Ortaokul Öğrencilerinin Modelleme Etkinlikleri Yoluyla Matematiksel İlişkilendirme Süreçlerine Yönelik Öz-Yeterlik İnançları ile Görüşlerinin İncelenmesi

Öz

Bu çalışmanın amacı ortaokul öğrencilerinin diğer disiplinlerle ilişkilendirme bağlamında hazırlanan modelleme etkinlikleriyle tasarlanmış bir öğrenme ortamında matematiksel ilişkilendirmeye yönelik öz-yeterlik inançları ile görüşlerini ortaya çıkarmaktır. Araştırmada iç içe deneysel karma yöntem tasarımı kullanılmıştır. Araştırma yedinci sınıf deney ve kontrol grubundaki toplam 61 öğrenciyle ön test, son test ve uygulama süreci dahil olmak üzere on beş hafta boyunca yürütülmüştür. Veri toplama aracı olarak matematiksel modelleme etkinlikleri, matematiksel ilişkilendirme öz-yeterlik ölçeği ile matematiksel ilişkilendirmeye yönelik ön ve son görüş formları uygulanmıştır. Grupların matematiksel ilişkilendirme öz-yeterliği açısından ön test ve son test puanları arasında istatistiksel olarak anlamlı bir fark olmadığı görülmüştür. Ancak süreç sonrasında matematiğin diğer disiplinlerle ilişkilendirilmesinin öğrencilerin matematiğe ve farklı derslere ilişkin görüşlerinin gelişimine katkı sağladığı belirlenmiştir.

Anahtar Kelimeler

• Matematiksel ilişkilendirme
• matematiksel modelleme
• ortaokul öğrencileri
• öz-yeterlik

Investigation of Middle School Students’ Opinions and Self-Efficacy Beliefs on Mathematical Connection with Using Modelling Tasks

Abstract

The purpose of this study is to determine the opinions and self-efficacy beliefs of middle school students towards mathematical connections before and after the process in a learning environment prepared in the context of connections with different disciplines and including modeling tasks. An embedded experimental mixed method design was used in the research. The study was conducted with a sum of sixty-one students in the seventh-grade experimental and control groups for fifteen weeks, including the pre-test¬, post-test, and application process. As a data collection tool, mathematical modelling tasks, mathematical connection self-efficacy scale, and pre-post opinion forms for mathematical connection were applied. It was observed that there is no statistically meaningful difference between the pre-test and post-test scores of the groups in terms of mathematical connection self-efficacy. However, after the process, it was specified that connecting mathematics with other disciplines assisted the development of students’ opinions on mathematics and different courses.

Keywords

• mathematical connection
• mathematical modeling
• middle school students
• self-efficacy.

References

1. Aşkar, P., & Umay, A. (2001). İlköğretim matematik öğretmenliği öğrencilerinin bilgisayarla ilgili öz-yeterlik algısı. Hacettepe University Journal of Education, 21(21), 1-8.
2. Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2015). Australian curriculum: Mathematics. Retrieved from https://www.australiancurriculum.edu.au/media/3480/mathematics-sequence-of-achievement.pdf
3. Baki, A. (2018). Matematiği öğretme bilgisi [Knowledge of teaching mathematics]. Pegem. https://doi.org/10.14527/9786052410318
4. Bandura, A. (1986). The explanatory and predictive scope of self-efficacy theory. Journal of Social and Clinical Psychology, 4(3), 359-373. https://doi.org/10.1521/jscp.1986.4.3.359
5. Blomhøj, M. (2007). Developing mathematical modelling competency through problem-based project work- experiences from Roskilde University [Conference presentation]. 9th International History, Philosophy, and Science Teaching conference, Calgary, Canada.
6. Blum, W., & Borromeo-Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45-58.
7. Blum, W., & Leiss, D. (2005). Filling up”-the problem of independence-preserving teacher interventions in lessons with demanding modelling tasks. In CERME 4–Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (pp. 1623-1633).
8. Borromeo-Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. The International Journal on Mathematics Education, 38(2), 86-95. https://doi.org/10.1007/BF02655883

9. Borromeo-Ferri, R. (2010). On the influence of mathematical thinking styles on learners’ modeling behavior. Journal für Mathematik-Didaktik, 31(1), 99-118. https://doi.org/10.1007/s13138-010-0009-8
10. Borromeo-Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer International Publishing. https://doi.org/10.1007/978-3-319-68072-9
11. Bossé, M. J. (2003). The Beauty of “and” and “or”: Connections within mathematics for students with learning. Mathematics & Computer Education, 37(1), 105-114.
12. Büyüköztürk, S. (2014). Sosyal bilimler için veri analizi el kitabı [Handbook of data analysis for the social sciences]. Pegem Akademi.
13. Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2019). Eğitimde bilimsel araştırma yöntemleri [Scientific research methods in education]. Pegem Akademi.
14. Cai, J., Cirillo, M., Pelesko, J. A., Borromeo-Ferri, R., Borba, M., Geiger, V., Stillman, G., English, L. D., Wake, G., Kaiser, G., Kwon, O., & Kwon, O. N. (2014). Mathematical modeling in school education: Mathematical, cognitive, curricular, instructional and teacher education perspectives. In Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 1, pp. 145-172). PME-NA.
15. Çepni, S. (2012). Araştırma ve proje çalışmalarına giriş [Introduction to Research and project studies] (Improved 6. Oppression). Celepler Matbaacılık.
16. Chamberlin, S. A., & Moon, S. M. (2005). Model-eliciting activities as a tool to develop and identify creatively gifted mathematicians. Journal of Middle Gifted Education, 17(1), 37-47. https://doi.org/10.4219/jsge-2005-393
17. Chigeza, P. (2013). Translating between and within representations: Mathematics as lived experiences and interactions. Mathematics Education Research Group of Australasia. (In V. Steinle, L. Ball & C. Bardini (Eds.), Mathematics education: Yesterday, today, and tomorrow. Melbourne, VIC: MERGA. 178-185.
18. Coşkun, M. (2013). Matematik derslerinde ilişkilendirmeye ne ölçüde yer verilmektedir?: Sınıf içi uygulamalardan örnekler [Unpublished master’s thesis]. Gaziantep University.
19. Council of Higher Education [CoHE]. (2018). Matematik öğretmenliği lisans programı [Mathematics teaching undergraduate program.]. Retrieved from https://www.yok.gov.tr/Documents/Kurumsal/egitim_ogretim_dairesi/Yeni-Ogretmen-Yetistirme-Lisans-Programlari/Ilkogretim_Matematik_Lisans_Programi.pdf.
20. Creswell, J. W., & Plano Clark, V. L. (2018). Mixed methods research. Trans. Eds. Dede, Y. & Demir S. B. Anı Yayıncılık.
21. Curriculum Planning and Development Division [CPDD]. (2012). O-Level mathematics teaching and learning syllabus. Singapore: Ministry of Education.
22. Czocher, J. A., Melhuish, K., & Kandasamy, S. S. (2019). Building mathematics self-efficacy of STEM undergraduates through mathematical modelling. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2019.1634223
23. Deveci, Ö. (2010). İlköğretim altıncı sınıf fen ve teknoloji dersi kuvvet ve hareket ünitesinde fen-matematik entegrasyonunun akademik başarı ve kalıcılık üzerine etkisi [Unpublished master’s thesis]. University of Çukurova.
24. DiGregorio, N., & Liston, D. D. (2018). Experiencing technical difficulties: Teacher self-efficacy and instructional technology. In: Hodges, C. (Eds), Self-Efficacy in Instructional Technology Contexts. Springer, Cham. https://doi.org/10.1007/978-3-319-99858-9_7
25. Domínguez, A., De La Garza, J., & Zavala, G. (2015). Models and modelling in an integrated Physics and mathematics course. In International perspectives on the teaching and learning of mathematical modelling (pp. 513-522). https://doi.org/10.1007/978-3-319-18272-8_43
26. Dorn, R. I., Douglass, J., Ekiss, G. O., Trapido-Lurie, B., Comeaux, M., Mings, R., Eden, R., Davis, C., Hind, E., & Ramakrishna, B. (2005). Learning geography promotes learning math: Results and implications of Arizona’s GeoMath grade K-8 program. Journal of Geography, 104(4), 151-159. https://doi.org/10.1080/00221340508978631
27. Doruk, B. K., & Umay, A. (2011). Matematiği günlük yaşama transfer etmede matematiksel modellemenin etkisi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41(41), 124-135.
28. Duman, S. Ö., & Aydoğan Yenmez, A. (2024). An investigation of students’ mathematical connection and metacognitive skills in the mathematical modelling process. International Journal of Mathematical Education in Science and Technology, 1-53. https://doi.org/10.1080/0020739X.2024.2404426
29. Eli, J. A. (2009). An exploratory mixed methods study of prospective middle grades teachers’ mathematical connections while completing investigative tasks in geometry [Unpublished doctoral dissertation]. University of Kentucky.
30. English, L. D. (2004). Mathematical modelling in the primary school. I. Putt, R. Faragher & M. Mclean (Eds.), Proceedings of the 27th Annual Conference of Mathematics Education Research Group of Australasia, Mathematics Education for The Third Millenium: Towards 2010 (pp. 207-214). Townsville: Merga.
31. English, L. D. (2006). Mathematical modeling in the primary school: Children’s construction of a consumer guide. Educational Studies in Mathematics, 63(3), 303-323. https://doi.org/10.1007/s10649-005-9013-1
32. English, L. D. (2007). Interdisciplinary modelling in the primary mathematics curriculum. In Watson, Jane and Beswick, Kim, (Eds.), Proceedings 30th Mathematics Education Research Group of Australasia Annual Conference (pp. 275-284), Hobart.
33. English, L. D. (2015). STEM: Challenges and opportunities for mathematics education. In Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 4-18). PME.
34. Eric, C. C. M. (2008). Using model-eliciting activities for primary mathematics classrooms. The Mathematics Educator, 11(1), 47-66.
35. Eurydice/EACEA/European Commission. (2012). Developing key competences at school in Europe: Challenges and opportunities for policy. Eurydice Report. Luxembourg: Publications Office of the European Union.
36. García-García, J., & Dolores-Flores, C. (2021a). Pre-university students’ mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 33, 1-22. https://doi.org/10.1007/s13394-019-00286-x
37. García-García, J., & Dolores-Flores, C. (2021b). Exploring pre-university students’ mathematical connections when solving Calculus application problems. International Journal of Mathematical Education in Science and Technology, 52(6), 912-936. https://doi.org/10.1080/0020739X.2020.1729429
38. Güder, Y., & Gürbüz, R. (2018). STEM eğitimine geçişte bir araç olarak disiplinler arası matematiksel modelleme oluşturma etkinlikleri: Öğretmen ve öğrenci görüşleri. Adıyaman University Journal of Educational Sciences, 8(2), 170-198. https://doi.org/10.17984/adyuebd.457626
39. Gürbüz, R., Erdem, Z. Ç., Şahin, S., Temurtaş, A., Doğan, C., Doğan, M. F., Çalık, M., & Çelik, D. (2018). Bir disiplinler arası matematiksel modelleme etkinliğinden yansımalar [Special Issue]. Adıyaman Üniversitesi Eğitim Bilimleri Dergisi, 8(2), 1-22. https://doi.org/10.17984/adyuebd.463270
40. Hindun, S., Sapitri, Y. E., & Rohaeti, E. E. (2019). İncreasement of mathematical connection ability and self-efficacy of students through problem-based learning approach with multimedia. (JIML) Journal of Innovative Mathematics Learning, 2(2), 74-81. https://doi.org/10.22460/jiml.v2i2.p74-81
41. Hodges, C. B., & Stackpole-Hodges, C. L. (2018). Guided reflective journaling with case-based instruction in a dysphagia course: Learner self-efficacy and reaction. In Hodges, C. (eds) Self-Efficacy in Instructional Technology Contexts (pp 89-100). Springer, Cham. https://doi.org/10.1007/978-3-319-99858-9_6
42. Johnson, B., & Christensen, L. (2014). Educational Research Quantitative, Qualitative, and Mixed Approaches (In 5th Ed., Trans. Ed. S. B. Demir). Eğiten Kitap.
43. Kaiser, G. (2020). Mathematical modelling and applications in education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 553-561). Springer. https://doi.org/10.1007/978-3-030-15789-0_101
44. Kaya, D. (2020). Altıncı sınıf öğrencilerinin matematiksel ilişkilendirme öz yeterlik düzeylerinin algılanan öğretmen duygusal destek, cinsiyet ve matematik başarısı açısından incelenmesi. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 14(1), 106-132. https://doi.org/10.17522/balikesirnef.605489
45. Kerpiç, A., & Bozkurt, A. (2011). Etkinlik tasarım ve uygulama prensipleri çerçevesinde 7. sınıf matematik ders kitabı etkinliklerinin değerlendirilmesi. Mustafa Kemal University Journal of Social Sciences Institute, 8(16), 303-318.
46. Kertil, M., & Gürel, C. (2016). Mathematical modeling: A bridge to STEM education. International Journal of Education in mathematics, science, and Technology, 4(1), 44-55. https://doi.org/10.18404/ijemst.95761
47. Kılıç, Z. (2020). Farklı disiplinler ile ilişkilendirme bağlamında matematiksel modelleme etkinliklerinin geliştirilmesi ve uygulanması: Ortaokul öğrencileri örneklemesi [Development and implementation of mathematical modeling activities in the context of connecting with different disciplines: the sample of middle school students] [Unpublished master’s thesis]. Dicle University.
48. Krawitz, J., & Schukajlow, S. (2018). Do students value modelling problems, and are they confident they can solve such problems? Value and self-efficacy for modelling, word, and intra-mathematical problems. ZDM Mathematics Education, 50, 143-157. https://doi.org/10.1007/s11858-017-0893-1
49. Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connection tasks. Educational Studies in Mathematics, 66(3), 349-371. https://doi.org/10.1007/s10649-006-9071-z
50. Lesh, R., Cramer, K., Doerr, H., Post, T., & Zawojewski, J. (2003). Model development sequences perspectives. Beyond constructivism: A models & modeling perspective on mathematics teaching, learning, and problem solving. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
51. Lesh, R., & Doerr, H. M. (Eds.). (2003). Beyond constructivism: A models and modeling perspective on mathematics problem solving, learning, and teaching (pp. 3-33). Mahwah, NJ: Lawrence Erlbaum Associates. https://doi.org/10.4324/9781410607713
52. Lingefjärd, T. (2006). Faces of mathematical modeling. ZDM: The International Journal on Mathematics Education, 38(2), 96-112. https://doi.org/10.1007/BF02655884
53. Maaß, K. (2005). Barriers and opportunities for the integration of modelling in mathematic classes: Results of an empirical study. Teaching Mathematics and its Applications, 2(3), 1-16. https://doi.org/10.1093/teamat/hri019
54. Maaß, K. (2006). What are modelling competencies? ZDM: Mathematics Education, 38(2), 113-142. https://doi.org/10.1007/BF02655885
55. Ministry of National Education [MoNE]. (2013). Ortaokul matematik dersi öğretim programı (5, 6, 7 ve 8. sınıflar) [Middle school mathematics curriculum: Grades 5,6,7,8]. MoNE.
56. Ministry of National Education [MoNE]. (2017). Matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). [Mathematics curriculum: Grades 1,2,3,4,5,6,7,8]. MoNE.
57. Ministry of National Education [MoNE]. (2018a). Matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). [Mathematics curriculum: Grades 1,2,3,4,5,6,7,8]. MoNE.
58. Ministry of National Education [MoNE]. (2018b). Matematik uygulamaları dersi öğretim programı (ortaokul ve imam hatip ortaokulu 5, 6, 7 ve 8. sınıflar) [Middle School Mathematics Applications Curriculum: Grades 5, 6, 7, 8]. MoNE.
59. Mousley, J. (2004). An aspect of mathematical understanding: The notion of “connected knowing.” In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 377–384). International Group for the Psychology of Mathematics Education.
60. Narlı, S. (2016). İlişkilendirme becerisi ve muhtevası [Connection skill and content]. Bingölbali, E., Arslan, S., & Zembat, İ. Ö. (Ed.), Matematik eğitiminde teoriler [Theories in mathematics education] (s. 539-563). Pegem Akademi.
61. National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.
62. National Curriculum Board. (2009). Shape of the Australian curriculum: Mathematics. http://www.acara.edu.au/verve/_resources/Australian_Curriculum_-_Maths.pdf.
63. Ontario Ministry of Education [OME]. (2002). The Ontario curriculum grades 11 and 12. On the Ministry of Education’s website at http://www.edu.gov.on.ca.
64. Özgen, K. (2013a). İlköğretim matematik öğretmen adaylarının matematiksel ilişkilendirmeye yönelik görüş ve becerilerinin incelenmesi. Electronic Turkish Studies, 8(8), 2001-2020. https://doi.org/10.7827/TurkishStudies.5321
65. Özgen, K. (2013b). Problem çözme bağlaminda matematiksel ilişkilendirme becerisi: öğretmen adaylari örneği. Education Sciences, 8(3), 323-345. https://doi.org/10.12739/NWSA.2013.8.3.1C0590
66. Özgen, K. (2016, May). Designing effective problem-based learning (PBL) problems: the sample of mathematics course, International Conference on Research in Education and Science (ICRES)., Bodrum, Turkey.
67. Özgen, K., & Bindak, R. (2018). Development of mathematical connection self-efficacy scale. Education Journal, 26(3), 913-924. https://doi.org/10.24106/kefdergi.413386
68. Parr, B., Edwards, M. C., & Leising, J. G. (2009). Selected effects of a curriculum integration intervention on the mathematics performance of middle students enrolled in an agricultural power and technology course: an experimental study. Journal of Agricultural Education, 50(1), 57-69. https://doi.org/10.5032/jae.2009.01057
69. Rodríguez-Nieto, C. A., Font Moll, V., Borji, V., & Rodríguez-Vásquez, F. M. (2022). Mathematical connections from a networking of theories between extended theory of mathematical connections and onto-semiotic approach. International Journal of Mathematical Education in Science and Technology, 53(9), 2364–2390. https://doi.org/10.1080/0020739X.2021.1875071
70. Sandalcı, Y. (2013). Matematiksel modelleme ile cebir öğretiminin öğrencilerin akademik başarılarına ve matematiği günlük yaşamla ilişkilendirmelerine etkisi [Unpublished master’s thesis]. Recep Tayyip Erdoğan University.
71. Schoenfeld, A. H. (2022). Why are learning and teaching mathematics so difficult? In Handbook of cognitive mathematics (pp. 1-35). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-44982-7_10-1
72. Schwarzer, R., & Fuchs, R. (1995). Changing risk behaviors and adopting health behaviors: The role of self-efficacy beliefs. In A. Bandura (Ed.), Self-efficacy in changing societies (pp. 259–288). Cambridge University Press. https://doi.org/10.1017/CBO9780511527692.011
73. Shulman, V., & Armitage, D. (2005). Project discovery: An urban middle school reform effort. Education and Urban Society, 37(4), 371-397. https://doi.org/10.1177/0013124505277688
74. Sriraman, B., & Dahl, B. (2009). On bringing interdisciplinary ideas to gifted education. In L.V. Shavinina (Ed). The International Handbook of Giftedness (pp. 1235-1256). Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6162-2_64
75. Sriraman, B., & Lesh, R. A. (2006). Modeling conceptions revisited. ZDM, 38(3), 247-254. https://doi.org/10.1007/BF02652808
76. Takaoğlu, Z. (2015). Matematiksel modelleme kullanılan fizik derslerinin öğretmen adaylarının ilgi, günlük hayat ve diğer derslerle ilişkilendirmelerine etkisi. Yüzüncü Yıl Üniversitesi Eğitim Fakültesi Dergisi, 12(1), 223-263.
77. Tekin Dede, A., & Bukova Güzel, E. (2014). Model Eliciting Activities: The theoretical structure and its example. Ondokuz Mayıs University Journal of Education, 33(1), 95-111. https://doi.org/10.7822/egt298
78. Ural, A. (2018). Matematiksel modelleme eğitimi [Mathematical modeling education]. Anı Yayıncılık.
79. Yavuz-Mumcu, H., & Aktaş, M. C. (2018). The investigation of the relationship between mathematical connection skills and self-efficacy beliefs. Journal of Mathematics Education, 3(1), 1-8.
80. Yıldırım, A., & Şimşek, H. (2005). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in the social sciences] (5th ed.). Seçkin Yayıncılık.
81. Yılmaz, M. (2022). Ortaokul öğrencilerinin matematiksel ilişkilendirme öz yeterlikleriyle problem çözme başarıları arasındaki ilişkinin incelenmesi [Unpublished master’s thesis]. Necmettin Erbakan University.
82. Zengin, Y. (2019). Development of mathematical connection skills in a dynamic learning environment. Education and Information Technologies, 24(3), 2175-2194. https://doi.org/10.1007/s10639-019-09870-x