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Secondary Teachers' Perspectives on Mathematical Modeling and Modeling Mathematics: Discovery, Appreciation, and Conflict

  • Ahmad M. Alhammouri (Department of Teacher Education, Jacksonville State University) ;
  • Joseph DiNapoli (Department of Mathematics, Montclair State University)
  • Received : 2023.03.13
  • Accepted : 2023.06.15
  • Published : 2023.09.30

Abstract

Recent international reform movements call for attention on modeling in mathematics classrooms. However, definitions and enactment principles are unclear in policy documents. In this case study, we investigated United States high-school mathematics teachers' experiences in a professional development program focused on modeling and its enactment in schools. Our findings share teachers' experiences around their discovery of different conceptualizations, appreciations, and conflicts as they envisioned incorporating modeling into classrooms. These experiences show how professional development can be designed to engage teachers with forms of modeling, and that those experiences can inspire them to consider modeling as an imperative feature of a mathematics program.

Keywords

References

  1. Alhammouri, A. M., Durkee, J., & Foley, G. D. (2017). Where to place a post? Engaging students in the mathematical modeling process. Ohio Journal of School Mathematics, 75, 42-49.
  2. Alhammouri, A. M., & Foley, G. D. (2019). Developing financial literacy and mathematical prowess by modeling using spreadsheets. MathAMATYC Educator, 10(3), 23-34.
  3. Alhammouri, A. M., Foley, G. D., & Dael, K. (2018). Tracking trout: Engaging students in modeling. Mathematics Teacher, 111(6), 416-423.
  4. Bleiler, S. K, Baxter, W. A., Stephens, C. D, & Barlow, A. T. (2015). Constructing meaning: Standards for mathematical practice. Teaching Children Mathematics, 21(6), 336-344.
  5. Bliss, K. M., Kathleen, R. F., & Benjamin, J. G. (2014). Math modeling: Getting started & getting solutions. Society for Industrial and Applied
  6. Butts, T. (1980/2013). Posing problems properly. In F. Fennell & W. R. Speer (Eds.), Defining mathematics education: 75th yearbook (pp. 257-268). National Council of Teachers of Mathematics. (Originally published in 1980 in S. Krulik & R.E. Reys (eds.), Problem solving in school Mathematics: Yearbook. National Council of Teachers of Mathematics).
  7. Cirillo, M., Pelesko, J. A., Felton-Koestler, M. D., & Rubel, L. (2016). Perspectives on modeling in school mathematics. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 3-16). National Council of Teachers of Teachers of Mathematics.
  8. Common Core Standards Writing Team (2013). Progressions for the Common Core Standards in mathematics (draft) high school, modeling. Institute for Mathematics and Education, University of Arizona.
  9. Consortium for Mathematics and Its Applications & Society for Industrial and Applied Mathematics. (2015). GAIMME: Guidelines for assessment and instruction in mathematical modeling education. COMAP and SIAM.
  10. Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Pearson.
  11. Creswell, J. W. (2013). Research design: Quantitative, qualitative, and mixed methods approaches (4th ed.). Sage.
  12. DiNapoli, J., & Miller. E. K. (2022). Recognizing, supporting, and improving student perseverance in mathematical problem-solving: The role of conceptual thinking scaffolds. Journal of Mathematical Behavior, 66, 1-20. https://doi.org/10.1016/j.jmathb.2022.100965
  13. Felton-Koestler, M. (2017). Common Core confusion about modeling. Teaching Children Mathematics, 22(5), 269-272.
  14. Foley, G. D., Butts, T. R., Phelps, S. W., & Showalter, D. A. (2014). Advanced quantitative reasoning: Mathematics for the world around us (Common Core edition). AQR Press.
  15. Foley, G. D., Butts, T. R., Phelps, S. W., Showalter, D. A., Ashurst, J. M., Gorsuch, R., Sinha, G., & Gold, L. A. (2016a). Modeling with algebra [Instructional materials for professional development institute]. Ohio University.
  16. Foley, G. D., Butts, T. R., Phelps, S. W., Showalter, D. A., Haren, C., Howard, L., Sinha, G., & Gold, L. A. (2016). Modeling with geometry [Instructional materials for professional development institute]. Ohio University.
  17. Gaston, J. L., & Lawrence, B. A. (2015). Supporting teachers' learning about mathematical modeling. Journal of Mathematics Research, 7(4), 1-11. https://doi.org/10.5539/jmr.v7n4p1
  18. Gould, H. (2013). Teachers' conceptions of mathematical modeling. Doctoral dissertation, Columbia University.
  19. Gould, H. (2016). What a modeling task looks like. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 179-186). National Council of Teachers of Teachers of Mathematics.
  20. Groshong, K. (2016). Different types of mathematical models. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 17-24). National Council of Teachers of Mathematics.
  21. Jung, H., & Brady, C. (2016). Roles of a teacher and researcher during in-situ professional development around the implementation of mathematical modeling tasks. Journal of Mathematics Teacher Education, 19(2), 277-295. https://doi.org/10.1007/s10857-015-9335-6
  22. Kaput, K. (2018). Evidence for Student-Centered Learning. Technical Report #ED581111. Education Evolving.
  23. Lesh, R. (1981). Applied mathematical problem solving. Educational Studies in Mathematics, 12, 235-264. https://doi.org/10.1007/BF00305624
  24. Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763-804). Information Age.
  25. Maass, K., & Gurlitt, J. (2011). LEMA - Professional development of teachers in relation to mathematical modelling. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.) Trends in Teaching and Learning of Mathematical Modelling, International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 629-639). Springer.
  26. National Governors Association [NGA] Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Author. Retrieved from http://corestandards.org/assets/CCSSI_Math%20Standards.pdf
  27. Patton, M. Q. (2002). Qualitative research & evaluation methods. Sage.
  28. Pollak, H. O. (1966). On individual exploration in mathematics education. In E. G. Begle (Ed.), The role of axiomatics and problem solving in mathematics (pp. 117-122). Conference Board of the Mathematical Sciences.
  29. Pollak, H. O. (2003). A history of the teaching of modeling. In G. M. A. Stanic & J. Kilpatrick (Eds.), History of school mathematics (pp. 647-672). National Council of Teachers of Mathematics.
  30. Shenton, A. K. (2004). Strategies for ensuring trustworthiness in qualitative research projects. Education for Information, 22(2), 63-75. http://dx.doi.org/10.3233/EFI-2004-22201
  31. Smith, M. & Stein, M. (2018). 5 practices for orchestrating productive mathematical discussions. National Council of Teachers of Mathematics.
  32. Stake, R. E. (2006). Multiple case study analysis. Guilford Press.
  33. Taite, G., Provost, A., Kim, Y., Forte, F., & Perkoski, A. (2023). Designing and implementing professional development on mathematical modeling. Presentation at the 27th Annual Association of Mathematics Teacher Educators Conference in New Orleans, LA.
  34. van de Walle, J. A. (2007). Elementary and middle school mathematics: Teaching developmentally. Pearson Education, Inc.
  35. Zawojewski, J. S., & Phillips, E. D. (2016). Understanding models and modeling. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 1-2). National Council of Teachers of Mathematics.