, Volume 50, Issue 1–2, pp 273–285 | Cite as

Impact of professional development involving modelling on teachers and their teaching

  • Katja MaassEmail author
  • Katrin Engeln
Original Article


This paper presents an international research study of long-term professional development courses on modelling. It addresses the question of scaling-up professional development. So far, there has been much research on small-scale professional development courses, but we know very little about what it means to scale up such a course and to reach out to large numbers of teachers. Therefore, our study researches the impact of a scaled up professional development course on teachers and their teaching, as perceived by the teachers themselves and their students. The course was designed on an international level for use in 12 countries. The results show that such a course can indeed lead to desired outcomes concerning the teachers and their teaching, and the research therefore adds to our understanding of scaling-up.


Mathematical modelling Inquiry-based learning Continuous professional development Scaling-up professional development International study Teachers’ and students’ perceptions on teaching 



The project PRIMAS has received funding from the European Union Seventh Framework Programme (FP7/2007–2013) under grant agreement no. 244380. This paper reflect only the authors’ views and the European Union is not liable for any use that may be made of the information contained herein.


  1. Adler, J., & Jaworski, B. (2009). Public writing in the field of mathematics teacher education. In R. Even & D. L. Ball (Eds.), The professional education and development of teachers of mathematics–the 15th ICMI study (pp. 249–254). New York: Springer.CrossRefGoogle Scholar
  2. Akker, J. v. d, Gravemeijer, K., McKenney, S., & Nieveen, N. (2006). Introducing educational design research. In J. V. D. Akker, K. Gravemeijer, S. McKenney & N. Nieveen (Eds.), Educational design research (Vol. 1, pp. 3–7). Oxford: Routledge Chapman & Hall.Google Scholar
  3. Alfieri, L., Brooks, P. J., Aldrich, N. J., & Tenenbaum, H. R. (2011). Does discovery-based instruction enhance learning? Journal of Educational Psychology, 103(1), 1–18.CrossRefGoogle Scholar
  4. Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM Mathematics Education, 45(6), 797–810.CrossRefGoogle Scholar
  5. Askew, M., Brown, M., Rhodes, V., Johnson, D., & Wiliam, D. (1997). Effective teachers of numeracy. London: Kings College.Google Scholar
  6. Barzel, B., & Selter, C. (2015). Die DZLM-Gestaltungsprinzipien für Fortbildungen. Journal für Mathematik-Didaktik, 36(2), 259–284.CrossRefGoogle Scholar
  7. Baumert, J., & Kunter, M. (2006). Stichwort: Professionelle Kompetenz von Lehrkräften. Zeitschrift für Erziehungswissenschaft, 9(4), 469–520.Google Scholar
  8. Baumert, J., & Kunter, M. (2013). The COACTIV model of teachers’ professional competence. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers: Results from the COACTIV project (Vol. 8). Berlin: Springer: Mathematics Teacher Education.Google Scholar
  9. Baumert, J., Kunter, M., Brunner, M., Krauss, S., Blum, W., & Neubrand, M. (2004). Mathematikunterricht aus Sicht der PISA–Schülerinnen und Schüler und ihrer Lehrkräfte. In P.-K. Deutschland (Ed.), PISA 2003–Der Bildungsstand der Jugendlichen in Deutschland–Ergebnisse des zweiten internationalen Vergleichs (pp. 314–354). Münster: Waxmann.Google Scholar
  10. Besser, M., Leiss, D., & Klieme, E. (2015). Wirkung von Lehrerfortbildungen auf Expertise von Lehrkräften zu formativem Assessment im kompetenzorientierten Mathematikunterricht. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 47(2), 110–122.CrossRefGoogle Scholar
  11. Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. B. Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: ICTMA14 (pp. 15–30). New York: Springer Science & Business Media.CrossRefGoogle Scholar
  12. Blum, W., & Leiss, D. (2005). Modellieren im Unterricht mit der” Tanken"-Aufgabe. mathematik lehren, 128, 18–21.Google Scholar
  13. Boaler, J. (2008). Bridging the gap between research and practice: International examples of success. In M. Menghini, F. Furinghetti, L. Giarcardi & F. Arzarella (Eds.), The first century of the International Commission on Mathematics Instruction (1908–2008): Reflecting and shaping the world of mathematics education. Roma: Instituto della Enciclopedia Italiana foundata da Giovanni Treccani.Google Scholar
  14. Clarke, D. (1994). Ten key principles from research for the professional development of mathematics teachers. In D. B. Aichele & A. F. Croxford (Eds.), Professional development for teachers of mathematics (pp. 37–48). Reston: NCTM.Google Scholar
  15. Clarke, D., & Hollingsworth, H. (2002). Elaborating a model of teacher professional growth. Teaching and teacher education, 18(8), 947–967.CrossRefGoogle Scholar
  16. Clausen, M. (2002). Unterrichtsqualität: Eine Frage der Perspektive? [Quality of instruction: A matter of persepctive?]. Münster: Waxmann.Google Scholar
  17. Coe, R. (2002). It’s the effect size, stupid: what effect size is and why it is important. In Paper presented at the annual conference of the British Educational Research Association, University of Exeter, 12–14 September 2002.Google Scholar
  18. De Jong, R., & Westerhof, K. J. (2001). The quality of student ratings of teacher behaviour. Learning Environments Research, 4(1), 51–85.CrossRefGoogle Scholar
  19. Dorier, J.-L., & García, F. J. (2013). Challenges and opportunities for the implementation of inquiry-based learning in day-to-day teaching. ZDM Mathematics Education, 45(6), 837–849.CrossRefGoogle Scholar
  20. Dorier, J.-L., & Maass, K. (2014). Inquiry-based mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 300–304). Dordrecht: Springer.Google Scholar
  21. Engeln, K., Euler, M., & Maass, K. (2013). Inquiry-based learning in mathematics and science: A comparative baseline study of teachers’ beliefs and practices across 12 European countries. ZDM Mathematics Education, 45(6), 823–836.CrossRefGoogle Scholar
  22. Euler, M. (2011). WP9: Report about the survey on inquiry-based learning and teaching in the European partner countries. PRIMAS: Promoting inquiry-based learning in mathematics and science education across Europe.Google Scholar
  23. Guskey, T. R. (2000). Evaluating professional development. Thousand Oaks: Cirwin Press.Google Scholar
  24. Hudson, S. B., McMahon, K. C., & Overstreet, C. M. (2002). The 2000 national survey of science and mathematics education: Compendium of tables. Chapel Hill: Horizon Research.Google Scholar
  25. Jackson, K., Cobb, P., Wilson, J., Webster, M., Dunlap, C., & Appelgate, M. (2015). Investigating the development of mathematics leaders’ capacity to support teachers’ learning on a large scale. ZDM Mathematics Education, 47(1), 93–104.CrossRefGoogle Scholar
  26. Kaiser, G., & Schwarz, B. (2010). Authentic modelling problems in mathematics education—Examples and experiences. Journal für Mathematik–Didaktik, 31(1), 51–76.CrossRefGoogle Scholar
  27. Kaiser, G., Schwarz, B., & Buchholz, N. (2011). Authentic modelling problems in mathematics education. In G. Kaiser, W. Blum, R. B. Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: ICTMA14 (pp. 591–602). New York: Springer Science & Business Media.CrossRefGoogle Scholar
  28. Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM Mathematics Education, 38(3), 302–310.CrossRefGoogle Scholar
  29. Krainer, K. (2011). Teachers as stakeholders in mathematics education research. In B. Ubuz (Ed.), Proceedings of the 35th conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 47–62). Ankara: Middle East Technical UniversityGoogle Scholar
  30. Lipowsky, F., & Rzejak, D. (2012). Lehrerinnen und Lehrer als Lerner–Wann gelingt der Rollentausch? Merkmale und Wirkungen wirksamer Lehrerfortbildungen. Schulpädagogik heute, 3(5), 1–17.Google Scholar
  31. Loucks-Horsley, S., Stiles, K. E., Mundry, S., Love, N., & Hewson, P. W. (2009). Designing professional development for teachers of science and mathematics. London: Corwin Press.Google Scholar
  32. Lüdtke, O., Trautwein, U., Kunter, M., & Baumert, J. (2006). Reliability and agreement of student ratings of the classroom environment: A reanalysis of TIMSS data. Learning Environments Research, 9(3), 215–230.CrossRefGoogle Scholar
  33. Maass, K. (2004). Mathematisches Modellieren im Unterricht. Hildesheim: Franzbecker.Google Scholar
  34. Maass, K. (2007). Modelling in class: What do we want students to learn. In C. Haines, P. Galbraith, W. Blum & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics–ICTMA 12 (pp. 63–78). Chichester: Horwood.CrossRefGoogle Scholar
  35. Maass, K. (2011). How can teachers’ beliefs affect their professional development? ZDM Mathematics Education, 43(4), 573–586.CrossRefGoogle Scholar
  36. Maass, K., & Artigue, M. (2013). Implementation of inquiry-based learning in day-to-day teaching: a synthesis. ZDM Mathematics Education, 45(6), 779–795.CrossRefGoogle Scholar
  37. Maass, K., & Doorman, M. (2013). A model for a widespread implementation of inquiry-based learning. ZDM Mathematics Education, 45(6), 887–899.CrossRefGoogle Scholar
  38. Marsh, H. W., Trautwein, U., Lüdtke, O., Köller, O., & Baumert, J. (2005). Academic self-concept, interest, grades and standardized test scores: reciprocal effects models of causal ordering. Child Development, 76(2), 397–416.Google Scholar
  39. McLaughlin, M. W., & Talbert, J. E. (2006). Building school-based teacher learning communities: Professional strategies to improve student achievement (Vol. 45). New York: Teachers College Press.Google Scholar
  40. Mischo, C., & Maass, K. (2013). The effect of teacher beliefs on student competence in mathematical modeling–An intervention study. Journal of Education and Training Studies, 1(1), 19–38.CrossRefGoogle Scholar
  41. Niss, M. (1992). Applications and modelling in school mathematics–Directions for future developement. Roskilde: IMFUFA Roskilde Universitetscenter.Google Scholar
  42. Niss, M., Blum, W., & Galbraith, P. L. (2007). Introduction. In W. Blum, P. L. Galbraith, H.-W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI Study (pp. 3–32). New York: Springer.CrossRefGoogle Scholar
  43. OECD (1998). Staying ahead: In-service training and teacher professional development: Paris: OECD Publishing.Google Scholar
  44. OECD (2009). Technical reportPISA 2006. Paris: OECD Publishing.CrossRefGoogle Scholar
  45. OECD (2014). TALIS 2013 results: An international perspective on teaching and learning. Paris: OECD Publishing.Google Scholar
  46. OECD (2016). PISA 2015 results (Volume II): Policies and practices for successful schools. PISA: OECD Publishing, Paris.Google Scholar
  47. Palm, T. (2007). Features and impact of the authenticity of applied mathematical school tasks. In W. Blum, P. L. Galbraith, H.-W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI Study (pp. 201–208). New York: Springer.CrossRefGoogle Scholar
  48. Perrin-Glorian, M.-J., Deblois, L., & Robert, A. (2008). Individual practicing mathematics teachers: Studies on their professional growth. In K. Krainer & T. Wood (Eds.), Participation in mathematics teacher education. Individuals, teams, communities and networks (Vol. 3, pp. 35–39). Rotterdam: Sense Publishers.Google Scholar
  49. Putnam, R. T., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational Researcher, 29(1), 4–15.CrossRefGoogle Scholar
  50. Radford, L. (2010). The anthropological turn in mathematics education and its implication on the meaning of mathematical activity and classroom practice. Acta Didactica Universitatis Comenianae Mathematics, 10, 103–120.Google Scholar
  51. Rocard, M., Csermely, P., Jorde, D., Lenzen, D., Walberg-Henriksson, H., & Hemmo, V. (2007). Rocard report: “Science education now: A new pedagogy for the future of Europe”. EU 22845, European Commission.Google Scholar
  52. Roesken-Winter, B., Hoyles, C., & Blömeke, S. (2015a). Evidence-based CPD: Scaling up sustainable interventions. ZDM Mathematics Education, 47(1), 1–12.CrossRefGoogle Scholar
  53. Roesken-Winter, B., Schüler, S., Stahnke, R., & Blömeke, S. (2015b). Effective CPD on a large scale: examining the development of multipliers. ZDM Mathematics Education, 47(1), 13–25.CrossRefGoogle Scholar
  54. Schukajlow, S., Krug, A., & Rakoczy, K. (2015). Effects of prompting multiple solutions for modelling problems on students’ performance. Educational Studies in Mathematics, 89(3), 393–417.CrossRefGoogle Scholar
  55. Shulman, L. S. (1986). Paradigms and research programs in the study of teaching: A contemporary perspective. In M. C. Wittrock (Ed.), Handbook of research in teaching (pp. 3–36). New York: Macmillan.Google Scholar
  56. Skott, J. (2013). Understanding the role of the teacher in emerging classroom practices: Searching for patterns of participation. ZDM Mathematics Education, 45(4), 547–559.CrossRefGoogle Scholar
  57. Swan, M. (2005). Improving learning in mathematics: Challenges and strategies. Sheffield: Teaching and Learning Division, Department for Education and Skills Standards Unit.Google Scholar
  58. Swan, M. (2006). Collaborative learning in mathematics: A challenge to our beliefs and practices. London: National Institute for Advanced and Continuing Education (NIACE) for the National Research and Development Centre for Adult Literacy and Numeracy (NRDC).Google Scholar
  59. Swan, M. (2007). The impact of task-based professional development on teachers’ practices and beliefs: A design research study. Journal of Mathematics Teacher Education, 10(4–6), 217–237.CrossRefGoogle Scholar
  60. Tirosh, D., & Graeber, A. O. (2003). Challenging and changing mathematics teaching classroom practices. In A. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick & F. Leung (Eds.), Second international handbook of mathematics education (pp. 643–687). Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  61. Valentine, J. C., & Cooper, H. (2003). Effect size substantive interpretation guidelines: issues in the interpretation of effect sizes. Washington, DC: What Works Clearinghouse.Google Scholar
  62. Vos, P. (2011). What is “authentic” in the teaching and learning of mathematical modelling? In G. Kaiser, W. Blum, R. B. Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 713–722). Dordrecht: Springer.CrossRefGoogle Scholar
  63. Weiss, I. R., Pasley, J. D., Smith, P. S., Banilower, E. R., & Heck, D. J. (2003). Looking inside the classroom. Chapel Hill: Horizon Research Inc.Google Scholar
  64. Zehetmeier, S., & Krainer, K. (2011). Ways of promoting the sustainability of mathematics teachers’ professional development. ZDM Mathematics Education, 43(6–7), 875–887.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2018

Authors and Affiliations

  1. 1.International Centre for STEM Education at University of education FreiburgFreiburgGermany
  2. 2.IPN-Leibniz Institute for Science and Mathematics EducationKielGermany

Personalised recommendations