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In-Service Teachers’ Transformation of a Mathematised Task into Modelling Tasks

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Advancing and Consolidating Mathematical Modelling

Abstract

In many countries, incorporating modelling as a part of day-to-day classes has been demonstrated to be a major challenge. This chapter focuses on in-service teachers with less experience in modelling teaching (‘novices’). This chapter aims to describe and analyse the novices’ activities to design modelling tasks based on mathematised tasks. The analysis results of the in-service teachers’ activities and artefacts revealed the following. It enables novice modelling teachers to (1) understand the characteristics of each criterion of the modelling task through activities that transform familiar textbook mathematised tasks into modelling tasks; and (2) develop and implement modelling lessons incorporating examples from students’ realities through Lesson Study during discussions with teachers from different backgrounds and researchers.

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References

  • Ang, K. C. (2018). Mathematical modelling for teachers: Resources, pedagogy and practice. Routledge. https://doi.org/10.4324/9781351247979

    Book  Google Scholar 

  • Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. C. Cho (Ed.), The proceedings of the 12th International Congress on Mathematical Education (pp. 73–96). Springer. https://doi.org/10.1007/978-3-319-12688-3

  • Borromeo Ferri, R. (2018). Learning how to teach mathematical modelling in school and teacher education. Springer. https://doi.org/10.1007/978-3-319-68072-9

    Book  Google Scholar 

  • Cai, J., Cirillo, M., Pelesko, J. P., Borromeo Ferri, R., Borba, M., Geiger, V., Stillman, G., English, L. D., Wake, G., Kaiser, G., & Kwon, O. N. (2014). Mathematical modeling in school education: Mathematical, cognitive, curricular, instructional and teacher education perspectives [Research Forum]. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the 38th conference of the International Group for the Psychology of Mathematics Education and the 36th conference of the North American Chapter of the Psychology of Mathematics Education (Vol. 1, pp. 145–172). PME. https://www.igpme.org/publications/current-proceedings/

  • Czocher, J. A. (2017). Mathematical modeling cycles as a task design heuristic. The Mathematics Enthusiast, 14(1–3), 129–140. https://doi.org/10.54870/1551-3440.1391

  • Fujii, T. (2015). The critical role of task design in lesson study. In A. Watson & M. Ohtani (Eds.), Task design in mathematics education: An ICMI study 22 (pp. 273–286). Springer. https://doi.org/10.1007/978-3-319-09629-2

  • Geiger, V., Galbraith, P., Niss, M., & Delzoppo, C. (2022). Developing a task design and implementation framework for fostering mathematical modelling competencies. Educational Studies in Mathematics, 109(2), 313–336. https://doi.org/10.1007/s10649-021-10039-y

    Article  Google Scholar 

  • Greefrath, G., & Vorhölter, K. (2016). Teaching and learning mathematical modelling. Approaches and developments from German speaking countries. Springer. https://doi.org/10.1007/978-3-319-45004-9

    Book  Google Scholar 

  • Ikeda, T. (2015). Mathematical modelling in Japan. In N. H. Lee & K. E. D. Ng (Eds.), Mathematical modelling: From theory to practice (pp. 83–96). World Scientific. https://doi.org/10.1142/8935

  • Julie, C., & Mudaly, V. (2007). Mathematical modelling of social issues in school mathematics in South Africa. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 503–510). Springer. https://doi.org/10.1007/978-0-387-29822-1

  • Kaiser, G. (2017). The teaching and learning of mathematical modelling. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 267–291). National Council of Teachers of Mathematics.

    Google Scholar 

  • Kaiser, G., & Brand, S. (2015). Modelling competencies: Past development and further perspectives. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice (pp. 129–149). Springer. https://doi.org/10.1007/978-3-319-18272-8

  • Kawakami, T., Saeki, A., & Kaneko, M. (2018). Secondary teachers constructing perspectives on developing mathematical modelling problems: Use of a modelling diagram for ‘Kyozaikenkyu'. In Hsieh, F.-J. (Ed.), Proceedings of the 8th ICMI-East Asian Regional Conference on Mathematics Education (Vol. 1, pp. 502–512). EARCOME.

    Google Scholar 

  • Leiß, D., & Wiegand, B. (2005). A classification of teacher interventions in mathematics teaching. ZDM—Mathematics Education, 37(3), 240–245. https://doi.org/10.1007/s11858-005-0015-3

  • Lewis, C. C., & Hurd, J. (2011). Lesson study step by step: How teacher learning communities improve instruction. Heinemann.

    Google Scholar 

  • Maaß, K. (2010). Classification scheme for modelling tasks. Journal für Mathematik-Didaktik, 31(2), 285–311. https://doi.org/10.1007/s13138-010-0010-2

    Article  Google Scholar 

  • Melville, M. D., & Corey, D. L. (2021). Kyouzaikenkyuu: An exploration of Japanese mathematics teachers’ daily planning practices. Journal of Mathematics Teacher Education, 25(3), 371–383. https://doi.org/10.1007/s10857-021-09493-5

  • Saeki, A., Kawakami, T., & Kaneko, M. (2019). A framework for designing mathematical modelling tasks using applied problems in math-textbooks. Journal of Science Education in Japan, 43(3), 220–232. https://doi.org/10.14935/jssej.43.220

  • Sevinc, S., & Lesh, R. (2018). Training mathematics teachers for realistic math problems: A case of modeling-based teacher education courses. ZDM—Mathematics Education, 50(1–2), 301–314. https://doi.org/10.1007/s11858-017-0898-9

    Article  Google Scholar 

  • Siller, H.-S., & Greefrath, M. (2020). Modelling tasks in central examinations based on the example of Austria. In G. A. Stillman, G. Kaiser, & E. Lampen (Eds.), Mathematical modelling education and sense making (pp. 383–392). Springer. https://doi.org/10.1007/978-3-030-37673-4

  • Stender, P., Krosanke, N., & Kaiser, G. (2017). Scaffolding complex modelling processes: An in-depth study. In G. A. Stillman et al. (Eds.), Mathematical modelling and applications: Crossing and researching boundaries in mathematics education (pp. 467–477). Springer. https://doi.org/10.1007/978-3-319-62968-1

  • Stillman, G. A. (2019). State of the art on modelling mathematics education—Lines of inquiry. In G. A. Stillman & J. P. Brown (Eds.), Lines of inquiry in mathematical modelling research in education (ICME-13 Monographs) (pp. 1–19). Springer. https://doi.org/10.1007/978-3-030-14931-4

  • Sugiyama, Y., Iitaka, S., Ito, S., et al. (2007). New arithmetic Grade 6 (Vol. 2). Tokyo-Shyoseki.

    Google Scholar 

  • Vos, P. (2011). What is ‘authentic’ in the teaching and learning of mathematical modelling? In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in the teaching and learning of mathematical modelling (pp. 713–718). Springer. https://doi.org/10.1007/978-94-007-0910-2

  • Wess, R., Klock, H., Siller, H.-S., & Greefrath, G. (2021). Measuring professional competence for the teaching of mathematical modelling. In F. K. S. Leung, G. A. Stillman, G. Kaiser, & K. L. Wong (Eds.), Mathematical modelling education in east and west (pp. 249–260). Springer. https://doi.org/10.1007/978-3-030-66996-6

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Acknowledgements

This work was supported by JSPS KAKENHI, Grant Numbers JP17K00975, JP15K00923, and JP17K14053. The study also received support from TSUCHIDA Satoshi (Kagoshima University), MATSUZAKI Akio (Saitama University), KOMEDA Shigekazu (Saga University), FUJIWARA Daiki (Junior High School of Ochanomizu University), MINENO Kosuke (Setagaya Junior High School, affiliated to Tokyo Gakugei University), TOMITA Masato (Shizuoka West High School), ARAOKA Kiyohide (Ebara-kita Elementary School), and Ooishi Akihiro (Kisaki Elementary School). We express our gratitude to the reviewers.

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Authors and Affiliations

  1. Kanazawa Institute of Technology, 7-1, Ohgigaoka, Nonoichi, Ishikawa, 921-8501, Japan

    Akihiko Saeki

  2. Teikyo Heisei University, 4-21-2 Nakano, Nakano-ku, Tokyo, 164-8530, Japan

    Masafumi Kaneko

  3. Utsunomiya University, 350 Mine-Machi, Utsunomiya, Tochigi, 321-8505, Japan

    Takashi Kawakami

  4. Yokohama National University, 79-2, Tokiwadai, Hodogaya-Ku, Yokohama, 240-8501, Japan

    Toshikazu Ikeda

Authors
  1. Akihiko Saeki
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  2. Masafumi Kaneko
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  3. Takashi Kawakami
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  4. Toshikazu Ikeda
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Correspondence to Akihiko Saeki .

Editor information

Editors and Affiliations

  1. Institute for Mathematics Education and Computer Science Education, University of Münster, Münster, Germany

    Gilbert Greefrath

  2. University of Algarve and UIDEF, Institute of Education, University of Lisbon, Faro, Portugal

    Susana Carreira

  3. Australian Catholic University, Ballarat, VIC, Australia

    Gloria Ann Stillman

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Saeki, A., Kaneko, M., Kawakami, T., Ikeda, T. (2023). In-Service Teachers’ Transformation of a Mathematised Task into Modelling Tasks. In: Greefrath, G., Carreira, S., Stillman, G.A. (eds) Advancing and Consolidating Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-031-27115-1_15

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  • DOI: https://doi.org/10.1007/978-3-031-27115-1_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-27114-4

  • Online ISBN: 978-3-031-27115-1

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