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Professional Development for Teaching Mathematics with Technology: Fostering Teacher and Facilitator Noticing

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The Mathematics Teacher in the Digital Era

Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 16))

Abstract

Professional development of facilitators has been highlighted as a decisive factor for scaling-up professional development (PD) efforts. However, research on facilitators is still burgeoning and, for many areas like teaching mathematics with technology, little research is available on how to professionalise facilitators. In this paper we question how to prepare facilitators to support teachers for teaching mathematics with multi-representational-tools (MRT). Teaching mathematics with MRT requires a teacher to notice the subtle ways in which technology supports students learning and the challenge for facilitators is to support such a nuanced teacher noticing. Therefore, we focus on the constructs of teacher and facilitator noticing when teaching with MRT, and describe the design and implementation of a video-case-based strategy to professionalise PD facilitators to support teachers noticing of students learning when working with MRT. For this we developed the Content-Activity-Technology-Model (CAT-Model) that helps to capture in graphic form the students’ learning processes when working with technology. This provides a more accessible format for teachers and facilitators, which can also be used to reconstruct teacher and facilitator noticing. Our analyses across the three levels of the CAT-Model leads us to identify the potential and challenges for this method and outline how the multi-level video-based design can be further improved.

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References

  • Aldon, G., & Trgalová, J. (2017). Proceedings of the 13th international conference on Technology in Mathematics Teaching. Technology in Mathematics Teaching ICTMT 13 Ecole Normale Supérieure de Lyon/Université Claude Bernard Lyon 1 3 to 6 July, 2017.

    Google Scholar 

  • Anderson, L. W., & Krathwohl, D. R. (Eds.). (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. Allyn & Bacon.

    Google Scholar 

  • Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practises in Cabri environments. Zentralblatt für Didaktik der Mathematik, 34(3), 66–72.

    Article  Google Scholar 

  • Ball, L., Drijvers, P., Ladel, S., Siller, H. S., Tabach, M., & Vale, C. (2018). Uses of technology in primary and secondary mathematics education. Springer.

    Book  Google Scholar 

  • Barzel, B., & Möller, R. (2001). About the use of the TI-92 for an open learning approach to power functions. Zentralblatt für Didaktik der Mathematik, 33(1), 1–5.

    Article  Google Scholar 

  • Barzel, B., Bebernik, R., Göbel, L., Pohl, M., Ruchniewicz, H., Schacht, F., & Thurm, D. (2020). Proceedings of the 14th international conference on Technology in Mathematics Teaching – ICTMT 14: Essen, Germany, 22nd to 25th of July 2019. https://doi.org/10.17185/duepublico/48820.

  • Beattie, H. L., Ren, L., Smith, W. M., & Heaton, R. M. (2017). Measuring elementary mathematics teachers’ noticing: Using child study as a vehicle. In E. O. Schack, M. H. Fisher, & J. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 321–338). Springer.

    Chapter  Google Scholar 

  • Biggs, J. (2003). Teaching for quality learning at university (2nd ed.). The Society for Research into Higher Education and Open University Press.

    Google Scholar 

  • Borko, H. (2004). Professional development and teacher learning: Mapping the terrain. Educational Researcher, 33(8), 3–15.

    Article  Google Scholar 

  • Borko, H., & Potari, D. (Eds.). (2020). Teachers of mathematics working and learning in collaborative groups (ICMI STUDY 25 conference proceedings). University of Lisbon.

    Google Scholar 

  • Borko, H., Koellner, K., & Jacobs, J. (2014). Examining novice teacher leaders’ facilitation of professional development. Journal of Mathematical Behavior, 33, 149–167.

    Article  Google Scholar 

  • Borko, H., Carlson, J., Deutscher, R., Boles, K. L., Delaney, V., Fong, A., … Villa, A. M. (2021). Learning to Lead: An approach to mathematics teacher leader development. International Journal of Science and Mathematics Education, 1–23.

    Google Scholar 

  • Clark-Wilson, A., & Hoyles, C. (2019). A research-informed web-based professional development toolkit to support technology-enhanced mathematics teaching at scale. Educational Studies in Mathematics, 102(3), 343–359.

    Article  Google Scholar 

  • Clark-Wilson, A., Robutti, O., & Sinclair, N. (2014). The mathematics teacher in the digital era: An international perspective on technology focused professional development. Springer.

    Book  Google Scholar 

  • Clark-Wilson, A., Robutti, O., & Thomas, M. (2020). Teaching with digital technology. ZDM Mathematics Education, 52, 1223–1242. https://doi.org/10.1007/s11858-020-01196-0

    Article  Google Scholar 

  • Drijvers, P. (1994). Graphics calculators and computer algebra systems: Differences and similarities. In H. Heugl & B. Kutzler (Eds.), Derive in education: Opportunities and strategies (pp. 189–200). Chartwell-Bratt.

    Google Scholar 

  • Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213–234.

    Article  Google Scholar 

  • Drijvers, P., Ball, L., Barzel, B., Heid, M. K., Cao, Y., & Maschietto, M. (2016). Uses of Technology in Lower Secondary Mathematics Education: A concise topical survey. Springer.

    Book  Google Scholar 

  • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131.

    Article  Google Scholar 

  • Ebers, P. (2020a). Videofälle zur Vorbereitung von Lehrkräften auf das Unterrichten mit digitalen Medien. In H.-S. Siller, W. Weigel, & J. F. Worler (Eds.), Beiträge zum Mathematikunterricht 2020 (pp. 1297–1300). WTM-Verlag.

    Google Scholar 

  • Ebers, P. (2020b). Development of video cases regarding technology use for professional development programs. In B. Barzel, R. Bebernik, L. Göbel, M. Pohl, H. Ruchniewicz, F. Schacht, & D. Thurm (Eds.), Proceedings of the 14th International Conference on Technology in Mathematics Teaching – ICTMT 14: Essen, Germany, 22nd to 25th of July 2019 (pp. 287–288). https://doi.org/10.17185/duepublico/48820

    Chapter  Google Scholar 

  • Elliott, R., Kazemi, E., Lesseig, K., Mumme, J., Carroll, C., & Kelley-Petersen, M. (2009). Conceptualizing the work of leading mathematical tasks in professional development. Journal of Teacher Education, 60(4), 364–379.

    Article  Google Scholar 

  • Ertmer, P. A., & Ottenbreit-Leftwich, A. T. (2010). Teacher technology change: How knowledge, confidence, beliefs, and culture intersect. Journal of Research on Technology in Education, 42(3), 255–284.

    Article  Google Scholar 

  • Goeze, A., Zottmann, J. M., Vogel, F., Fischer, F., & Schrader, J. (2014). Getting immersed in teacher and student perspectives? Facilitating analytical competence using video cases in teacher education. Instructional Science, 42(1), 91–114. https://doi.org/10.1007/s11251-013-9304-3

    Article  Google Scholar 

  • Goldsmith, L. T., Doerr, H. M., & Lewis, C. C. (2014). Mathematics teachers’ learning: A conceptual framework and synthesis of research. Journal of Mathematics Teacher Education, 17(1), 5–36.

    Article  Google Scholar 

  • Goodwin, C. (1994). Professional vision. American Anthropologist, 96(3), 606–633.

    Article  Google Scholar 

  • Grugeon, B., Lagrange, J.-B., Jarvis, D., Alagic, M., Das, M., & Hunscheidt, D. (2010). Teacher education courses in mathematics and technology: Analyzing views and options. In C. Hoyles & J.-B. Lagrange (Eds.), Mathematics education and technology—Rethinking the terrain (pp. 329–345). Springer.

    Google Scholar 

  • Guin, D., & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. The International Journal of Computers for Mathematical Learning, 3(3), 195–227.

    Article  Google Scholar 

  • Hegedus, S., Laborde, C., Brady, C., Dalton, S., & Siller, H.-St., Tabach, M., Trgalova, J., & Moreno-Armella, L. (2017). Uses of Technology in Upper Secondary Mathematics Education. Springer.

    Book  Google Scholar 

  • Heid, M. K., & Blume, G. W. (Eds.). (2008). Research on technology and the teaching and learning of mathematics: Volume 1: Research synthesis. Information Age Publishing.

    Google Scholar 

  • Hogan, T., Rabinowitz, M., & Craven, J. A., III. (2003). Representation in teaching: Inferences from research of expert and novice teachers. Educational Psychologist, 38(4), 235–247. https://doi.org/10.1207/S15326985EP3804_3

    Article  Google Scholar 

  • Hoyles, C., & Lagrange, J. B. (Eds.). (2010). Mathematics education and technology: Rethinking the terrain. Springer.

    Google Scholar 

  • Jacobs, J., Seago, N., & Koellner, K. (2017). Preparing facilitators to use and adapt mathematics professional development materials productively. International Journal of STEM Education, 4(30), 1–14.

    Google Scholar 

  • Kilic, H. (2018). Pre-service mathematics teachers’ noticing skills and scaffolding practices. International Journal of Science and Mathematics Education, 16(2), 377–400.

    Article  Google Scholar 

  • Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75–86. https://doi.org/10.1207/s15326985ep4102_1

    Article  Google Scholar 

  • Koc, Y., Peker, D., & Osmanoglu, A. (2009). Supporting teacher professional development through online video case study discussions: An assemblage of preservice and inservice teachers and the case teacher. Teaching and Teacher Education, 25, 1158–1168.

    Article  Google Scholar 

  • Krammer, K., Schnetzler, C. L., Ratzka, N., Reusser, K., Pauli, C., Lipowsky, F., & Klieme, E. (2008). Lernen mit Unterrichtsvideos: Konzeption und Ergebnisse eines netzgestützten Weiterbildungsprojekts mit Mathematiklehrpersonen aus Deutschland und der Schweiz. Beiträge zur Lehrerbildung, 26(2), 178–197.

    Google Scholar 

  • Kuzle, A., & Biehler, R. (2015). Examining mathematics mentor teachers’ practices in professional development courses on teaching data analysis: Implications for mentor teachers’ programs. ZDM, 47(1), 39–51.

    Article  Google Scholar 

  • Lee, M. Y., & Choy, B. H. (2017). Mathematical teacher noticing: The key to learning from lesson study. In E. Schack, M. Fisher, & J. Wilhelm (Eds.), Teacher Noticing: Bridging and broadening perspectives, contexts, and frameworks. Research in mathematics education (pp. 121–140). Springer.

    Chapter  Google Scholar 

  • Lesseig, K., Elliott, R., Kazemi, E., Kelley-Petersen, M., Campbell, M., Mumme, J., & Carroll, C. (2017). Leader noticing of facilitation in videocases of mathematics professional development. Journal of Mathematics Teacher Education, 20(6), 591–619.

    Article  Google Scholar 

  • Leufer, N., Prediger, S., Mahns, P., & Kortenkamp, U. (2019). Facilitators’ adaptation practices of curriculum material resources for professional development courses. International Journal of STEM Education, 6(1), 1–18.

    Article  Google Scholar 

  • Mackey, K. (1999). Do we need calculators? In Z. Usiskin (Ed.), Mathematics education dialogues (p. 3). NCTM.

    Google Scholar 

  • Peters-Dasdemir, J., Holzäpfel, L., Barzel, B., & Leuders, T. (2020). Professionalization of facilitators in mathematics education: A competency framework. In M. Inprasitha, N. Changsri, & N. Boonsena (Eds.), Proceedings of the 44th conference of the International Group for the Psychology of mathematics education (interim volume) (pp. 457–465). PME.

    Google Scholar 

  • Pierce, R., & Stacey, K. (2010). Mapping pedagogical opportunities provided by mathematics analysis software. International Journal of Computers for Mathematical Learning, 15(1), 1–20.

    Article  Google Scholar 

  • Poehler, B. (2020). Role of facilitators in supporting teacher collaboration during PD courses on language-responsive mathematics teaching. In H. Borko & D. Potari (Eds.), ICMI study 25: Teachers of mathematics working and learning in collaborative groups (pp. 516–523). University of Lisbon.

    Google Scholar 

  • Praetorius, A.-K., McIntyre, N. A., & Klassen, R. M. (2017). Reactivity effects in video-based classroom research: An investigation using teacher and student questionnaires as well as teacher eye-tracking. Zeitschrift für Erziehungswissenschaft, 20(1), 49–74.

    Article  Google Scholar 

  • Prediger, S. (2019). Investigating and promoting teachers’ expertise for language-responsive mathematics teaching. Mathematics Education Research Journal, 31(4), 367–392.

    Article  Google Scholar 

  • Prediger, S., Roesken-Winter, B., & Leuders, T. (2019). Which research can support PD facilitators? Strategies for content-related PD research in the three-tetrahedron model. Journal of Mathematics Teacher Education, 22(4), 407–425.

    Article  Google Scholar 

  • Psycharis, G., & Kalogeria, E. (2018). Studying the process of becoming a teacher educator in technology-enhanced mathematics. Journal of Mathematics Teacher Education, 21(6), 631–660.

    Article  Google Scholar 

  • Ratnayake, I., Thomas, M., & Kensington-Miller, B. (2020). Professional development for digital technology task design by secondary mathematics teachers. ZDM, 52(7), 1423–1437.

    Article  Google Scholar 

  • Rittle-Johnson, B., & Schneider, M. (2015). Developing conceptual and procedural knowledge of mathematics. In R. C. Kadosh & A. Dowker (Eds.), Oxford handbook of numerical cognition (pp. 1118–1134).

    Google Scholar 

  • Rittle-Johnson, B., Schneider, M., & Star, J. R. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27(4), 587–597.

    Article  Google Scholar 

  • Roesken-Winter, B., Schueler, S., Stahnke, R., & Bloemeke, S. (2015). Effective CPD on a large scale: Examining the development of multipliers. ZDM, 47(1), 13–25.

    Article  Google Scholar 

  • Roesken-Winter, B., Stahnke, R., Prediger, S., & Gasteiger, H. (2021). Towards a research base for implementation strategies addressing mathematics teachers and facilitators. ZDM–mathematics. Education, 1–13.

    Google Scholar 

  • Schoenfeld, A. (2011). Noticing matters. A lot. Now what? In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 3–14). Routledge.

    Google Scholar 

  • Schueler, S., & Roesken-Winter, B. (2018). Compiling video cases to support PD facilitators in noticing productive teacher learning. International Journal of STEM Education, 2018(5), 50. https://doi.org/10.1186/s40594-018-0147-y

    Article  Google Scholar 

  • Sherin, M. G. (2004). New perspectives on the role of video in teacher education. In J. Brophy (Ed.), Using video in teacher education (pp. 1–27). Elsevier Science.

    Google Scholar 

  • Sherin, M. G. (2007). The development of teachers’ professional vision in video clubs. In R. Goldman, R. Pea, B. Barron, & S. J. Deny (Eds.), Video research in the learning sciences (pp. 383–395). Erlbaum.

    Google Scholar 

  • Sherin, M. G., & Russ, R. S. (2015). Teacher noticing via video. In B. Calandra & P. J. Rich (Eds.), Digital video for teacher education (pp. 3–20). Routledge.

    Google Scholar 

  • Sherin, M. G., & van Es, E. A. (2009). Effects of video club participation on teachers’ professional vision. Journal of Teacher Education, 60(1), 20–37.

    Article  Google Scholar 

  • Sherin, M. G., Jacobs, V., & Philipp, R. (2011a). Situating the study of teacher noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 3–14). Routledge.

    Chapter  Google Scholar 

  • Sherin, M. G., Russ, R. S., & Colestock, A. (2011b). Accessing mathematics teachers’ in-the-moment noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing; seeing through teachers’ eyes (pp. 79–94). Routledge.

    Chapter  Google Scholar 

  • Sherman, M. F. (2012). Supporting students’ mathematical thinking during technology-enhanced investigations using DGS. In D. Martinovic, D. McDougall, & Z. Karadag (Eds.), Technology in mathematics education: Contemporary issues (pp. 147–182). Informing Science Institute.

    Google Scholar 

  • Stahnke, R., Schueler, S., & Roesken-Winter, B. (2016). Teachers’ perception, interpretation, and decision-making: A systematic review of empirical mathematics education research. ZDM, 48(1–2), 1–27.

    Article  Google Scholar 

  • Thomas, M. O. J., & Palmer, J. (2014). Teaching with digital technology: Obstacles and opportunities. In A. Clark-Wilson, N. Sinclair, & O. Robutti (Eds.), The mathematics teacher in the digital era (pp. 71–89). Springer.

    Chapter  Google Scholar 

  • Thurm, D. (2017). Psychometric evaluation of a questionnaire measuring teacher beliefs regarding teaching with technology. In B. Kaur, W. K. Ho, T. L. Toh, & B. H. Choy (Eds.), Proceedings of the 41st Conference of the International Group for the Psy-chology of Mathematics Education (Bd. 4) (pp. 265–272).

    Google Scholar 

  • Thurm, D. (2020). Digitale Werkzeuge im Mathematikunterricht integrieren: Zur Rolle von Lehrerüberzeugungen und der Wirksamkeit von Fortbildungen. Springer.

    Book  Google Scholar 

  • Thurm, D., & Barzel, B. (2020). Effects of a professional development program for teaching mathematics with technology on teachers’ beliefs, self-efficacy and practices. ZDM Mathematics Education, 52, 1411–1422. https://doi.org/10.1007/s11858-020-01158-6

    Article  Google Scholar 

  • Thurm, D., & Barzel, B. (2021). Teaching mathematics with technology: A multidimensional analysis of teacher beliefs and practice. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-021-10072-x

  • Thurm, D., Bozkurt, G., Barzel, B., Sacristán, A. I. & Ball, L. (2023). A review of research on professional development for teaching mathematics with digital technology. In B. Pepin, G. Gueudet, & J. Choppin (Eds.), Handbook for Digital Resources in Mathematics Education. Springer.

    Google Scholar 

  • Trouche, L., & Drijvers, P. (2010). Handheld technology for mathematics education: Flashback into the future. ZDM, 42(7), 667–681.

    Article  Google Scholar 

  • van Es, E. A. (2011). A framework for learning to notice students’ thinking. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 134–151). Routledge.

    Google Scholar 

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Thurm, D., Ebers, P., Barzel, B. (2022). Professional Development for Teaching Mathematics with Technology: Fostering Teacher and Facilitator Noticing. In: Clark-Wilson, A., Robutti, O., Sinclair, N. (eds) The Mathematics Teacher in the Digital Era. Mathematics Education in the Digital Era, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-031-05254-5_1

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