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Journal of Educational Research in Mathematics -
Vol. 31, No. 2

[ Article ] | |

Journal of Educational Research in Mathematics - Vol. 31, No. 1, pp.35-62 | |

Abbreviation: JERM | |

ISSN: 2288-7733 (Print) 2288-8357 (Online) | |

Print publication date 28 Feb 2021 | |

Received 09 Jan 2021 Revised 01 Feb 2021 Accepted 04 Feb 2021 | |

DOI: https://doi.org/10.29275/jerm.2021.02.31.1.35 | |

Promoting In-service Teacher’s Mathematical Modeling Teaching Competencies by Implementing and Modifying Mathematical Modeling Tasks | |

Jung, Hye-Yun ^{*} ; Lee, Kyeong-Hwa^{**}^{, †}
| |

*Associate Research Fellow, Korea Institute for Curriculum and Evaluation, South Korea (hy0501@kice.re.kr) | |

**Professor, Seoul National University, South Korea (khmath@snu.ac.kr) | |

Correspondence to : ^{†}Professor, Seoul National University, South Korea, khmath@snu.ac.kr | |

Abstract

The purpose of this study is to investigate how teachers demonstrate ‘mathematical modeling teaching competencies’ (MMTCs) by implementing and modifying mathematical modeling tasks, as well as to suggest how teacher education should support teachers for teaching mathematical modeling. A teacher with three years of teaching experience participated in this study. Data sources include transcripts, student worksheets, interviews and the researcher’s field notes. The findings indicate that the participant edited tasks to improve the realism and complexity of mathematical modeling tasks. The edits included simplifying and specifying; the participant also decomposed tasks into multiple subtasks. Through iterative implementations and modifications, the participant improved his MMTCs in four dimensions -- diagnostic, theoretical, task, and instructional dimensions were promoted in relays and cyclically. The implementation and modification of the task contributed to connecting theoretical knowledge and practical competencies to mathematical modeling. The study recommends the following areas of need in order to develop teachers’ MMTCs: combining theoretical and practical experiences, improving teachers’ diagnostic competencies, and creating teacher-researcher communities.

Keywords: mathematical modeling teaching competency, teacher education, task implementation, task modification |

References

1. |
Ärlebäck, J. B., Doerr, H. M., & O'Neil, A. H. (2013). A modeling perspective on interpreting rates of change in context. Mathematical thinking and learning, 15(4), 314-336. |

2. |
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. |

3. |
Ben-Zvi, D., & Arcavi, A. (2001). Junior high school students' construction of global views of data and data representations. Educational studies in mathematics, 45(1-3), 35-65. |

4. |
Blomhøj, M., & Kjeldsen, T. H. (2013). Students’ mathematical learning in modelling activities. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 141-152). Dordrecht: Springer. |

5. |
Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. A. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: ICTMA14 (pp. 15-30). Dordrecht: Springer. |

6. |
Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), The Proceedings of the 12 (pp. 73-96). Cham: Springer International Publishing.^{th} International Congress on Mathematical Education |

7. |
Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45-58. |

8. |
Borromeo Ferri, R. (2014). Mathematical modeling: The teacher’s responsibility. In B. Dickman, & A. Sanfratello (Eds.), Proceedings Conference on Mathematical Modeling (pp. 26-31). New York: Columbia University. |

9. |
Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling: In school and teacher education. New York: Springer. |

10. |
Borromeo Ferri, R., & Blum, W. (2010). Mathematical modelling in teacher education - experience from a modelling seminar. In V. Durand- Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the sixth Congress of the European Society for Research in Mathematics Education (pp. 2046-2055). Lyon: Institut national de recherche pédagogique. |

11. |
Boston, M. D., & Smith, M. S. (2011). A ‘task-centric approach’ to professional development: Enhancing and sustaining mathematics teachers’ ability to implement cognitively challenging mathematical tasks. ZDM Mathematics Education, 43, 965-977. |

12. |
Chang, H. W., Kim, E. H., Kang, Y. J., & Choi, H. R. (2018). Teaching & learning analysis of mathematical modeling in 6th grade elementary school class using ‘Amount of Milk’. School Mathematics, 20(4), 547-572. |

13. |
Choi, J. S. (2017). Prospective teachers’ perception of mathematical modeling in elementary class. Journal of Educational Research in Mathematics, 27(2), 313-328. |

14. |
Creswell, J. W. (2007). Qualitative inquiry & research design. Sage Publishing Inc. |

15. |
Creswell, J. W. (2014). Research: Qualitative, quantitative, and mixed methods approaches (4th ed.). California: Sage Publications, Inc. |

16. |
Doerr, H. M., & English, L D. (2003). A modeling perspective on studnets’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110-136. |

17. |
Edwards, A. (2001). Researching pedagogy : A sociocultural agenda. Pedagogy, Culture and Society, 9(2), 161-186. |

18. |
Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM, 38(2), 143-162. |

19. |
Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400. |

20. |
Jaworski, B. (2008). Building and sustaining inquiry communities in mathematics teaching development: Teachers and didacticians in collaboration. In K. Krainer, & T. Wood (Eds.), International handbook of mathematics teacher education: Volume 3 (pp. 309-330). Brill Sense. |

21. |
Jung, H. Y. (2019). A middle school mathematics teacher’s noticing observed in the mathematical modeling lesson. Journal of Learner-Centered Curriculum and Instruction, 20(20), 1021-1046. |

22. |
Kaiser, G. (2017). The teaching and learning of mathematical modeling. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 267-291). Reston, VA: The National Council of Teachers of Mathematics. |

23. |
Kaiser G., & Stender P. (2013) Complex modelling problems in co-operative, self-directed learning environments. In G. Stillman, G, Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 277-293). Springer, Dordrecht. |

24. |
Kim, M. K. (2010). Mathematical modeling in the elementary school curriculum. Seoul: Kyowoosa. |

25. |
Lazowski, R. A., & Hulleman, C. S. (2016). Motivation interventions in education: A meta-analytic review. Review of Educational research, 86(2), 602-640. |

26. |
Lee, D. H. (2017). Case study on collaboration between pre-service and in-service elementary mathematics teacher. School Mathematics, 19(2), 405-421. |

27. |
Lee, K., Seo, M., Lee, E., Park, M., & Song, C. (2019). Learning of teacher community through designing of mathematical induction tasks: A case of a co-learning inquiry community. Journal of Educational Research in Mathematics, 29(3), 425-452. |

28. |
Lee, K. H., Song, C. G., & Jung, H. Y. (2019). Change of teacher knowledge through task design in the teacher-researcher community : Focused on knowledge of students in the area of derivatives application. The Mathematical Education, 58(2), 299-317. |

29. |
Lesh, R., & Doerr, H. M. (2009). Symbolizing, communicating, and mathematizing: Key components of models and modeling. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design (pp. 361-383). Mahwah, NJ: Lawrence Erlbaum Associates. |

30. |
Maaß, K. (2010). Classification scheme for modelling tasks. Journal für Mathematik-Didaktik, 31(2), 285-311. |

31. |
Mousoulides, N., Christou, C., & Sriraman, B. (2008). A modeling perspective on the teaching and learning of mathematical problem solving. Mathematical Thinking and Learning, 10, 293-304. |

32. |
Palsdottir, G., & Sriraman, B. (2017). Teacher’s views on modeling as a creative mathematical activity. In R. Leikin, & B. Sriraman (Eds.), Creativity and giftedness (pp. 47-55). Switzerland: Springer. |

33. |
Pang, J. S. (2011). Prospective teachers' analysis and conception of elementary mathematics instruction. Journal of Elementary Mathematics Education in Korea, 15(2), 221-246. |

34. |
Pino-Fan, L. R., Godino, J. D., & Font, V. (2018). Assessing key epistemic features of didactic-mathematical knowledge of prospective teachers: The case of the derivative. Journal of Mathematics Teacher Education, 21(1), 63-94. |

35. |
Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 81-104. |

36. |
Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. S. (2009). Implementing standards-based mathematical instruction: A casebook for professional development. New York: Teachers College Press. |

37. |
Stender, P., & Kaiser, G. (2015). Scaffolding in complex modelling situation. ZDM Mathematics Education, 47, 1255-1267. |

38. |
Stillman, G., Galbraith, P., Brown, J., & Edwards, I. (2007). A framework for success in implementing mathematical modelling in the secondary classroom. Mathematics: Essential research, essential practice, 2, 688-697. |

39. |
Sullivan, P., Clarke, D., & Clarke, B. (2013). Teaching with tasks for effective mathematics learning. Springer Science & Business Media. |

40. |
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, 217-237. |

41. |
Thanheiser, E. (2017). Commentary on mathematical tasks and the student: Coherence and connectedness of mathematics, cycles of task design, and context of implementation. ZDM, 49(6), 965-969. |

42. |
Wilkerson, M. H., & Laina, V. (2018). Middle school students’ reasoning about data and context through storytelling with repurposed local data. ZDM, 50(7), 1223-1235. |

43. |
Zaslavsky, O., & Leikin, R. (2004). Professional development of mathematics teacher educators: Growth through practice. Journal of Mathematics Teacher Education, 7(1), 5-32. |

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Submitting manuscripts for peer review as well as other correspondences can either be made via online by an email (ksesm@daum.net) or sending a mail at Secretariat of

Journal of Educational Research in Mathematics, #1305 Daewoo The'O Ville, 115 Hangang-daero, Yongsan-gu, Seoul, 04376, Republic of Korea (Tel: +82‐2‐797‐7780, Fax: +82‐2‐797‐7750).

Submitting manuscripts for peer review as well as other correspondences can either be made via online by an email (ksesm@daum.net) or sending a mail at Secretariat of

Journal of Educational Research in Mathematics, #1305 Daewoo The'O Ville, 115 Hangang-daero, Yongsan-gu, Seoul, 04376, Republic of Korea (Tel: +82‐2‐797‐7780, Fax: +82‐2‐797‐7750).