Preservice teachers' beliefs towards mathematics and mathematical modelling in modelling processes
Mathematics and mathematical modelling in modelling processes
Abstract
The aim of this study is to investigate pre-service mathematics teachers’ beliefs towards mathematics and modelling in mathematical modelling processes. To achieve this aim, a phenomenology design was utilized. The study was conducted with 30 elementary level pre-service mathematics teachers receiving mathematical modelling courses. A semi-structured interview form was used to explore teachers’ beliefs. At the end of the study, it was seen that mathematical modelling applications caused an increase of application-oriented beliefs. It was also observed that pre-service teachers who had schema and formalism-oriented beliefs evaluated mathematical modelling practices as time consuming and incomprehensible. Findings imply that modelling applications should be included in all levels of mathematics instructional curricula, in addition to the undergraduate curriculum.References
Ambrose, R. (2004). Initiating change in prospective elementary school teachers’ orientations to mathematics teaching by building on beliefs. Journal of Mathematics Teacher Education, 7(2), 91-119. https://doi.org/10.1023/B:JMTE.0000021879.74957.63
Ärlebäck, J. B. (2009, January). Towards understanding teachers’ beliefs and affects about mathematical modelling. In Proceedings of the sixth congress of the European society for research in mathematics education (pp. 2096-2105).
Berry, J., & Houston, K. (1995). Mathematical modelling. Bristol: J.W.Arrowsmith Ltd.
Beswick, K. (2005). The belief/practice connection in broadly defined contexts. Mathematics Education Research Journal, 17(2), 39–68. https://doi.org/10.1007/BF03217415
Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1, 45-58.
Doerr, H. M., & English, L. D. (2003). A modelling perspective on students' mathematical reasoning about data. Journal for Research in Mathematics Education, 34, 110-136. DOI: 10.2307/30034902
Doruk, B. K. (2010). The effect of mathematical modeling on transferring mathematics into daily life (Unpublished doctoral dissertation). Hacettepe University, Ankara, Turkey.
Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C., & Baş, S. (2014). Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches. Educational Sciences: Theory and Practice, 14(4), 1621-1627. DOI: 10.12738/estp.2014.4.2039
Eleftherios, K., & Theodosios, Z. (2007). Students’ beliefs and attitudes about studying and learning mathematics. In Proceedings of the 31st Conference on the International Group for the Psychology of Mathematics Education, (Vol. 3, pp. 97-104).
Ernest, P. (1989). The knowledge, beliefs, and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13-33. https://doi.org/10.1080/0260747890150102
Ernest, P. (1991). The philosophy of mathematics education. London: Farmer.
Ferri, R. B. (2011). Effective mathematical modelling without blockages–a commentary. In Trends in teaching and learning of mathematical modelling, (pp. 181-185). Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0910-2_19
Ferri, R. B. (2013). Mathematical modelling in European education. Journal of Mathematics Education at Teachers College, 4(2), 18-24. https://doi.org/10.7916/jmetc.v4i2.624
Galligan, L., Axelsen, T., Pennicott, T., Addie, R., Galbraith, P., & Woolcott, G. (2019). It’s part of my life and the modelling process. Journal of Mathematics Teacher Education, 22(4), 355-378. https://doi.org/10.1007/s10857-019-09426-3
Grigutsch, S., Raatz, U., & Törner, G. (1998). Einstellungen gegenüber Mathematik bei Mathematiklehrern (Mathematics teachers’ epistemological beliefs about the nature of mathematics). Journal für Mathematik-Didaktik (Journal of Mathematics Education), 19, 3–45. https://doi.org/10.1007/BF03338859
Handal, B., (2003). Teachers’ mathematical beliefs: A review. The Mathematics Educator, 13(2), 47-57.
Kaiser, G. (2006, July). The mathematical beliefs of teachers about applications and modelling–results of an empirical study. In Proceedings of the 30th Conference of the Int. Group for the Psychology of Mathematics Education (PME) (Vol. 3, pp. 393-400).
Kaiser, G., & Maaß, K. (2007). Modelling in lower secondary mathematics classroom—problems and opportunities. In Modelling and applications in mathematics education (pp. 99-108). Boston: Springer. https://doi.org/10.1007/978-0-387-29822-1_8
Lesh, R. A., & Doerr, H. M. (2003). Foundations of models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh and H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3-33). Mahwah, NJ: Lawrence Erlbaum Associates.
Lesh, R., & Lehrer, R. (2000). Iterative refinement cycles for videotape analyses of conceptual change. In A. Kelly, and R. Lesh (Eds.), Handbook of Research Design in Mathematics and Science Education (pp. 665–708). Mahwah, NJ: Lawrence Erlbaum Associates.
Maaß, K. (2005). Barriers and opportunities for the integration of modelling in mathematics classes: results of an empirical study. Teaching Mathematics and Its Applications: International Journal of the IMA, 24(2-3), 61-74. DOI: 10.1093/teamat/hri019
Mason, L., & Scrivani, L. (2004). Enhancing students’ mathematical beliefs: An intervention study. Learning and instruction, 14(2), 153-176. https://doi.org/10.1016/j.learninstruc.2004.01.002
Mischo, C., & Maaß, K. (2012). Which personal factors affect mathematical modelling? The effect of abilities, domain specific and cross domain-competences and beliefs on performance in mathematical modelling. Journal of Mathematical Modelling and Application, 1(7), 2-19.
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. https://doi.org/10.11114/jets.v1i1.24
Mutodi P., & Ngirande, H (2014). The influence of students’ perceptions on mathematics performance: A case of a selected high school in South Africa. Mediterranean Journal of Social Sciences, 5(3), 431-445. DOI: 10.5901/mjss.2014.v5n3p431
Ng, K. E. D. (2013). Teacher Readiness in mathematical modelling: are there differences between pre-service and in-service teachers?. In Teaching mathematical modelling: connecting to research and practice (pp. 339-348). Springer, Dordrecht.
https://doi.org/10.1007/978-94-007-6540-5_28
Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri [Qualitative Research & Evaluation Methods] (M. Bütün & S. B. Demir, Trans.). Ankara: PegemA Akademi. (Original work published 2002)
Pehkonen, E., & Törner, G. (1996). Mathematical beliefs and different aspects of their meaning. International Review on Mathematical Education (ZDM), 28, 101–108.
Pepin, B., & Roesken-Winter, B. (2015). Foreword. In B. Pepin, & B. Roesken-Winter (Ed.), From beliefs to dynamic affect systems in mathematics education (pp. v-x). London/New York: Springer. https://doi.org/10.1007/978-3-319-06808-4
Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257– 315). Charlotte, NC: National Council of Teachers of Mathematics & Information Age Publishing.
Ramirez, R. (2017). Teachers’ Beliefs about Mathematical Modelling: An Exploratory Study. Tenth Congress of the European Society for Research in Mathematics Education (CERME-10). 1-5 February, Dublin, Ireland. Retrieved from https://keynote.conference-services.net/resources/444/5118/pdf/CERME10_0221.pdf
Rozelle, J., & Wilson, S. (2012). Opening the black box of field experiences: How cooperating teachers' beliefs and practices shape student teachers' beliefs and practices. Teaching and Teacher Education, 28, 1196-1205. https://doi.org/10.1016/j.tate.2012.07.008
Stillman, G., & Brown, J. P. (2011). Pre-service secondary mathematics teachers’ affinity with using modelling tasks in teaching years 8–10. In Trends in teaching and learning of mathematical modelling (pp. 289-298). Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0910-2_29
Tekin Dede A., & Bukova Güzel, E. (2013). Examining the mathematics teachers’ design process of the model eliciting activity: Obesity problem. Elementary Education Online, 12(4), 1100-1119.
Thompson, A. G. (1992). Teachers' beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127-146). New York: Macmillan.
Viholainen, A., Asikainen, M., & Hirvonen, P. E. (2014). Mathematics student teachers’ epistemological beliefs about the nature of mathematics and the goals of mathematics teaching and learning in the beginning of their studies. Eurasia Journal of Mathematics, Science & Technology Education, 10(2), 159-171.
https://doi.org/10.12973/eurasia.2014.1028a
Wilkins, J. L., & Ma, X. (2003). Modeling change in student attitude toward and beliefs about mathematics. The Journal of Educational Research, 97(1), 52-63. https://doi.org/10.1080/00220670309596628
Zawojewski, J. (2010). Problem solving versus modeling. In R. Lesh, P. L. Galbraith, C. R. Haines & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies: ICTMA 13 (pp. 237-243). New York, NY: Springer. https://doi.org/10.1007/978-94-007-6271-8_20
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