Research Article

Mathematics Teachers’ Inclusion of Modelling and Problem Posing in Their Mathematics Lessons: An Exploratory Questionnaire

Simone Passarella 1 *
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1 Department of Mathematics, University of Padova, Padova, ITALY* Corresponding Author
European Journal of Science and Mathematics Education, 9(2), April 2021, 43-56, https://doi.org/10.30935/scimath/10773
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ABSTRACT

In this paper the results of a questionnaire about mathematics teachers’ inclusion in their teaching of mathematical modelling and problem posing are presented. To make teachers able to choose a coherent teaching method for a mathematical topic, teachers’ knowledge of valuable methods for the teaching of mathematics should be fostered. In this sense, studying teachers’ practice of modelling and problem posing is crucial in order to know if and which kind of support and professional development they need on such educational strategies. The questionnaire was administrated to Italian in-service mathematics teachers of primary and secondary school. Findings indicate that despite teachers implement regularly some aspects of mathematical modelling in their lessons, they ask more materials to support their preparation and practice. Problem posing, instead, might be more integrated in the classroom work, and consequently in teachers’ professional development courses.
Keywords: mathematical problem posing, mathematical modelling, exploratory study, questionnaire

CITATION (APA)

Passarella, S. (2021). Mathematics Teachers’ Inclusion of Modelling and Problem Posing in Their Mathematics Lessons: An Exploratory Questionnaire. European Journal of Science and Mathematics Education, 9(2), 43-56. https://doi.org/10.30935/scimath/10773

REFERENCES

  1. Appova, A., & Taylor, C.E. (2019). Expert mathematics teacher educators’ purposes and practices for providing prospective teachers with opportunities to develop pedagogical content knowledge in content courses. Journal of Mathematics Teacher Education, 22(2), 179-204. https://doi.org/10.1007/s10857-017-9385-z
  2. Arikan, E.E., & Unal, H. (2014). Development of the structured problem posing skills and using metaphoric perception. European Journal of Science and Mathematics Education, 2(3), 155-166. https://doi.org/10.30935/scimath/9408
  3. Ball, L. D., Thames, M. H., & Phelps, G. (2008). Content Knowledge for Teaching: What Makes It Special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  4. 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 12th International Congress on Mathematical Education (pp. 73-96). Berlin: Springer. https://doi.org/10.1007/978-3-319-12688-3_9
  5. Blum, W., & Niss, M. (1991). Applied Mathematical Problem Solving, Modelling, Applications, and Links to Other Subjects - State, Trends and Issues in Mathematical Instruction. Educational Studies in Mathematics, 22(1), 37-68. https://doi.org/10.1007/BF00302716
  6. Blume, B. D., Ford, J. K., Baldwin, T. T., & Huang, J. L. (2010). Transfer of Training: A Meta-Analytic Review. Journal of management, 36(4), 1065-1105. https://doi.org/10.1177/0149206309352880
  7. Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83(1), 37-55. https://doi.org/10.1007/s10649-012-9441-7
  8. Borromeo Ferri, R. (2006). Ùtheoretical and empirical differentiations of phases in the modelling process. ZDM-The International Journal on Mathematics Education, 38(2), 86-95. https://doi.org/10.1007/BF02655883
  9. Borromeo Ferri, R., & Blum, W. (2010). Mathematical Modelling in Teacher Education Experiences from a Modelling Seminar. In: V. Durand-Guerrier, S. Soury Lavergne, & F. Arzarello (Eds), CERME-6 - Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (pp. 2046-2055). INRP, Lyon 2010. http://ife.ens-lyon.fr/editions/editions-electroniques/cerme6/
  10. Borromeo Ferrri, R. (2018). Learning How to Teach Mathematical Modeling in School and Teacher Education. Springer International Publishing. https://www.springer.com/gp/book/9783319680712
  11. Cai J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem-posing Research in Mathematics Education: Some Answered and Unanswered Questions. Mathematical Problem Posing (pp.3-34), New York: Springer. 10.1007/978-1-4614-6258-3_1
  12. Cohen, L., Manion, L., & Morrison K. (2011). Research Methods in Education. Routledge. https://www.routledge.com/Research-Methods-in-Education/Cohen-Manion-Morrison/p/book/9781138209886
  13. Council Recommendation. (2018). Council Recommendation of 22 May 2018 on Key Competencies for Lifelong Learning. Official Journal of The European Union, 2018/C 189/01. https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:32018H0604(01)&rid=7
  14. DeLange, J. (1987). Mathematics, Insight and Meaning. Utrecht: CD-Press.
  15. English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83-106. https://doi.org/10.2307/749719
  16. Freudenthal, H. (1973). Mathematics as an Educational Task. Reidel.
  17. Freudenthal, H. (1991). Revisiting mathematics education. China lectures. Kluwer.
  18. Gellert, U., & Jablonka, E. (2007). Mathematization - Demathematization. In U. Geller & E. Jablonka (Eds), Mathematization and demathematization: Social, philosophical and educational ramifications (pp. 1-18). Sense Publisher.
  19. Gravemeijer, K. (1997). Commentary solving word problems: a case of modelling. Learning and Instruction, 7, 389-397. https://doi.org/10.1016/S0959-4752(97)00011-X
  20. Gravemeijer, K., & Doorman, M. (1999). Context Problems in Realistic Mathematics Education: A Calculus Course as an Example. Educational Studies in Mathematics, 39(1-3), 111-129. https://doi.org/10.1023/A:1003749919816
  21. Hansen, R., & Hana, G. M. (2015). Problem Posing from a Modelling Perspective, In F.M. Singer, N.F. Ellerton, & J. Cai (Eds.), Mathematical Problem Posing: From Research to Effective Practice (pp. 35-46). Springer. https://www.springer.com/gp/book/9781461462576
  22. Ikeda, T. (2007). Possibilities for, and obstacles to teaching applications and modelling in the lower secondary levels. In W. Blum, et al. (Eds), Modelling and Applications in Mathematics Education (pp. 457-462). Springer. https://www.springer.com/gp/book/9780387298207
  23. Kaiser, G. (2017). The teaching and Learning of Mathematical Modeling. In J. Cai (Ed.), Compendium for Research in Mathematics Education (pp. 267-291), NCTM. https://www.nctm.org/Store/Products/Compendium-for-Research-in-Mathematics-Education-eChapter-11-The-Teaching-and-Learning-of-Mathematical-Modeling-(Download)/
  24. Kilpatrick, J. (1987). Problem formulating: Where do good problems come from?. In A. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 127-147). Erlbaum.
  25. Kopparla, M., Bicer, A., Vela, K., Lee, Y., Bevan, D., Kwon, H., Caldwell, C., Capraro, M. M., & Capraro, R. M. (2018). The effect of problem-posing intervention types on elementary students’ problem-solving. Educational Studies, 45(6), 708-725. https://doi.org/10.1080/03055698.2018.1509785
  26. Lee, Y., Capraro, R. B., & Capraro, M. M. (2018). Mathematics Teacher’ Subject Matter Knowledge and Pedagogical Content Knowledge in Problem Posing. International Electronic Journal of Mathematics Education, 13(2), 75-90. https://doi.org/10.12973/iejme/2698
  27. Lunne, S., Schnell, S., & Biehler, R. (2020). Motivation of out-of-field teachers for participating in professional development courses in mathematics. European Journal of Teacher Education. Published online: 4 August 2020. https://doi.org/10.1080/02619768.2020.1793950
  28. Maass, K., Doorman, M., Jonker, V., & Wijers, M. (2019). Promoting active citizenship in mathematics teaching. ZDM Mathematics Education, 51, 991-1003. https://doi.org/10.1007/s11858-019-01048-6
  29. Ministero dell’Istruzione, dell’Università e della Ricerca. (2012). Indicazioni Nazionali per il Curricolo della Scuola dell’Infanzia e del Primo Ciclo di Istruzione [National Guidelines for the Kindergarten and First Cycle of Education Curriculum]. MIUR. http://www.indicazioninazionali.it/wp-content/uploads/2018/08/Indicazioni_Annali_Definitivo.pdf
  30. National Council of Teachers of Mathematics. (2000). Principle and Standard for School Mathematics. NCTM. https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/
  31. Osana, H. P., & Pelczer, I. (2015). A Review on Problem Posing in Teacher Education. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical Problem Posing: From Research to Effective Practice (pp. 469-492). Springer. https://www.springer.com/gp/book/9781461462576
  32. Peng, A., Cao, L., & Yu, B. (2020). Reciprocal Learning in Mathematics Problem Posing and Problem Solving: An Interactive Study between Canadian and Chinese Elementary School Students. Eurasia Journal of Mathematics, Science and Technology Education, 16(12), em1913. https://doi.org/10.29333/ejmste/9130
  33. Pollak, H. (1979). The Interaction between Mathematics and Other School Subjects. In UNESCO (Eds.), New Trends in Mathematics Teaching (vol. IV, pp. 232-248). Paris.
  34. Pollak, H. (2003). A history of the teaching of modeling. In G. M. A. Stanic & J. Kilpatrick (Eds.), A history of school mathematics (pp. 647-669). NCTM.
  35. Porsch, R., & Whannell, R. (2019). Out-of-Field Teaching Affecting Students and Learning: What Is Known and Unknown. In L. Hobbs & G. Torner (Eds.), Examining the Phenomenon of Teaching Out-of-field: International Perspectives on Teaching as a Non-specialist (pp. 179-191). Springer Singapore. https://www.springer.com/gp/book/9789811333651
  36. Schukajlow, S., Kaiser, G., & Stillman, G. (2018). Empirical research on teaching and learning of mathematical modelling: a survey on the current state of-the-art. ZDM Mathematics Education, 50(3), 5-18. https://doi.org/10.1007/s11858-018-0933-5
  37. Schulman, L. S. (1986). Those who understand: Knowledge growth in teaching, Educational Researcher, 15(2), 4-14. https://doi.org/10.2307/1175860
  38. Shahbari, J., & Daher, W. (2016). Pre-service teachers’ mathematical models’ features. European Journal of Science and Mathematics Education, 4(4), 523-533. https://doi.org/10.30935/scimath/9491
  39. Silver, E. A. (1994). On mathematical problem solving. For the learning of mathematics, 14(1), 19-28. https://doi.org/10.2307/749366
  40. Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521-539. https://doi.org/10.2307/749846
  41. Silver, E. A., Mamona-Downs, J., Leung, S., & Kenney, P. A. (1996). Posing Mathematical Problems: An Exploratory Study. Journal for Research in Mathematics Education, 27(3), 293-309. https://doi.org/10.5951/jresematheduc.27.3.0293
  42. Stein, M., Smith, M., Henningsen, M., & Silver, E. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. Teachers College Press. https://eric.ed.gov/?id=ED442659
  43. Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics, In P. C. Clarkson (Ed.), Technology in mathematics education (pp. 518-525). Mathematics Education Research Group of Australasia, The University of Melbourne.
  44. Van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic Mathematics Education, In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 521-525). Springer. https://doi.org/10.1007/978-3-030-15789-0
  45. Verschaffel, L., De Corte, E., & Borghart, I. (1997). Pre-service teachers’ conceptions and beliefs about the role of real-word knowledge in mathematical modelling of school word problems. Learning and Instruction, 7(4), 339-359. https://doi.org/10.1016/S0959-4752(97)00008-X
  46. Xie, J., & Masingila, J. O. (2017). Examining Interactions between Problem Posing and Problem Solving with Prospective Primary Teachers: A Case of Using Fractions. Educational Studies in Mathematics, 96(1), 101-118. https://doi.org/10.1007/s10649-017-9760-9