Analyzing teachers’ knowledge based on their approach to the information provided by technology

Helena Rocha 1 *
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1 CICS.NOVA, Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa, Lisbon, PORTUGAL
* Corresponding Author
EUR J SCI MATH ED, Volume 11, Issue 1, pp. 132-145. https://doi.org/10.30935/scimath/12522
Published Online: 10 October 2022, Published: 01 January 2023
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ABSTRACT

Teachers’ knowledge plays a central role in technology integration. In this study we analyze situations, where there is some divergence between the mathematical results and the information offered by the graphing calculator (lack of mathematical fidelity), putting the focus in the teachers and in their approaches. The goal of this study is to analyze, in the light of knowledge for teaching mathematics with technology (KTMT) model, the teachers’ professional knowledge, assuming the situations of lack of mathematical fidelity as having the potential to reveal some characteristics of their knowledge. Specifically, considering the teaching of functions at 10th grade (age 16), we intend to analyze: (1) What knowledge do the teachers have of technology and of its mathematical fidelity? (2) What can the teachers’ options related to situations of lack of mathematical fidelity tell us about their knowledge in other KTMT domains? The study adopts a qualitative and interpretative approach based on the case studies of two teachers. Data were collected by interviews and class observation, being the analysis guided by the KTMT model. The main result points to the relevance of the mathematics and technology knowledge. However, there is evidence of some difficulties to integrate the information provided by the technology with the mathematics, and also of some interference of the teaching and learning and technology knowledge, and specifically of the knowledge related to the students. This suggests that the analysis of the teachers’ actions in relation to situations of lack of mathematical fidelity, can be useful to characterize their KTMT.

CITATION

Rocha, H. (2023). Analyzing teachers’ knowledge based on their approach to the information provided by technology. European Journal of Science and Mathematics Education, 11(1), 132-145. https://doi.org/10.30935/scimath/12522

REFERENCES

  • Anabousy, A., Tabach, M. (2022). In-service mathematics teachers’ pedagogical technology knowledge development in a community of inquiry context. Mathematics, 10, 1-18. https://doi.org/10.3390/math10193465
  • Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  • Bogdan, R., & Biklen, S. (1997). Investigação qualitativa em educação–Uma introdução à teoria e aos métodos [Qualitative research in education–An introduction to theory and methods]. Porto Editora.
  • Burrill, G. (1992). The graphing calculator: A tool for change. In J. Fey, & C. Hirsch (Eds.), Calculators in mathematics education (pp. 14-22). NCTM.
  • Cavanagh, M., & Mitchelmore, M. (2003). Graphics calculators in the learning of mathematics: Teacher understandings and classroom practices. Mathematics Teacher Education and Development, 5, 3-18.
  • Chen, J.-C., & Lai, Y.-L. (2015). A brief review of researches on the use of graphing calculator in mathematics classrooms. International Journal of Learning, Teaching and Educational Research, 14(2), 163-172.
  • Clark-Wilson, A., & Noss, R. (2015) Hiccups within technology mediated lessons: A catalyst for mathematics teachers’ epistemological development. Research in Mathematics Education, 17(2), 92-109. https://doi.org/10.1080/14794802.2015.1046476
  • Clark-Wilson, A., Robutti, O., & Thomas, M. (2020). Teaching with digital technology. ZDM, 52(7), 1223-1242. https://doi.org/10.1007/s11858-020-01196-0
  • Dick, T. (2008). Keeping the faith: Fidelity in technological tools for mathematics education. In G. Blume, & M. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Cases and perspectives (pp. 333-340). NCTM.
  • Drijvers, P., Ball, L., Barzel, B., Heid, M., Cao, Y., & Maschietto, M. (2016). Uses of technology in lower secondary mathematics education: A concise topical survey. Springer. https://doi.org/10.1007/978-3-319-33666-4_1
  • Guin, D., & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematical Learning, 3, 195-227. https://doi.org/10.1023/A:1009892720043
  • Hoyles, C. (2018) Transforming the mathematical practices of learners and teachers through digital technology. Research in Mathematics Education, 20(3), 209-228. https://doi.org/10.1080/14794802.2018.1484799
  • Hoyles, C., & Lagrange, J. (Eds.) (2010). Mathematics education and technology–Rethinking the terrain. Springer. https://doi.org/10.1007/978-1-4419-0146-0
  • Mishra, P., & Koehler, M. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017-1054. https://doi.org/10.1111/j.1467-9620.2006.00684.x
  • Olawoyin, O., Kribs, C., & Joswick, C. (2021). Embracing pivotal teaching moments: Elementary teachers’ role in advancing high cognitive levels of mathematics discourse. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-021-00374-x
  • Olive, J., Makar, K., Hoyos, V., Kor, L., Kosheleva, O., & Strässer (2010). Mathematical knowledge and practices resulting from access to digital technologies. In C. Hoyles, & J. Lagrange (Eds.), Mathematics education and technology–Rethinking the terrain (pp.133-178). Springer. https://doi.org/10.1007/978-1-4419-0146-0_8
  • Pimm, D. (2014). Integrated circuits. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era (pp. v-xii). Springer.
  • Rocha, H. (2013). Knowledge for teaching mathematics with technology–A new framework of teacher knowledge. In A. Lindmeier, & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (pp. 105-112). PME.
  • Rocha, H. (2014). Different representations in mathematics teaching with technology. In S. Oesterle, C. Nicol, P. Liljedahl, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (pp. 384). PME.
  • Rocha, H. (2020). Using tasks to develop pre-service teachers’ knowledge for teaching mathematics with digital technology. ZDM, 52(7), 1381-1396. https://doi.org/10.1007/s11858-020-01195-1
  • Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281. https://doi.org/10.1007/s10857-005-0853-5
  • Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
  • Stockero, S., & Zoest, L. (2013). Characterizing pivotal teaching moments in beginning mathematics teachers’ practice. Journal of Mathematics Teacher Education, 16, 125-147. https://doi.org/10.1007/s10857-012-9222-3
  • Tabach, M., & Trgalová, J. (2019). The knowledge and skills that mathematics teachers need for ICT integration: The issue of standards. In G. Aldon, & J. Trgalová (Eds.), Technology in mathematics teaching (pp. 183-203). Springer. https://doi.org/10.1007/978-3-030-19741-4_8
  • Thurm, D., & Barzel, B. (2021). Teaching mathematics with technology: A multidimensional analysis of teacher beliefs. Educational Studies in Mathematics, 109, 41-63. https://doi.org/10.1007/s10649-021-10072-x
  • Yin, R. (2003). Case study research–Design and methods. SAGE.
  • Zbiek, R., Heid, M., Blume, G., & Dick, T. (2007). Research on technology in mathematics education. In F. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1169-1207). NCTM.