Investigation of Pre-service Science Teachers' and Science Teachers' Mathematical Modeling Competencies

Abstract

This study on mathematical modelling (MM) in science education aims to examine the mathematical modelling competencies (MMC) of pre-service science teachers and teachers. For this purpose, a qualitative study was conducted with 12 pre-service science teachers and teachers. A case study design was used in the research. The study's data were obtained through activity forms, interviews and observation techniques. Descriptive analysis was used to determine the MMY by considering the sub-competencies revised by Çakmak (2019) in line with Borromeo Ferri's (2006) MMC. When MMY was examined, it was concluded that MMC developed in the process, the most successful MMY was comprehension, and the most unsuccessful MMC was simplification and construction. Contrary to the literature, it was determined that reaching real conclusions from mathematical results was fine. It is seen that newly graduated and experienced science teachers have an equal level of MMC, while pre-service science teachers have less MMC. In the process, competence was exhibited least in biology and chemistry and most in physics. It is recommended to increase MM studies for science education and to provide MM courses at a minimum undergraduate level and in-service training to experience MM practices.

Keywords

• mathematical modelling
• mathematical modelling competencies
• science teachers

Fen Öğretmen Adaylarının ve Fen Öğretmenlerinin Matematiksel Modelleme Yeterliklerinin İncelenmesi

Abstract

Fen eğitiminde matematiksel modelleme (MM) kullanımına yönelik yapılan bu çalışmanın amacı fen öğretmen adaylarının ve öğretmenlerinin matematiksel modelleme yeterliklerini (MMY) incelemektir. Bu amaç doğrultusunda 12 fen öğretmen adayı ve öğretmeni ile nitel bir araştırma yürütülmüştür. Araştırmada durum çalışması deseni kullanılmıştır. Etkinlik formları, görüşme ve gözlem teknikleri ile araştırmanın verileri elde edilmiştir. MMY’ni belirlemek için Borromeo Ferri (2006)’nin MMY doğrultusunda Çakmak (2019)’ ın revize ettiği alt yeterlikler gözetilerek betimsel analiz kullanılmıştır. MMY incelendiğinde süreç içerisinde MMY’nin geliştiği, en başarılı anlama, en başarısız olunan basitleştirme ve yapılandırma MMY olduğu sonucuna varılmıştır. Literatürün aksine matematiksel sonuçlardan gerçek sonuçlara varmakta sorun yaşanmadığı tespit edilmiştir. Yeni mezun fen öğretmenlerinin ve deneyimli fen öğretmenlerinin MMY eşit düzeyde olduğu görülürken fen öğretmen adaylarının MMY’ nin daha az olduğu görülmektedir. Süreçte en az biyoloji ve kimya, en çok fizik konularında yeterlik sergilenmiştir. Fen eğitimine yönelik MME çalışmalarının artırılması, asgari lisans düzeyinde MM derslerinin verilmesi ve hizmet içi eğitimlerle MM uygulamalarını deneyimlendirme çalışmalarının yapılması önerilmektedir.

Keywords

• matematiksel modelleme
• matematiksel modelleme yeterlikleri
• fen öğretmenleri

References

1. Akgün, L., Çiltaş, A., Deniz, D., Çiftçi, Z., & Ahmet, I. Ş. I. K. (2013). İlköğretim matematik öğretmenlerinin matematiksel modelleme ile ilgili farkındalıkları [Elementary mathematics teachers' awareness of mathematical modelling]. Adıyaman Üniversitesi Sosyal Bilimler Enstitüsü Dergisi (12), 1-34. https://doi.org/10.14520/adyusbd.410
2. Anhalt, C. O., & Cortez, R. (2016). Developing understanding of mathematical modeling in secondary teacher preparation. Journal of Mathematics Teacher Education, 19, 523-545. https://doi.org/10.1007/s10857-015-9309-8
3. Antonius, S., Haines, C., Jensen, T. H., Niss, M., & Burkhardt, H. (2007). Classroom activities and the teacher. In Modelling and applications in mathematics education (pp. 295-308). Springer.
4. Başkan, Z. (2011). Doğrusal ve düzlemde hareket ünitelerinin matematiksel modelleme kullanılarak öğretiminin öğretmen adaylarının öğrenmelerine etkileri [The effectiveness of teaching one and two dimensional motion on prospective teachers’ learning using mathematical modeling] (Doctoral dissertation). Karadeniz Technical University, Trabzon.
5. Berry, J. S., & Houston, S. K. (1995). Mathematical modelling. Edward Arnold.
6. Biccard, P., & Wessels, D. C. J. (2011). Documenting the development of modelling competencies of grade 7 mathematics students. In G. Kaiser, W. Blum, R. B. Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 375-383). Springer.
7. Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. B. Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 15-30). Springer. https://doi.org/10.1007/978-94-007-0910-2_3
8. Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45-58.

9. Blomhøj, M., & Jensen, T. H. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching Mathematics and Its Applications, 22(3), 123-139.
10. Blum, W., & Leiß, D. (2007). How do teachers deal with modeling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 222-231). Horwood Publishing.
11. Blum, W., & Leiß, D. (2008). Investigating quality mathematics teaching – The DISUM project. In C. Bergsten, & B. Grevholm (Eds.), Developing and researching quality in mathematics teaching and learning: Proceedings of MADIF 5 (pp. 3-16). Linköping University.
12. Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik, 38(2), 86-95.
13. Borromeo Ferri, R. (2007). Modelling problems from a cognitive perspective. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 260-270). Horwood Publishing.
14. Borromeo Ferri, R. (2010). On the influence of mathematical thinking styles on learners’ modeling behavior. Journal für Mathematik-Didaktik, 31, 99-118.
15. Borromeo Ferri, R. (2011). Effective mathematical modelling without blockages- A commentary. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 181-185). Springer.
16. Borromeo Ferri, R. (2012, July). Mathematical thinking styles and their influence on teaching and learning mathematics. Paper presented at the meeting of the 12th International Congress on Mathematical Education, Seoul, Korea.
17. Brand, S. (2014). Effects of a holistic versus an atomistic modelling approach on students’ mathematical modelling competencies. In Proceedings of the joint meeting of PME 38 and PME-NA 36 (pp. 185-191). PME.
18. Bukova Güzel, E. (2019). Matematik eğitiminde matematiksel modelleme [Mathematical modeling in mathematics education]. Pegem Academy.
19. Bukova Güzel, E., & Uğurel, I. (2010). Matematik öğretmen adaylarının analiz dersi akademik başarıları ile matematiksel modelleme yaklaşımları arasındaki ilişki [The relationship between pre-service mathematics teachers' academic achievement in analysis course and their mathematical modeling approaches]. Ondokuz Mayıs University Journal of Education Faculty, 29(1), 69-90.
20. Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches. Sage.
21. Creswell, J. W., & Miller, D. L. (2000). Determining validity in qualitative inquiry. Theory into Practice, 39, 124-130.
22. Çakmak, Z. (2019). Matematik öğretmeni adaylarının matematiksel modelleme süreçlerinin bilişsel açıdan incelenmesi [The investigation of mathematical modelling processes of pre-service mathematics teachers from a cognitive perspective] (Doctoral dissertation). Atatürk University, Erzurum.
23. Çiltaş, A. (2011). Dizi ve seriler konusunun matematiksel modelleme yoluyla öğretiminin ilköğretim matematik öğretmeni adaylarının öğrenme ve modelleme becerileri üzerine etkisi [The effect of teaching sequences and series subject through mathematical modeling on the learning and modeling skills of prospective elementary mathematics teachers] (Doctoral dissertation). Atatürk University, Erzurum.
24. Çiltaş, A., & Işık, A. (2013). The effect of instruction through mathematical modelling on modelling skills of prospective elementary mathematics teachers. Educational Sciences: Theory & Practice, 13(2), 1187-1192.
25. Doerr, H. M. (2007). What knowledge do teachers need for teaching mathematics through applications and modeling? In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modeling and applications in mathematics education (ICMI 14) (pp. 69-78). Springer.
26. Doruk, B. K. (2010). Matematiği günlük yaşama transfer etmede matematiksel modellemenin etkisi [The impact of mathematical modeling in transferring mathematics to daily life] (Doctoral dissertation). Hacettepe University, Ankara.
27. Erbaş, A. K., Çetinkaya, B., Çakıroğlu, E., & Alacası, C. (2013). Ortaöğretim matematik eğitiminde matematiksel modelleme: hizmet içi ve hizmet öncesi öğretmen eğitimi [Mathematical modeling in secondary mathematics education: in-service and pre-service teacher training] https://app.trdizin.gov.tr/publication/project/detail/TVRReU5qRXg
28. English, L. D. (2006). Mathematical modeling in the primary school: Children's construction of a consumer guide. Educational Studies in Mathematics, 63, 303-323.
29. Gatabi, A. R., & Abdolahpour, K. (2013). Investigating students’ modeling competency through grade, gender, and location. In B. Ubuz, C. Haser, & M. A. Mariotti (Eds.), Proceedings of the 8th congress of the European society for research in mathematics education (CERME 8) (pp. 1070-1077). Middle East Technical University.
30. Glesne, C. (2016). Becoming qualitative researchers: An introduction. Pearson.
31. Güç, F. A. (2015). Matematiksel modelleme yeterliklerinin geliştirilmesine yönelik tasarlanan öğrenme ortamlarında öğretmen adaylarının matematiksel modelleme yeterliklerinin değerlendirilmesi [Evaluation of pre-service teachers' mathematical modeling competencies in learning environments designed to develop mathematical modeling competencies] (Doctoral dissertation). Karadeniz Technical University, Trabzon.
32. Greefrath, G. (2020). Mathematical modelling competence: Selected current research developments. Avances de Investigación en Educación Matemática, 17, 38-51.
33. Greefrath, G., & Vos, P. (2021). Video-based word problems or modelling projects—Classifying ICT-based modelling tasks. In Mathematical modelling education in East and West (pp. 489-499). Springer.
34. Güder, Y. (2019). Matematiksel modelleme yoluyla disiplinler arası geçiş [Interdisciplinary transition through mathematical modeling] (Doctoral dissertation). Adıyaman University Adıyaman.
35. Henning, H., & Keune, M. (2007). Levels of modelling competencies. In Modelling and applications in mathematics education (pp. 225-232). Springer.
36. Ji, X. (2012, July). A quasi-experimental study of high school students’ mathematics modelling competence. Paper presented at the meeting of the 12th International Congress on Mathematical Education, Seoul, Korea.
37. Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 110-119). Horwood Publishing.
38. Kaiser, G. (2020). Mathematical modelling and applications in education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 553-561). Springer.
39. Kaiser, G., Blomhøj, M., & Sriraman, B. (2006). Towards a didactical theory for mathematical modelling. Zentralblatt für Didaktik der Mathematik, 38(2), 82-85. https://doi.org/10.1007/BF02655882
40. 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.
41. Kaiser, G., & Grünewald, S. (2015). Promotion of mathematical modelling competencies in the context of modelling projects. In N. H. Lee & N. K. E. Dawn (Eds.), Mathematical modelling from theory to practice (pp. 21-39). World Scientific Publishing.
42. Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. Zentralblatt für Didaktik der Mathematik, 38(3), 302-310.
43. Kaiser, G., & Stender, P. (2013). Complex modelling problems in co-operative, self-directed learning environments. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 611-620). Springer.
44. Karasar, N. (2016). Bilimsel araştırma yöntemi: Kavramlar, ilkeler, teknikler (30th ed.). Anı Yayıncılık.
45. Kapur, J. N (2023). Mathematical Modeling. Berlin, Boston: Mercury Learning and Information (pp, 300). https://doi.org/10.1515/9781683928737
46. Kenan, A., & Polat, R. (2022). Matematik ve fen öğretmen eğitiminde kullanıma yönelik matematiksel modelleme etkinlikleri geliştirme çalışması [Developing mathematical modeling activities for use in mathematics and science teacher education]. Academic Social Resources Journal, 7(36), 472-483.
47. Kertil, M. (2008). Matematik öğretmen adaylarının problem çözme becerilerinin modelleme sürecinde incelenmesi [Investigation of prospective mathematics teachers' problem-solving skills in the modeling process] (Doctoral dissertation). Marmara University, Istanbul.
48. Koç, D. (2020). An investigation on thesis and dissertations on mathematical modeling in Turkey in the last two decades (Master's thesis). Middle East Technical University, Ankara.
49. Korkmaz, E. (2010). İlköğretim matematik ve sınıf öğretmeni adaylarının matematiksel modellemeye yönelik görüşleri ve matematiksel modelleme yeterlikleri [Elementary mathematics and classroom teacher candidates' views on mathematical modeling and their mathematical modeling competencies] (Doctoral dissertation). Balıkesir University, Balıkesir.
50. Koceva Lazarova, L., Stojkovic, N., & Stojanova, A. (2022). The importance of mathematical modeling in STEM education. STEM Education Notes, 1(1), 9-18.
51. Leiss, D., & Blum, W. (2010). The role of the situation model in mathematical modelling: Task analyses, student competencies, and teacher interventions. Journal für Mathematik-Didaktik, 31, 119-141.
52. Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modelling perspective on mathematics teaching, learning and problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning and teaching (pp. 3-33). Lawrence Erlbaum.
53. Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought revealing activities for students and teachers. In R. Lesh & A. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 591-645). Lawrence Erlbaum.
54. Maaß, K. (2006). What are modelling competencies? Zentralblatt für Didaktik der Mathematik, 38(2), 113-142.
55. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage.
56. Molina-Toro, J. F., Rendón-Mesa, P. A., & Villa-Ochoa, J. (2019). Research trends in digital technologies and modeling in mathematics education. Eurasia Journal of Mathematics, Science and Technology Education, 15(8), 1-13.
57. Niss, M., Blum, W., & Galbraith, P. (2007). How to replace the word problems. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3-32). Springer.
58. Sriraman, B. (2006). Conceptualizing the model-eliciting perspective of mathematical problem solving. In Proceedings of the fourth congress of the European society for research in mathematics education (CERME 4) (pp. 1686-1695). Universitat Ramon Llull.
59. Stohlmann, M. (2012). YouTube incorporated with mathematical modelling activities: Benefits, concerns, and future research opportunities. International Journal for Technology in Mathematics Education, 19(3).
60. Tekin, A., & Bukova Güzel, E. (2011). Ortaöğretim matematik öğretmenlerinin matematiksel modellemeye ilişkin görüşlerinin belirlenmesi [Determination of secondary mathematics teachers' views on mathematical modeling]. In Proceedings of Mehmet Akif Ersoy University Faculty of Education, 8-10 September, Burdur.
61. Tekin-Dede, A., & Bukova-Güzel, E. (2018). A rubric development study for the assessment of modeling skills. The Mathematics Educator, 27(2).
62. Yıldırım, A., & Şimşek, H. (2018). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in social sciences] (13th ed.). Seçkin Yayıncılık.
63. Yıldız, Ş., & Yenilmez, K. (2019). Matematiksel modelleme ile ilgili lisansüstü tezlerin tematik içerik analizi [Thematic content analysis of graduate theses on mathematical modeling]. Eskişehir Osmangazi University Journal of Social Sciences, 20, 1-22.
64. Zawojewski, J. S., Lesh, R., & English, L. (2003). A models and modelling perspective on the role of small group learning activities. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning and teaching (pp. 337-358). Lawrence Erlbaum.