Enacting core practices of effective mathematics pedagogy with GeoGebra

Isaac Benning

Abstract


This research study was conducted to identify core practices of enacting effective mathematics pedagogy with GeoGebra, a software application for teaching and learning mathematics. Eleven Ghanaian in-service mathematics teachers were engaged in a twelve-month professional development programme where they developed GeoGebra-based mathematics lessons, which they taught to their peers and subsequently to students in the classroom. The teachers’ actions and views about using GeoGebra to enact mathematics lessons were examined with the aim to specify the core practices of effective mathematics pedagogy. Data was collected through interviews, focus group discussions, lesson plans, and lesson observations. The results provided evidence that teachers were able to enact core practices, to different degrees, within five central themes of effective mathematics pedagogy: creating a mathematical setting, providing worthwhile mathematical tasks, orchestrating mathematical discussions, making mathematical connections, and assessing students’ learning. Further analysis of the data provided evidence for theorising 31 core practices across these central themes of effective mathematics pedagogy. Following their engagement in the professional development programme, the teachers enacted these practices to greater or lesser extent. However, it was problematic for most teachers to effectively engage their students in a deep mathematical discussion. The findings from this study have implications for high school mathematics curriculum, effective mathematics pedagogy literature, and professional development for technology integration in teaching and learning.


Keywords


effective mathematics pedagogy; GeoGebra; professional development; technology integration; teachers’ technology knowledge

Full Text:

PDF

References


Andresen, M., & Misfeldt, M. (2010). Essentials of teacher training sessions with GeoGebra. International Journal for Technology in Mathematics Education, 17(4), 169-176.

Anthony, G., & Walshaw, M. (2007). Effective pedagogy in mathematics/pāngarau: Best evidence synthesis iteration [BES]. Ministry of Education.

Anthony, G, Walshaw, M (2009). Effective pedagogy in mathematics. International Academy of Education, International Bureau of Education.

Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7(3), 245-274.

Braun, V., & Clarke, V. (2013). Successful qualitative research: A practical guide for beginners. SAGE Publications.

Bulut, M., & Bulut, N. (2011). Pre-service teachers' usage of dynamic mathematics software. Turkish Online Journal of Educational Technology, 10(4), 294-299.

Calder, N., Brown, T., Hanley, U., & Darby, S. (2006). Forming conjectures within a spreadsheet environment. Mathematics Education Research Journal, 18(3), 100-116.

Davies, R. S. (2011). Understanding technology literacy: A framework for evaluating educational technology integration. TechTrends, 55(5), 45-52.

Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning. A project of the National Council of teachers of mathematics (pp. 225-256). Information Age Publishing.

Geiger, V., Forgasz, H., Tan, H., Calder, N., & Hill, J. (2012). Technology in mathematics education. In B. Perry, T. Lowrie, T. Logan, A. MacDonald, & J. Greenless (Eds.), Research in Mathematics Education in Australasia 2008-2011, (pp.111-114). Sense Publishers.

Gervasoni, A., Hunter, R., Bicknell, B., & Sexton, M. (2012). Powerful pedagogical actions in mathematics education. In B. Perry, T. Lowrie, T. Logan, A. MacDonald, J. Greenlees (Eds.), Research in mathematics education in Australasia 2008-2011 (pp. 193-218). Sense Publishers.

Getenet, S. T., Beswick, K., & Callingham, R. A. (2014). Professionalizing in-service teachers' focus on technological pedagogical and content knowledge. Education and Information Technologies, 21,19-34. https://doi.org/10.1007/s10639-013-9306-4

Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester, (Ed.), Second Handbook of Research on Mathematics Teaching and Learning, (pp. 371-404). Information Age Publishing.

Hohenwarter, M., Jarvis, D., & Lavicza, Z. (2009). Linking geometry, algebra, and mathematics teachers: GeoGebra software and the establishment of the International GeoGebra Institute. The International Journal for Technology in Mathematics Education, 16(2), 83-87.

Hudson, R. (2012). Modelling secondary mathematics teachers’ use and non-use of technology in teaching. [Doctoral dissertation, University of Wollongong]. http://ro.uow.edu.au/theses/3673

Ingram, N. (2011). Affect and identity: The mathematical journeys of adolescents. [Doctoral dissertation, University of Otago]. http://hdl.handle.net/10523/1919

Ingram, N. (2013). Mathematical engagement skills. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics education: Yesterday, today, and tomorrow (Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia, (pp. 402-409). Melbourne, Australia: MERGA.

Jacobs, V. R., & Spangler, D. A. (2017). Research on core practices in K-12 mathematics teaching. In J. Cai (Ed.), Compendium for research in mathematics education (pp.766-792). National Council of Teachers of Mathematics.

Jupri, A., Drijvers, P., & van den Heuvel-Panhuizen, M. (2015). Improving grade 7 students’ achievement in initial algebra through a technology-based intervention. Digital Experiences in Mathematics Education, 1(28). https://doi.org/10.1007/s40751-015-0004-2.

Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: How children learn mathematics. National Research Council.

Martin, T.S., & Speer, W. R. (2009). Mathematics teaching today. Teaching Children Mathematics, 15(7), 400-403.

Middleton, J., Jansen, A., & Goldin, G. A. (2017). The complexities of mathematical engagement: Motivation, affect, and social interactions. In J. Cai (Ed.), Compendium for research in mathematics education, (pp. 667--699). National Council of Teachers of Mathematics.

Ministry of Education. (2019). Kindergarten curriculum (KG 1&2). Accra, Ghana: National Council for Curriculum and Assessment (NaCCA).

Ministry of Education, Science and Sports. (2007). Teaching syllabus for mathematics. Accra, Ghana: Ministry of Education, CRDD.

Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017-1054.

National Council of Teachers of Mathematics. (1980). An agenda for action: Recommendations for school mathematics of the 1980s. NCTM.

National Council of Teachers of Mathematics. (2007). Mathematics teaching today. Reston, VA: NCTM.

Newmann, F. M., & Wehlage, G. G., (1993). Five standards of authentic instruction. Educational Leadership, 50(7), 8-12.

Prodromou, T. P., Lavicza, Z. P., & Koren, B. M. (2015). Increasing students' involvement in technology-supported mathematics lesson sequences. The International Journal for Technology in Mathematics Education, 22(4), 169-177.

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.

Smith, J. (1999). Active learning of mathematics. Mathematics Teaching in the Middle School, 5(2), 108-110.

Springer, L., Stanne, M. E., & Donovan, S. S. (1999). Effects of small-group learning on undergraduates in science, mathematics, engineering, and technology: A meta-analysis. Review of Educational Research, 69(1), 21-51.

Stein, M. K., Engle, R. A., Smith, M. S., &. Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313-340.

Thomas, D. R. (2006). A general inductive approach for analysing qualitative evaluation data. American Journal of Evaluation, 27(2), 237-246.

Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press.


Refbacks

  • There are currently no refbacks.