Çevrimiçi Öğrenme Ortamlarında Matematiksel Modelleme: Öğrenci Zorlukları

Öz

Bu araştırmanın amacı, çevrim içi öğrenme ortamlarında (ÇÖO) eş zamanlı olarak gerçekleştirilen matematiksel modelleme sürecinde ortaokul öğrencilerinin karşılaştığı zorlukları incelemektir. Türkiye’de bir devlet ortaokulunun 8. sınıfında öğrenim gören 11 öğrenci (8 kız, 3 erkek) üzerinde durum çalışması yöntemiyle gerçekleştirilen bu araştırma, 6 hafta süresince ses ve görüntü kaydı alınarak yürütülmüştür. Katılımcılar, çeşitli matematiksel modelleme problemlerini grup iş birliği ile dinamik matematik yazılımı (DMY) GeoGebra kullanarak tamamlamışlardır. Bu bağlamda, öğrencilerin modelleme sürecinin hangi aşamasında ne tür zorluklarla karşılaştıkları detaylı bir şekilde ele alınılarak incelenmiştir. Çevrim içi matematiksel modelleme (ÇMM) sürecinde öğrencilerin zorlandıkları temalar; teknik zorluklar, bilgi erişimi ve güvenilirlik, sınırlı görünüm, görev paylaşımı, sınırlı etkileşim, zamanlama ve süre kısıtlamaları olarak belirlenmiştir. Modelleme sürecinde dijital araçların kullanımı, öğrencilere birçok avantaj sunarken, aynı zamanda teknik sorunlara da yol açabilmektedir. Matematikselleştirme ve matematiksel çalışma aşamalarında, özellikle dinamik matematik yazılımından kaynaklanan zorluklar dikkat çekici bir şekilde ortaya çıkmıştır. Ayrıca öğrencilerin farklı kaynaklardan bilgi edinirken karşılaştıkları zorlukların çözüm önerilerini zaman zaman olumsuz etkilediği tespit edilmiştir. ÇMM sürecinde öğrenciler akranları, öğretmenleri ve teknoloji ile sınırlı etkileşimleri modelleme döngüsünün farklı aşamalarında çeşitli zorluklara neden olmuştur. Gelecekteki araştırmalar, OMM süreçlerinde öğrencilerin teknik zorlukları aşarak etkileşim ve iş birliğini artıracak yöntemler geliştirmeye odaklanmalıdır.

Anahtar Kelimeler

• Matematiksel Modelleme
• Çevrimiçi Öğrenme
• Zorluklar
• GeoGebra
• GeoGebra

Mathematical Modeling in Online Learning Environments: Student Challenges

Öz

This research aims to examine the difficulties encountered by secondary school students in the mathematical modeling process applied synchronous in online learning environments (OLEs). The research was conducted on 11 8th grade students (8 girls, 3 boys) studying in a public secondary school in Türkiye, using the case study method, by recording audio and videos for 6 weeks. Participants worked collaboratively within a group to complete various problems using the Dynamic Mathematics Software (DMS) GeoGebra. The themes that students had difficulty with in the Online Mathematical Modeling (OMM) process were determined as technical difficulties, access to information and reliability, limited view, shared tasks, limited interaction, time management and time constraints. Using digital tools and instruments in the modeling process offers many advantages to students, however it can also create technical problems. Conspicuous difficulties encountered in the Mathematization and Working Mathematically process is noted, particularly in relation to the DMS. In addition, it was found that the difficulties encountered by students while obtaining information from different sources sometimes negatively affected their solution suggestions. Limitations about the students' interactions with their peers, teachers, and technology during the OMM process caused various difficulties in the stages of the modeling cycle. Future research should focus on developing methods to increase students' interaction and collaboration in OMM processes by overcoming technical difficulties.

Anahtar Kelimeler

• Mathematical Modeling
• Online Learning
• Challenges
• GeoGebra

Kaynakça

1. Adedoyin, O. & Soykan, E. (2020). COVID-19 pandemic and online learning: The challenges and opportunities. Interactive Learning Environments, 31(2), 863-875. https://doi.org/10.1080/10494820.2020.1813180
2. Adnan, M., & Boz, B. (2015). Faculty members’ perspectives on teaching mathematics online: does prior online learning experience count?. Turkish Online Journal of Qualitative Inquiry, 6(1), 21-38. https://doi.org/10.17569/tojqi.60223
3. Alabdulaziz, M. S. (2021). COVID-19 and the use of digital technology in mathematics education. Education and Information Technologies, 26, 7609-7633. https://doi.org/10.1007/s10639-021-10602-3
4. Apuke, O. and Iyendo, T. (2018). University students' usage of the internet resources for research and learning: forms of access and perceptions of utility. Heliyon, 4(12), e01052. https://doi.org/10.1016/j.heliyon.2018.e01052
5. Arefaine, N., Michael, K., & Assefa, S. (2022). GeoGebra Assisted Multiple Representations for Enhancing Students’ Representation Translation Abilities in Calculus. Asian Journal of Education and Training, 8(4), 121–130. https://doi.org/10.20448/edu.v8i4.4309
6. Aversi-Ferreira, T. A., Cordeiro-de-Oliveira, K., Lima, S. V. A. M. de, Santos, W. F. dos, Costa, C. A., Resende, E. B., Moraes-Siqueira, J. S. de, Ferreira, J. P., & Andrade, J. M. S. (2021). The perceptions of students and instructor in a graduate mathematical modeling class: An experience with remote education. Research, Society and Development, 10(6), e2310615223. https://doi.org/10.33448/rsd-v10i6.15223
7. Basilaia, G. and Kvavadze, D. (2020). Transition to online education in schools during a sars-cov-2 coronavirus (COVID-19) pandemic in georgia. Pedagogical Research, 5(4). https://doi.org/10.29333/pr/7937
8. Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. R. Haines, P. L. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics (pp. 222-231). Horwood. https://doi.org/10.1533/9780857099419.5.221.

9. Bringula, R., Reguyal, J. J., Tan, D. D., & Ulfa, S. (2021). Mathematics self-concept and challenges of learners in an online learning environment during COVID-19 pandemic. Smart Learning Environments, 8(1), 1-23. https://doi.org/10.1186/s40561-021-00168-5
10. Çevik, Y., & Cihangir, A. (2020). Tam sayıların modellenmesine ilişkin durum çalışması. Necmettin Erbakan Üniversitesi Ereğli Eğitim Fakültesi Dergisi, 2(2), 136-151. https://doi.org/10.51119/ereegf.2020.2
11. Çevikbaş, M., Greefrath, G., & Siller, H. S. (2023, April). Advantages and challenges of using digital technologies in mathematical modelling education–a descriptive systematic literature review. Frontiers in Education, 8, 1142556. https://doi.org/10.3389/feduc.2023.1142556
12. Chang, Y. and Lee, E. (2022). Addressing the challenges of online and blended stem learning with grounded design. Australasian Journal of Educational Technology, 163-179. https://doi.org/10.14742/ajet.7620
13. Coşkun Şimşek, M., İnam, B., Yebrem Özdamar, S., & Turanlı, N. (2022). Matematik öğretmenlerinin gözünden uzaktan eğitim. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 37(2), 629-653. https://doi.org/10.16986/huje.2021073768
14. Coksoyler, A., & Bozkurt, G. (2021). Bilişsel perspektif bağlamında matematiksel modelleme süreci: Altıncı sınıf öğrencilerinin deneyimleri. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, (52), 480-502. https://doi.org/10.53444/deubefd.930216
15. Daher, W. M., & Shahbari, J. A. (2015). Pre-service teachers’ modelling processes through engagement with model eliciting activities with a technological tool. International Journal of Science and Mathematics Education, 13, 25-46. https://doi.org/10.1007/s10763-013-9464-2
16. Deniz, S., & Kurt, G. (2022). Investigation of mathematical modeling processes of middle school students in Modeling activities (MEAs): A STEM approach. Participatory Educational Research, 9(2), 150-177. https://doi.org/10.17275/per.22.34.9.2
17. El-Sabagh, H. A. (2021). Adaptive e-learning environment based on learning styles and its impact on development students’ engagement. International Journal of Educational Technology in Higher Education, 18(1). https://doi.org/10.1186/s41239-021-00289-4
18. Erbas, A., Kertil, M., Çetinkaya, B., Cakiroglu, E., Alacaci, C., & Bas, S. (2014). Mathematical modeling in mathematics education: Basic concepts and approaches. Educational Sciences: Theory and Practice, 14(4), 1621-1627. https://doi.org/10.12738/estp.2014.4.2039
19. Etemad-Sajadi, R. (2016). The impact of online real-time interactivity on patronage intention: the use of avatars. Computers in Human Behavior, 61, 227-232. https://doi.org/10.1016/j.chb.2016.03.045
20. Fan, Y., Zhang, J., Zu, D., & Zhang, H. (2021). An automatic optimal course recommendation method for online math education platforms based on bayesian model. International Journal of Emerging Technologies in Learning (Ijet), 16(13), 95. https://doi.org/10.3991/ijet.v16i13.24039
21. Geiger, V. (2011). Factors affecting teachers’ adoption of innovative practices with technology and mathematical modelling. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Trends in teaching and learning of mathematical modelling: ICTMA14 (pp. 305-314). Springer. https://doi.org/10.1007/978-94-007-0910-2_31
22. Greefrath, G., Hertleif, C., & Siller, H. S. (2018). Mathematical modelling with digital tools—a quantitative study on mathematising with dynamic geometry software. ZDM, 50, 233-244. https://doi.org/10.1007/s11858-018-0924-6
23. Gündüzalp, M. (2019). Examining the mathematical modeling skills of 11th grade students [11. sınıf öğrencilerinin matematiksel modelleme becerilerinin incelenmesi] (Doctoral dissertation, Marmara Üniversitesi). Turkey.
24. Gürlen, E., Demirkaya, A. S., & Doğan, N. (2019). Uzmanların PISA ve TIMSS sınavlarının eğitim politika ve programlarına etkisine ilişkin görüşleri. Mehmet Akif Ersoy University Journal of Education Faculty, (52), 287-319. https://doi.org/10.21764/maeuefd.599615
25. Hankeln, C., & Greefrath, G. (2021). Mathematische Modellierungskompetenz fördern durch Lösungsplan oder Dynamische Geometrie-Software? Empirische Ergebnisse aus dem LIMo-Projekt. Journal für Mathematik-Didaktik, 42(2), 367-394. https://doi.org/10.1007/s13138-020-00178-9
26. Hıdıroğlu, Ç. N. (2022). Mathematics student teachers' task design processes: The case of history, theory, technology, and modeling. Journal of Pedagogical Research, 6(5), 17-53. https://doi.org/10.33902/JPR.202217094
27. Hıdıroğlu, Ç. N., Özaltun Çelik, A., Kula Ünver, S., & Bukova Güzel, E. (2018). Prospective mathematics teachers' actions in technology-aided mathematical modeling process: Distance problem. Erzincan University Journal of Education Faculty, 20(3). https://doi.org/10.17556/erziefd.441732
28. Kaiser, G., Schwarz, B., & Tiedemann, S. (2010). Future teachers’ professional knowledge on modelling. In R. Lesh, P. L. Galbraith, C. R. Haines & A. Hurford (Eds.), Modelling students’ mathematical modelling competencies (pp. 433-444). Springer. https://doi.org/10.1007/978-1-4419-0561-1_37
29. Kaygısız, İ. (2023). P4C Supported Mathematical Modeling Applications of Primary School Students: A Teaching Experiment. Kaygı. Bursa Uludağ University Faculty of Arts and Sciences Journal of Philosophy, 22(3), 386-422. https://doi.org/10.20981/kaygi.1335022
30. Kaygısız, İ., & Şenel, E. A. (2022). Mathematical modeling in primary school: Students’ opinions and suggestions on modeling activities applied as a teaching experiment. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 16(1), 88-134. https://doi.org/10.17522/balikesirnef.1033981
31. Kiili, C., Coiro, J., & Räikkönen, E. (2019). Students’ evaluation of information during online inquiry: Working individually or in pairs. The Australian Journal of Language and Literacy, 42(3), 167-183. https://doi.org/10.1007/BF03652036
32. Klock, H., & Siller, H. S. (2020). A time-based measurement of the intensity of difficulties in the modelling process. In Mathematical modelling education and sense-making (pp. 163-173). https://doi.org/10.1007/978-3-030-37673-4_15
33. Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In Beyond constructivism (pp. 3-33). Routledge.
34. Lesh, R., Young, R., & Fennewald, T. (2010). Modelling in K-16 mathematics classrooms–and beyond. In R. Lesh, P. Galbraith, C. Haines, & A. Hurford (Eds.), Modelling students’ mathematical modelling competencies (pp. 275-283). Springer. https://doi.org/10.1007/978-1-4419-0561-1_24
35. Lingefjärd, T. (2000). Mathematical modeling by prospective teachers using technology (Doctoral dissertation, University of Georgia). Retrieved from http://files.eric.ed.gov
36. Lo, C. K., Cheung, K. L., Chan, H. R., & Chau, C. L. E. (2021). Developing flipped learning resources to support secondary school mathematics teaching during the COVID-19. Interactive Learning Environments. https://doi.org/10.1080/10494820.2021.1981397
37. Meisya, S., & Arnawa, I. M. (2021). The development of mathematical learning devices based on Modeling activities and GeoGebra. Journal of Physics: Conference Series, 1742(1), 012034. https://doi.org/10.1088/1742-6596/1742/1/012034
38. Merck, M. F., Gallagher, M. A., Habib, E., & Tarboton, D. (2021). Engineering students’ perceptions of mathematical modeling in a learning module centered on a hydrologic design case study. International Journal of Research in Undergraduate Mathematics Education, 7, 351-377. https://doi.org/10.1007/s40753-020-00131-8
39. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Thousand Oaks, CA: Sage.
40. Molina-Toro, J. F., Rendón-Mesa, P. A., & Villa-Ochoa, J. A. (2022). Contradictions in mathematical modeling with digital technologies. Education and Information Technologies, 27(2), 1655-1673. https://doi.org/10.1007/s10639-021-10676-z
41. Morton, W. and Durandt, R. (2023). Learning first-year mathematics fully online: were students prepared, how did they respond?. Eurasia Journal of Mathematics Science and Technology Education, 19(6), em2272. https://doi.org/10.29333/ejmste/13189
42. Özkan, M. (2021). An action research about secondary school students’ modeling competencies in regular polygons [Ortaokul öğrencilerinin düzgün çokgenler konusunda modelleme yeterlikleri üzerine bir eylem araştırması] (Doctoral dissertation, Marmara Üniversitesi). Turkey.
43. Perin, A., & Campos, C. (2022). Reading and interpretation of statistical graphics by 2nd year students of high school. In Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics. https://doi.org/10.52041/iase.icots11.t2f1
44. Radmehr, F. and Goodchild, S. (2022). Switching to fully online teaching and learning of mathematics: the case of norwegian mathematics lecturers and university students during the COVID-19 pandemic. International Journal of Research in Undergraduate Mathematics Education, 8(3), 581-611. https://doi.org/10.1007/s40753-021-00162-9
45. Rutherford, T., Duck, K., Rosenberg, J. M., & Patt, R. (2022). Leveraging mathematics software data to understand student learning and motivation during the COVID-19 pandemic. Journal of Research on Technology in Education, 54(sup1), S94-S131. https://doi.org/10.1080/15391523.2021.1920520
46. Sağıroğlu, D., & Karataş, İ. (2018). Matematik öğretmenlerinin matematiksel modelleme yöntemine yönelik etkinlik oluşturma ve uygulama süreçlerinin incelenmesi. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 12(2), 102-135. https://doi.org/10.17522/balikesirnef.506423
47. Saka, E., & Çelik, D. (2018). Matematik Öğretmeni Adaylarının Matematiksel Modelleme Sürecinde Bilgisayar Kullanımları Üzerine Bir İnceleme. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 9(3), 618-635. https://doi.org/10.16949/turkbilmat.409160
48. Salsabila, N. H., Lu'luilmaknun, U., Triutami, T. W., & Wulandari, N. P. (2022). Online learning obstacles for mathematics education students during pandemic. Al Khawarizmi: Jurnal Pendidikan dan Pembelajaran Matematika, 5(2), 76-83. https://doi.org/10.22373/jppm.v5i2.11544
49. Santi, E. A., Gorghiu, G., & Pribeanu, C. (2022). Students' Engagement and Active Participation During the Pandemic. Informatica Economica, 26(1), 5-15. https://doi.org/10.24818/issn14531305/26.1.2022.01
50. Schaap, S., Vos, P., & Goedhart, M. (2011). Students overcoming blockages while building a mathematical model: Exploring a framework. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling, vol 1 (pp. 137-146). Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0910- 2_15
51. Siller, H.-S., & Greefrath, G. (2010). Mathematical modelling in class regarding to technology. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (CERME6) (pp. 2136-2145). ENS Lyon: Institute National de Recherche Pédagogique.
52. Soon, W., Lioe, L. T., & McInnes, B. (2011). Understanding the difficulties faced by engineering undergraduates in learning mathematical modelling. International Journal of Mathematical Education in Science and Technology, 42(8), 1023-1039. https://doi.org/10.1080/0020739x.2011.573867
53. Tekin Dede, A. (2017). Examination of the relationship between modelling competencies and class level and mathematics achievement. Elementary Education Online, 16(3), 1201-1219. https://doi.org/10.17051/ilkonline.2017.330251
54. Tekin Dede, A. (2022). The role of mathematical modeling in curricula and project works. In E. Bukova Güzel, M. F. Doğan, & A. Özaltun Çelik (Eds.), Matematiksel Modelleme: Teoriden Uygulamaya Bütünsel Bakış (pp. 71-99). Pegem Akademi.
55. Tonbuloğlu, İ., & Çukurbaşı, B. (2023). K-12 teachers' use of technology that enriches the online learning process. Elektronik Sosyal Bilimler Dergisi, 22(87), 1257-1279. https://doi.org/10.17755/esosder.1276190
56. Wassie, Y. and Zergaw, G. (2019). Some of the potential affordances, challenges and limitations of using GeoGebra in mathematics education. Eurasia Journal of Mathematics Science and Technology Education, 15(8). https://doi.org/10.29333/ejmste/108436
57. Wulanjani, A. N., Anggraeni, C. W., & Yunianti, S. S. (2022). Investigating the dimensions of students’ interaction in listening online learning environment amidst COVID-19 pandemic. Indonesian Journal of Applied Linguistics, 12(2), 321-333. https://doi.org/10.17509/ijal.v12i2.51083
58. Yılmaz, D. D., Gurel, Z. Ç., & Sagirli, M. O. (2023). Comparing the learning environments related to mathematical modelling through distance education. International Journal for Mathematics Teaching and Learning, 24(1), 17-39. https://doi.org/10.4256/ijmtl.v24i1.459
59. Yin, R. K. (1994). Case study research: Design and methods. Sage Publications.
60. Yohannes, Y., Juandi, D., Diana, N., & Sukma, Y. (2021). Mathematics Teachers’ Difficulties in Implementing Online Learning during the COVID-19 Pandemic. Journal of Hunan University Natural Sciences, 48(5), 87–98.
61. Zulkarnaen, R. (2018). Why is mathematical modeling so difficult for students? In AIP Conference Proceedings (Vol. 2021, No. 1, p. 060026). AIP Publishing LLC. https://doi.org/10.1063/1.5062790