Matematik Öğretiminde Model Oluşturma Etkinlikleri Tasarım Sürecinin İncelenmesi

Abstract

Bu çalışmanın amacı, matematik öğretmen adaylarının model oluşturma etkinlikleri tasarlama sürecini incelemektir. Bu çalışmada örnek olay incelemesi tercih edilmiştir. Bu araştırmanın çalışma grubunu Kastamonu Üniversitesi Eğitim Fakültesi İlköğretim Matematik Öğretmenliği Lisans Programında 2019-2020 eğitim öğretim yılında öğrenim gören 15 matematik öğretmeni adayı oluşturmaktadır. Bu araştırmada, bütüncül bir yaklaşımla tasarlanan ve "teorik bilgi" esas alınarak tasarlanan öğrenme ortamları oluşturulmuştur. Matematiksel modelleme eğitim süreci ve model oluşturma etkinlikleri tasarım süreci olarak planlanan araştırma süreci 10 hafta sürmüştür. Araştırmanın verileri model oluşturma etkinlikleri tasarım süreci çalışma yaprakları aracılığıyla toplanmıştır. Veri toplama aracından elde edilen veriler içerik analizine tabi tutulmuştur. Araştırma sonucunda, model oluşturma etkinlikleri tasarım aşamalarında bazı farklılıklar olsa da, grupların benzer süreçleri içerdiği tespit edilmiştir. Yazma aşamaları, model oluşturma etkinliklerinin bağlamının belirlenmesi, değişkenlere ve varsayımlara karar verilmesi, senaryo yazılması ve görsel unsurların eklenmesi şeklinde ilerlemiştir. Kontrol aşamasında grupların dikkat ettiği unsurlar arasında model oluşturma etkinlikleri tasarım ilkelerine uyum, metin kontrolü, görsel düzenleme, çözüm adımlarının gerçekleştirilmesi (model ve veri uyumluluğu) yer almıştır.

Keywords

• Model oluşturma etkinlikleri
• matematiksel modelleme
• matematik öğretmen adayı eğitimi

Process of Designing Model Eliciting Activities in Mathematics Teaching

Abstract

The aim of this study is to analyze prospective mathematics teachers’ process of designing model eliciting activities. Case study was preferred in this study. The study group of this research consists of 15 mathematics teacher candidates studying at Kastamonu University Faculty of Education Primary Mathematics Teaching Undergraduate Program during the academic year of 2019-2020. In this research, learning environments designed based on a holistic approach and based on "theoretical knowledge" were created. The research process took 10 weeks which are planned as mathematical modeling training process and MEA design process. Data of the study were collected through MEA design process worksheets. The data obtained from the data collection tool were subjected to content analysis. As a result of the research, it was determined that PMT groups included similar processes although there were some differences in the MEA design stages. The writing stages proceeded as determining the context of the MEA, deciding on variables and assumptions, writing the scenario and adding visual elements. In the control phase, the elements that the groups pay attention to include compliance with MEA principles, text control, visual editing, performing solution steps (model and data compatibility).

Keywords

• Model eliciting activities
• mathematical modelling
• prospective mathematics teacher education

References

1. Arcavi, A. (2002). The everyday and the academic in mathematics. In M.E. Brenner and J. N. Moschkovich (Eds.), Every day and academic mathematics in the classroom, (pp. 12-29). Virginia: National Council of Teacher of Mathematics.
2. Aydın-Güç, F (2015). Examining mathematical modeling competencies of teacher candidates in learning environments designed to improve mathematical modeling competencies. (Unpublished doctoral dissertation). Karadeniz Technical University, Institute of Education Science, Trabzon.
3. Baki, A., & Aydın-Güç, F. (2014a). Matematik öğretmeni adaylarının gerçek yaşam bağlamlarını ele alma yaklaşımları [Approaches of prospective mathematics teachers to real-life contexts]. 11. National Education of Science and Mathematics Congress. Çukurova University, Adana, Türkiye.
4. Baki, A., & Aydın-Güç, F. (2014b). Pre-service mathematics teachers’ misconceptions on the mathematical model validation process. International Teacher Education Conference, Sharjah, United Arab Emirates.
5. Bengtsson, M. (2016). How to plan and perform a qualitative study using content analysis. Nursing Plus Open, 2, 8-14.
6. Berry, J., & Houston, K. (1995). Mathematical modelling. Bistrol: J. W. Arrow smith Ltd.
7. Blomhoj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work. The International Journal on Mathematics Education, 38(2), 163-177.
8. Blomhoj, M., & Jensen, T. H. (2007). What's all the fuss about competencies? Experiences with using a competence perspective on mathematics education to develop the teaching of mathematical modelling. In W. Blum, P. L. Galbraith, H. W. Henn, and M. Niss (Eds.), Modelling and Applications in Mathematics Education (pp. 45-56). New York: Springer.

9. Blum, W., & Kaiser, G. (1997). Vergleichende empirische Untersuchungen zu mathematischen Anwendungsfähigkeiten von englischen und deutschen Lernenden (unpublished document).
10. Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, application, and links to other subjects-state, trends, and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37-68.
11. Borromeo-Ferri, R. (2010). On the influence of mathematical thinking styles on learners' modeling behaviour. Journal für Mathematikdidaktik, 31(1), 99-118.
12. Borromeo-Ferri, R. (2014) Mathematical modeling – the teacher’s responsibility. In B. Dickman & A. Sanfratello (Eds.), Proceedings from the Teachers College Mathematical Modeling Oktoberfest (pp. 26-31). New York: Teachers College Columbia University.
13. Bukova Güzel, E., Tekin Dede, T., Hıdıroğlu, Ç. N., Kula Ünver, S., & Özaltun Çelik, A. (2016). Matematik eğitiminde matematiksel modelleme: Araştırmacılar, eğitimciler ve öğrenciler için [Mathematical modeling in mathematics education: For researchers, educators and students]. Ankara: Pegem Academy.
14. Busse, A. (2005). Individual ways of dealing with the context of realistic tasks—first steps towards a typology. The International Journal on Mathematics Education, 37(5), 354-360.
15. Chinnappan, M. (2010). Cognitive load and modelling of an algebra problem. Mathematics Education Research Journal, 22(2), 8-23.
16. Crabtree, B. F., & Miller, W. L. (Eds.). (1999). Doing qualitative research. Sage Publications.
17. Creswell, J. W. (2013). Steps in conducting a scholarly-mixed methods study. DBER Speaker series. University of Nebraska Discipline-Based Education Research Group.
18. Crouch, R., & Haines, C. (2004). Mathematical modelling: Transitions between the real world and mathematical model. International Journal of Mathematical Education in Science and Technology, 35(2), 197-206.
19. Dede, A. T., Hıdıroglu, Ç. N., & Güzel, E. B. (2017). Examining of model eliciting activities developed by mathematics student teachers. Journal on Mathematics Education, 8(2), 223-242.
20. Doerr, H.M. (1997). Experiment, simulation, and analysis: an integrated instructional approach to the concept of force. International Journal of Science Education, 19, 265-282. Eysenbach, G., & Köhler, C. (2002). How do consumers search for and appraise health information on the world wide web? Qualitative study using focus groups, usability tests, and in-depth interviews. BMJ, 324(7337), 573-577.
21. Ferri, R. B., & Blum, W. (2013). Barriers and motivations of primary teachers for implementing modelling in mathematics lessons. In Eighth Congress of European Research in Mathematics Education (CERME 8), Antalya, Turkey.
22. Fox, J. (2006). A justification for mathematical modelling experiences in the preparatory classroom. Proceedings 29th Annual Conference of the Mathematics Education Research Group of Australasia 1, 21-228.
23. Glesne, C., & Peshkin, A. (1992). Becoming qualitative researchers. New York, NY: White Plains.
24. Guba, E. G., & Lincoln, Y. S. (2004). Competing paradigms in qualitative research: Theories and issues. Approaches to qualitative research: A reader on theory and practice, 17-38.
25. Herget, W., Jahnke, T., & Kroll, W. (2001). Produktive Aufgaben für den Mathematikunterricht in der Sekundarstufe I. Berlin, Cornelsen.
26. Hıdıroğlu, Ç. N., & Bukova Güzel, E. (2014). Using GeoGebra in mathematical modeling: The height-foot length problem. Pamukkale University Journal of Education, 36(2), 29-44.
27. Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. The International Journal on Mathematics Education, 38(3), 302-310.
28. Lesh, R. A., & Doerr, H. (2003). Foundations of model and modelling perspectives on mathematic teaching and learning. In R. A. Lesh, and H. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics teaching, learning and problem solving (pp. 3-33). Mahwah, NJ: Lawrence Erlbaum.
29. Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual developing. Mathematical Thinking and Learning, 5(2-3), 157-189.
30. Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In R. Lesh, and A. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 591-645). Hillsdale, NJ: Lawrence Erlbaum.
31. Maaß, K. (2006). What are modelling competencies? The International Journal on Mathematics Education, 38(2), 113-142.
32. McMillan, J. H. (1996). Educational research: Fundamentals for the consumer. New York, NY: HarperCollins College Publishers. Merriam, S. B. (1988). Case study research in education: A qualitative approach. Jossey-Bass.
33. Merriam, S. B., & Grenier, R. S. (Eds.). (2019). Qualitative research in practice: Examples for discussion and analysis. John Wiley & Sons.
34. Miles, M. B. & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage.
35. Ministry of National Education- MoNE. (2005). Curriculum and guide of mathematics in middle school (6-8. grades). Ankara.
36. Ministry of National Education- MoNE. (2017). Curriculum of mathematics (Elementary and Middle-School 1, 2, 3, 4, 5, 6, 7, and 8. grades). Ankara.
37. National Council of Teachers of Mathematics [NCTM]. (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.
38. National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
39. Niss, M., Blum, W., & Galbraith, P. L. (2007). Introduction. In M. Niss, W. Blum, H. Henn, and P. L. Galbraith (Eds.), Modelling and Applications in Mathematics Education (pp. 3-32). New York: Springer.
40. Özer Keskin, Ö. (2008). A research of developing the pre-service secondary mathematics teachers mathematical modelling performance. (Unpublished doctoral dissertation). Gazi University, Institute of Education Science, Ankara.
41. Patton, M. Q. (2002). Two decades of developments in qualitative inquiry: A personal, experiential perspective. Qualitative social work, 1(3), 261-283.
42. Stillman, G. (2012). Applications and modelling research in secondary classrooms: What have we learnt?. 12th International Congress on Mathematical Education Program. COEX, Seoul, Korea. Retrieved from http://www.icme12.org/upload/submission/1923_f.pdf (02 September 2019).
43. Tekin, A. (2012). Mathematics teachers views concerning model eliciting activities, developmental process and the activities themselves. (Unpublished master’s thesis). Dokuz Eylül University, Institute of Education Science, İzmir.
44. Tekin, A., Hıdıroğlu, Ç.N., & Bukova Güzel, E. (2010). Öğrenciler matematiksel modellemede birlikte çalıştıklarında hangi yaklaşımları sergiliyorlar? [What approaches students take when working together in mathematical modeling]. IX. Mathematics Symposium, Karadeniz Technical University, 20-22 September 20110, Trabzon, Turkey.
45. Tekin, A., & Bukova Güzel, E. (2011). Ortaöğretim matematik öğretmenlerinin matematiksel modellemeye ilişkin görüşlerinin belirlenmesi [Determination of high school mathematics teachers' views on mathematical modeling]. XX. Symposium of Education Science. Mehmet Akif Ersoy University Faculty of Education, 8-10 December 2011, Burdur, Turkey.
46. Tekin Dede, A., & Bukova Güzel, E. (2013a). Model eliciting activity: Obesity problem. Elementary Education Online, 12(4), 1100-1119.
47. Tekin Dede, A., & Bukova Güzel, E. (2013b). Mathematics teachers’ views concerning model eliciting activities, developmental process and the activities themselves. Bartın University Journal of Faculty of Education, 2(1), 288-299.
48. Umay, A. (2003). Some clues on how much preschool teacher candidates ready to teach mathematics. Hacettepe University Journal of Education, 26, 176-181.
49. Ural, A. (2014). Examining prospective mathematics teachers’ abilities of mathematical modeling. Dicle University Journal of Ziya Gökalp Faculty of Education, 23, 110-141.
50. Ural, A. (2018). Matematiksel modelleme eğitimi [Mathematical modeling training]. Ankara: Anı Publishing.
51. Vinner, S. (2007). Mathematics education-procedures, rituals and man‘s search for meaning. The Journal of Mathematical Behavior, 26(1), 1-10.
52. Vorhölter, K., Kaiser, G., & Ferri, R. B. (2014). Modelling in mathematics classroom instruction: An innovative approach for transforming mathematics education. In Transforming mathematics instruction (pp. 21-36). Cham: Springer.
53. Yoon, C., Dreyfus, T., & Thomes, M. (2010). How high is the tramping track? Mathematising and applying in a calculus model-eliciting activity. Mathematics Education Research Journal, 22(2), 141-157.