Investigation of Learning Environment Based on Mathematical Modeling Activities

Öz

This study aimed to examine change in students' mathematical knowledge in a learning environment based on mathematical modeling activities. The study conducted with six students (13-year-old) and examined the seventh graders’ eight mathematical modeling activities prepared for the acquisition of the area measurement subject through applications, video and sound recordings, student solution reports, and researcher notes. To support the data in the implementation process, individual interviews were held with the students. The findings of the study revealed that teaching through mathematical modeling method supports students' area measurement knowledge and skills significantly. This development is supported through learning opportunities that arise in the mathematical modeling process. The formation of the unit square concept in the development of students’ area measurement knowledge and skills and the explanation of the area measurement relation by associating it with the unit square created a locomotive effect. The findings of the study showed that mathematical modeling applications should be included in the curriculum.

Anahtar Kelimeler

• area measurement
• learning environment
• mathematical modeling

Matematiksel Modelleme Etkinliklerine Dayalı Öğrenme Ortamının İncelenmesi

Öz

Bu araştırma, matematiksel modelleme etkinliklerine dayalı öğrenme ortamında öğrencilerin matematiksel bilgilerindeki değişime ilişkin sonuçlar sunmaktadır. Yedinci sınıfta öğrenim gören 6 öğrenciyle (13 yaş) yürütülen araştırmada, alan ölçme konusunun kazanımlarına yönelik olarak hazırlanan 8 adet matematiksel modelleme etkinliği uygulamaları, video ve ses kayıtları, öğrenci çözüm raporları ve araştırmacı notları aracılığıyla incelenmiştir. Uygulama sürecindeki verileri desteklemek amacıyla, öncesinde ve sonrasında öğrencilerle bireysel görüşmeler gerçekleştirilmiştir. Araştırmada elde edilen sonuçlar, matematiksel modelleme yöntemiyle yapılan öğretimin öğrencilerin alan ölçme bilgi ve becerilerini önemli ölçüde desteklediği yönündedir. Söz konusu gelişimin, matematiksel modelleme sürecinde ortaya çıkan öğrenme fırsatları yoluyla desteklendiği sonucuna ulaşılmıştır. Öğrencilerin alan ölçme bilgi ve becerilerinin gelişiminde birim kare kavramının oluşması ve alan ölçme bağıntısının birim kareyle ilişkilendirilerek açıklanması, bir lokomotif etkisi oluşturmuştur. Sonuçlar, matematiksel modelleme uygulamalarının öğretim programında yer alması gerektiğini gösterir niteliktedir. Anahtar kelimeler: alan ölçme, matematiksel modelleme, öğrenme ortamı

Anahtar Kelimeler

• alan ölçme
• matematiksel modelleme
• öğrenme ortamı

Kaynakça

1. Abassian, A., Safi, F., Bush, S., & Bostic, J. (2020). Five different perspectives on mathematical modeling in mathematics education. Investigations in Mathematics Learning, 12(1), 53-65.
2. Ärlebäck, J. B., Doerr, H. M., & O'Neil, A. H. (2013). A modeling perspective on interpreting rates of change in context. Mathematical thinking and learning, 15(4), 314-336.
3. Baturo, A., & Nason, R. (1996). Student teachers' subject matter knowledge within the domain of area measurement. Educational studies in mathematics, 31(3), 235-268.
4. Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of mathematical modelling and application, 1(1), 45-58.
5. Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects—State, trends and issues in mathematics instruction. Educational studies in mathematics, 22(1), 37-68.
6. Güzel, E. B., Dede, A. T., Hıdıroğlu, Ç. N., Ünver, S. K., & Çelik, A. Ö. (2016). Mathematical modeling in mathematics education: for researchers, educators, and students, In E. B. Güzel (Ed.), Pegem Atıf İndeksi, 001-146.
7. Common Core State Standards for Mathematics (CCSM), (2011). Retrieved January 15, 2017, from http://www.corestandards.org/wp-content/uploads/Math_Standards1.pdf.
8. Dickson, L. (1989). Area of a rectangle. In K. Hart, D. C. Johnson, M. Brown, L. Dickson, & R. Clarkson (Eds.).Children’s mathematical frameworks 8-13: A study of classroom teaching (89-125). England, Windsor:NFER-Nelson Publishing Company.

9. Dunne, T., & Galbraith, P. (2003). Mathematical modelling as pedagogy–impact of an immersion program. In Q. X. Ye, W. Blum, K. Houston, & Q.Y. Jiang (Eds.), Mathematical modelling in education and culture (pp-16-30). Horwood Publishing Chichester, England.
10. Erdem, Z. Ç., Doğan, M. F., Gürbüz, R., & Şahin, S. (2017). The reflections of mathematical modeling in teaching tools: Textbook analysis. Adıyaman Üniversitesi Eğitim Bilimleri Dergisi, 7(1), 61-86.
11. Ellis, A. B., Ozgur, Z., Kulow, T., Dogan, M. F., & Amidon, J. (2016). An exponential growth learning trajectory: Students’ emerging understanding of exponential growth through covariation. Mathematical thinking and learning, 18(3), 151-181.
12. English, L. D. (2003). Mathematical modelling with young learners. S. J. Lamon, W. A. Parker ve S. K. Houston (Eds), Mathematical modelling: A way of life (pp. 3-18). Chichester: Horwood Publishing.
13. Ferri, R. B. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer International Publishing.
14. Freeman, A. L., (2014). The Impact Of Small-Group Mathematıcal Modelıng Actıvıtıes On Students’ Understandıng Of Lınear And Quadratıc Functıons [Doctora Thesis], Columbia University, Columbia.
15. Galbraith, P. (2012). Models of modelling: Genres, purposes or perspectives. Journal of Mathematical Modelling and application, 1(5), 3-16.
16. Harel, G., & Lesh, R. (2003). Local conceptual development of proof schemes in a cooperative learning setting. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching, (pp- 359-382).
17. Hart, K. M. (1981). Measurement. In K. M. Hart, D. Kerslake, M. L. Brown, G. Ruddock, D. E. Küchemann, & M. McCartney (Eds.), Children’s understanding of mathematics: 11-16 (pp. 9-22). London: John Murray.
18. Hitt, F., & González-Martín, A. S. (2015). Covariation between variables in a modelling process: The ACODESA (collaborative learning, scientific debate and self-reflection) method. Educational studies in mathematics, 88(2), pp(201-219).
19. Huang, H. M. E., & Witz, K. G. (2013). Children’s conceptions of area measurement and their strategies for solving area measurement problems. Journal of Curriculum and Teaching, 2(1), pp (10-26).
20. Jones, M. & Alony, I. (2011). Guiding the Use of Grounded Theory in Doctoral Studies: An Example from the Australian Film Industry, International Journal of Doctoral Studies, 6, pp (95- 114).
21. Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), pp(302-310).
22. Kamii, C., & Kysh, J. (2006). The difficulty of “length× width”: Is a square the unit of measurement?. The Journal of Mathematical Behavior, 25(2), pp(105-115).
23. Lehrer, R. (2003). Developing understanding of measurement. In J. Kilpatrick, W. G. Martin, & D. Schrifter (Eds.), A research companion to Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics. (pp. 179-192)
24. Lesh, R., & Carmona, G. (2003). Piagetian conceptual systems and models for mathematizing everyday experiences. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp-71-96). Mahwah, NJ: Lawrence Erlbaum.
25. Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3-33). Mahwah, NJ: Lawrence Erlbaum.
26. 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). Hillsdale, NJ: Lawrence Erlbaum
27. Maaß, K. (2006). What are modelling competencies?. ZDM, 38(2), pp(113-142).
28. Miles, M. B. ve Huberman, A. M. (1994). Qualitative data analysis: An expande sourcebook (2nd ed.). Thousand Oaks, CA: Sage.
29. Ministry of National Education [MEB], (2018). The Board of Education, secondary school mathematics program (5th, 6th, 7th and 8th grade) curriculum. Retrieved February 20, 2018, from "http://mufredat.meb.gov.tr/Programlar.aspx".
30. Ng, K. E. D. (2011). Mathematical knowledge application and student difficulties in a design-based interdisciplinary project. In G.Kaiser, W. Blum, R. Borromeo Ferri & G.
31. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 107-116). Springer, Dordrecht.
32. Niss, M., Blum, W., and 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.
33. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
34. Ottesen, J. T. (2001). Do not ask what mathematics can do for modelling. In The Teaching and Learning of Mathematics at University Level (pp. 335-346). Springer, Dordrecht.
35. Outhred, L. N., & Mitchelmore, M. C. (2000). Young children's intuitive understanding of rectangular area measurement. Journal for research in mathematics education, pp(144-167).
36. Park, J., Park, M. S., Park, M., Cho, J., & Lee, K. H. (2013). Mathematical modelling as a facilitator to conceptualization of the derivative and the integral in a spreadsheet environment. Teaching Mathematics and its Applications: An International Journal of the IMA, 32(3), 123-139.
37. Reynolds, A., & Wheatley, G. H. (1996). Elementary students’ construction and coordination of units in an area setting. Journal for Research in Mathematics Education, 27, pp (564-581).
38. Simon, M. A. & Blume, G. W. (1994). Building and understanding multiplicative relationships: A study of prospective elementary teachers. Journal for Research in Mathematics Education, 25(5), pp (472-494).
39. Stohlmann, M., DeVaul, L., Allen, C., Adkins, A., Ito, T., Lockett, D., & Wong, N. (2016). What Is Known about Secondary Grades Mathematical Modelling--A Review. Journal of Mathematics Research, 8(5), 12.
40. Stephan, M., & Clements, D. H. (2003). Linear and area measurement in prekindergarten to grade 2. In Douglas. H. Clements & George. W. Bright (Eds.), Learning and Teaching Measurement 2003 Yearbook (s. 3-16). Reston,VA: NCTM.
41. Şahin, S. (2019). Investigation of mathematical modeling problem posing competencies of mathematics teachers [Doctoral dissertation], Adıyaman University, Adıyaman.
42. Yıldırım, A., & Şimşek, H. (2003). Qualitative research methods in the social sciences. Seçkin Yayıncılık.
43. Yin, R. K. (2009).Case study research: Design and methods (Vol. 5). California, London: Sage.
44. Zacharos, K. (2006). Prevailing educational practices for area measurement and students’ failure in measuring areas. The Journal of Mathematical Behavior, 25(3), 224-239.