 9th Conference of European Research in Mathematics (CERME9), Prague.

Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer Academic Publishers.

Brousseau, G. & Gibel, P. (2005). Didactical handling of students' reasoning processes in problem solving situations. Educational Studies in Mathematics, 59 (1), 13-58. https://doi.org/10.1007/s10649-005-2532-y

Bryman, A. (2001). Social research methods. Oxford University Press. Carvalho

Borba, M. de & Llinares, S. (2012). Online mathematics teacher education: overview of an emergent field of research. ZDM, 44 (6), 697-704. https://doi.org/10.1007/s11858-012-0457-3

Cohen, L., Manion, L. & Morrison, K. (2000). Research methods in education. New York: RoutledgeFalmer.

Grevholm, B. (2010). Mathematics teacher education: a Scandinavian perspective. In G. Anthony & B. Grevholm (Eds.), Teachers of mathematics: recruitment and retention, professional development and identity (pp. 93-100). Roskilde: IMFUFA.

Gueudet, G. (2015). Resources at the core of mathematics teachers' work. In S. J. Cho (Ed.), Selected regular lectures from the 12th international congress on mathematical education (pp. 235-251). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-17187-6_14

Gueudet, G. & Trouche, L. (2012). Teachers' work with resources: documentation geneses and professional geneses. In G. Gueudet, B. Pepin & L. Trouche (Eds.), From text to "lived" resources: mathematics curriculum materials and teacher development (pp. 23-41). New York: Springer. https://doi.org/10.1007/978-94-007-1966-8_2

Henningsen, M. & Stein, M. K. (1997). Mathematical tasks and student cognition: classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28 (5), 524-549. https://doi.org/10.2307/749690

Hew, K. F. & Hara, N. (2007). Knowledge sharing in online environments: a qualitative case study. Journal of the American Society for Information Science and Technology, 58 (14), 2310-2324. https://doi.org/10.1002/asi.20698

Jonsson, B., Norqvist, M. Liljekvist, Y. & Lithner, J. (2014). Learning mathematics through algorithmic and creative reasoning. Journal of Mathematical Behaviour, 36, 20-32. https://doi.org/10.1016/j.jmathb.2014.08.003

Karpf, D. (2012). Social science research methods in Internet time. Information, Communication & Society, 15 (5), 639-661. https://doi.org/10.1080/1369118X.2012.665468

Krippendorff, K. (2004). Content analysis: an introduction to its methodology. Thousand Oaks: Sage.

Landqvist, F. & Teigland, R. (2005). Collective action in electronic networks of practice: an empirical study of three online social structures. In P. Van Den Besselaar, G. De Michelis, J. Preece & C. Simone (Eds.), Communities and technologies 2005: proceedings of the second Communities and Technologies Conference, Milano, 2005 (pp. 359-375). Dordrecht: Springer. https://doi.org/10.1007/1-4020-3591-8_19

Lesh, R. & Zawojewski, J. (2007). Problem solving and modeling. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763-804). Charlotte: Information Age Pub.

Lester, F. K. (1983). Trends and issues in mathematical problem-solving research. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 229-261). New York: Academic Press.

Lester, F. K. (Ed.) (2007). Second handbook of research on mathematics teaching and learning. Charlotte: Information Age.

Liljekvist, Y., Bommel, J. van & Olin-Scheller, C. (in press). Professional learning communities in a web 2.0 world: rethinking the conditions for professional development. In I. H. Amzat, N. P. Valdes & B. Yusuf (Eds.), Teacher empowerment toward professional development and practices: perspectives across borders. New York: Springer.

Lithner, J. (2003). Students' mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52 (1), 29-55. https://doi.org/10.1023/A:1023683716659

Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67 (3), 255-276. https://doi.org/10.1007/s10649-007-9104-2

Lithner, J. (2015). Learning mathematics by creative or imitative reasoning. In S. J. Cho (Ed.), Selected regular lectures from the 12th international congress on mathematical education (pp. 487-506). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-17187-6_28

Manca, S. & Ranieri, M. (2014). Teachers' professional development in online social networking sites. In J. Viteli & M. Leikomaa (Eds.), Proceedings of EdMedia: world conference on educational media and technology 2014 (pp. 2229-2234). Waynesville: AACE.

Margolinas, C. (Ed.). (2013). Task design in mathematics education: proceedings of ICMI study 22. Oxford: ICMI.

Niss, M. (2003). Mathematical competencies and the learning of mathematics: the Danish KOM project. In A. Gagatis & S. Papastavridis (Eds.), Proceedings of the 3rd Mediterranean conference on mathematical education (pp. 115-124). Athens: Hellenic Mathematical Society.

Olofsson, A. D. (2008). Lektion.se - an informal Swedish online learning community for shared teacher professional development: a study with focus on frequent users of the discussion forums. Tidskrift för Lärarutbildning och Forskning, (3-4), 133-147.

Olofsson, A. D. (2010). Discussions in online learning community forums: Do they facilitate teachers professional development? The University of the Fraser Valley Research Review, 3 (2), 54-68.

Palm, T., Boesen, J. & Lithner, J. (2011). Mathematical reasoning requirements in Swedish upper secondary level assessments. Mathematical Thinking and Learning, 13 (3), 221-246. https://doi.org/10.1080/10986065.2011.564994

Pepin, B., Gueudet, G. & Trouche, L. (2013). Re-sourcing teachers' work and interactions: a collective perspective on resources, their use and transformation. ZDM, 45 (7), 929-943. https://doi.org/10.1007/s11858-013-0534-2

Potari, D. & Jaworski, B. (2002). Tackling complexity in mathematics teaching development: using the teaching triad as a tool for reflection and analysis. Journal of Mathematics Teacher Education, 5 (4), 351-380. https://doi.org/10.1023/A:1021214604230

Pririe, S. E. B. & Schwartzenberger, R. L. E. (1988). Mathematical discussion and mathematical understanding. Educational Studies in Mathematics, 19 (4), 459-470. https://doi.org/10.1007/BF00578694

Ranieri, M., Manca, S. & Fini, A. (2012). Why (and how) do teachers engage in social networks? An exploratory study of professional use of Facebook and its implications for lifelong learning. British Journal of Educational Technology, 43 (5), 754-769. https://doi.org/10.1111/j.1467-8535.2012.01356.x

Rourke, L. & Anderson, T. (2004). Validity in quantitative content analysis. Educational Technology Research and Development, 52 (1), 5-18. https://doi.org/10.1007/BF02504769

Rutherford, C. (2010). Facebook as a source of informal teacher professional development. In Education, 16 (1), 60-74. Retrieved from http://ined.uregina.ca/index.php/ineducation/article/view/76 https://doi.org/10.37119/ojs2010.v16i1.76

Ruthven, K (2016). The re-sourcing movement in mathematics teaching: some European initiatives. In M. Bates & Z. Usiskin (Eds.), Digital curricula in school mathematics (pp. 75-86). Charlotte: Information Age Publishing.

Schoenfeld, A. H. (1992). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). New York: MacMillan.

Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando: Academic Press.

Skolverket. (2009). Redovisning av uppdrag om uppföljning av IT-användning och IT-kompetens i förskola, skola och vuxenutbildning. Stockholm: Skolverket.

Skolverket. (2011). Läroplan för grundskolan, förskoleklassen och fritidshemmet 2011, Lgr11. Stockholm: Skolverket.

Taflin, E. (2007). Matematikproblem i skolan: för att skapa tillfällen till lärande (Doctoral thesis). Department of mathematics and mathematical statistics, Umeå university.

Triggs, P. & John, P. (2004). From transaction to transformation: information and communication technology, professional development and the formation of communities of practice. Journal of Computer Assisted Learning, 20 (6), 426-439. https://doi.org/10.1111/j.1365-2729.2004.00101.x

Van Acker, F., Vermeulen, M., Kreijns, K., Lutgerink, J. & Buuren, H. van (2014). The role of knowledge sharing self-efficacy in sharing open educational resources. Computers in Human Behavior, 39, 136-144. https://doi.org/10.1016/j.chb.2014.07.006

Vavasseur, C. B. & MacGregor, S. K. (2008). Extending content-focused professional development through online communities of practice. Journal of Research on Technology in Education, 40 (4), 517-536. https://doi.org/10.1080/15391523.2008.10782519