Etkinlik Analizi ve Tasarlama Sürecinde Matematik Öğretmen Adaylarının Etkinliklerin Sunduğu Olanakları Dikkate Alma Durumları

Abstract

Bu kolektif durum çalışmasının amacı, ilköğretim matematik öğretmen adaylarının (MÖA) etkinlik analizi bağlamında etkinliklerin sunduğu matematiksel ve pedagojik olanakları dikkate alma durumlarını ve bu dikkate aldıkları durumları özgün etkinlik tasarımlarına nasıl yansıttıklarını anlamaktır. Bu amaç doğrultusunda veriler, beş matematik öğretmeni adayının seçtikleri etkinliklerin analizine ilişkin yazılı raporlarından, eğitmen notlarından ve adayların tasarladıkları etkinliklerden dört aşamada elde edilmiştir. MÖA’lar Aşama-1'de matematiksel bir etkinliği analiz etmiş, Aşama-2'de daha önceden yaptığı analizleri gözden geçirmiş, Aşama-3'te ders eğitmeninin yaptığı bir etkinlik uygulamasını gözlemlemiş ve Aşama-4'te özgün bir etkinlik tasarlamışlardır. MÖA’lar etkinliklerin matematiksel niteliklerini belirlemeye yönlendirildikçe, etkinliklerin matematiksel ve pedagojik yönlerini daha fazla tanımlamışlardır. Eğitmenin notlarına göre, MÖA’lar iyi etkinliklerin karmaşık süreçler içerdiğini düşünmektedirler ve bu nedenle uygulamanın önemli öğretim aşamalarını gözden kaçırmaktadırlar. Son olarak, öğretimsel sorulara dikkat eden MÖA’lar, diğerlerine göre daha yüksek bilişsel istem düzeyine sahip etkinlikleri uygun şekilde tasarlamışlardır. Sonuç olarak, MÖA’lar matematiksel ve pedagojik unsurları bakımından özgün etkinlikleri değerlendirme ve tasarlama konusunda yardıma ihtiyaç duymaktadır.

Keywords

• Öğretmen Adayları
• Dikkate Alma Durumları
• Öğretmen Adayları
• Etkinlik Tasarlama
• Etkinlik Olanakları
• Etkinlik Analizi

Pre-Service Mathematics Teachers’ Attention to Tasks’ Affordances While Analyzing and Designing Tasks

Abstract

The objective of this collective case study is to comprehend how pre-service mathematics teachers (PMTs) attend to mathematical and pedagogical affordances in task analysis and how their attention reflects their original task-design. To achieve this, we acquired data from written reports analyzing their selected tasks, instructor notes, and the designed tasks of five PMTs over four phases. PMTs conducted an analysis of a task during Phase 1, revised their analysis in Phase 2, had the opportunity to observe a task implementation provided by the course instructor in Phase 3, and designed an original task during Phase 4. As a result of being prompted to identify the mathematical elements of the activities, PMTs described more mathematical and pedagogical aspects of the tasks. Based on the instructor's notes, PMTs have a belief that quality tasks require intricate procedures, leading to critical instructional phases being overlooked during implementation. Furthermore, the PMTs, who paid attention to the instructional questions, appropriately designed tasks with a higher level of cognitive demand. Therefore, PMTs require assistance in evaluating and designing original tasks with regards to their mathematical and pedagogical elements.

Keywords

• Attention
• Pre-Service Teachers
• Task’s Affordances
• Task Analysis
• Task Design

References

1. Ayalon, M., Naftaliev, E., Levenson, E.S., & Levy, S. (2021). Prospective and in-service mathematics teachers’ attention to a rich mathematics task while planning its implementation in the classroom. International Journal of Science and Mathematics Education, 19(8),1695-1716.
2. Ayalon, M., & Hershkowitz, R. (2018). Mathematics teachers' attention to potential classroom situations of argumentation. The Journal of Mathematical Behavior, 49,163-173.
3. Ball, D.L., & Forzani, F. (2011). Building a common core for learning to teach: And connecting professional learning to practice. American Educator, 35,17–21.
4. Chapman, O. (2013). Mathematical-task knowledge for teaching. Journal of Mathematics Teacher Education, 16(1),1-6.
5. Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five traditions (2nd ed.). Sage Publications.
6. Fraenkel, J.R., Wallen, N.E., & Hyun, H. H. (2012). How to design and evaluate research in education. McGraw-hill.
7. Hallman-Thrasher, A. (2017). Prospective elementary teachers’ responses to unanticipated incorrect solutions to problem-solving tasks. Journal of Mathematics Teacher Education, 20(6),519-555.
8. Healy, L., Fernandes, S. H. A. A., & Frant, J. B. (2013). Designing tasks for a more inclusive school mathematics. Task design in mathematics education. Proceedings of ICMI Study, 22, 61-69.

9. Hughes, E. K. (2006). Lesson planning as a vehicle for developing pre-service secondary teachers’ capacity to focus on students’ mathematical thinking (PhD dissertation). University of Pittsburgh.
10. Jacobs, V.R., Lamb, L.L., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.
11. Johnson, R., Severance, S., Penuel, W.R., & Leary, H. (2016). Teachers, tasks, and tensions lessons from a research practice partnership. Journal of Mathematics Teacher Education, 19(2),169-185.
12. Kaur, B. (2010). A study of mathematical tasks from three classrooms in Singapore. In Y. Shimizu, B. Kaur, R. Huang, & D. Clarke (Eds.), Mathematical Tasks in Classrooms Around the World (pp.15-33). Sense Publishers. https://doi.org/10.1163/9789460911507_003
13. Lee, E. J., Lee, K. H. & Park, M. (2019). Developing preservice teachers’ abilities to modify mathematical tasks: Using noticing-oriented activities. International Journal of Science and Mathematics Education, 17(5), 965-985.
14. Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM-Mathematics Education, 49(6), 937-949.
15. Mason, J. (1998). Enabling teachers to be real teachers: Necessary levels of awareness and structure of attention. Journal of Mathematics Teachers Education, 1(3),243-267.
16. Mason, J. (2008). Being mathematical with and in front of learners: Attention, awareness, and attitude as sources of differences between teacher educators, teachers and learners. In B. Jaworski & T. Wood (Eds.), The international handbook of mathematics teacher education: The mathematics teacher educator as a developing professional (Vol. 4, pp.31-56). Sense Publishers.
17. Monarrez, A., & Tchoshanov, M. (2020). Unpacking teacher challenges in understanding and implementing cognitively demanding tasks in secondary school mathematics classrooms. International Journal of Mathematical Education in Science and Technology, 53(8), 2026-2045.
18. Özgeldi, M., & Esen, Y. (2010). Analysis of mathematical tasks in Turkish elementary school mathematics textbooks. Paper presented at the Procedia-Social and Behavioral Sciences, 2(2),2277-2281.
19. Paparistodemou, E., Potari, D., & Pitta-Pantazi, D. (2014). Prospective teachers’ attention on geometrical tasks. Educational Studies in Mathematics, 86(1),1–18.
20. Rimma, N. (2016). What makes a mathematical task interesting? Educational Research and Reviews, 11(16), 1509-1520.
21. Schoepf, S., & Klimow, N. (2022). Collective Case Study: Making Qualitative Data More Impactful. In Conceptual Analyses of Curriculum Inquiry Methodologies (pp. 252-266). IGI Global.
22. Schlesinger, L., Jentsch, A., Kaiser, G., König, J., & Blömeke, S. (2018). Subject-specific characteristics of instructional quality in mathematics education. ZDM, 50(3),475-490.
23. Sherin, M., & van Es, E. (2005). Using video to support teachers’ ability to notice classroom interactions. Journal of technology and teacher education, 13(3),475-491.
24. Silver, E.A., & Herbst, P. (2007). Theory in mathematics education scholarship. In F. K. Lester (Ed). Second handbook of research on mathematics teaching and learning (Vol.1, pp.39-67).
25. Smith, M.S., Bill, V., & Hughes, E.K. (2008). Thinking through a lesson: Successfully implementing high-level tasks. Mathematics Teaching in The Middle School,14(3),132-138.
26. Son, J. W., & Kim, O.K. (2015). Teachers’ selection and enactment of mathematical problems from textbooks. Mathematics Educational Research Journal, 27(4),491-518.
27. Stake, R. E. (1995). The art of case study research. Sage.
28. Stein, M.K., Smith, M.S., Henningsen, M.A. & Silver, E.A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. Teachers College Press.
29. Stein, M.K., Grover, B.W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455-488.
30. Stein, M.K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50-80.
31. Stein, M.K., & Smith, M.S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics teaching in the middle school, 3(4), 268-275.
32. Stephan, M., Pugalee, D., Cline, J., & Cline, C. (2017). Lesson imagining in math and science: Anticipating student ideas and questions for deeper STEM learning. Alexandria, VA: ASCD.
33. Stephens, A. C. (2006). Equivalence and relational thinking: Preservice elementary teachers’ awareness of opportunities and misconceptions. Journal of Mathematics Teacher Education, 9(3),249-278.
34. Sullivan, P., Clarke, D., Clarke, D., & Roche, A. (2013). Teachers’ decisions about mathematics tasks when planning. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow (Proceedings of the 36th annual conference of the Mathematics Research Group of Australasia) (pp. 626-633). MERGA.
35. Sullivan, P., & Mousley, J. (2001). Thinking teaching: Seeing mathematics teachers as active decision makers. In F.-L. Lin & T. Cooney (Eds.), Making sense of mathematics teacher education (pp.147–163). Springer.
36. Sun, J., & Van Es, E.A. (2015). An exploratory study of the influence that analyzing teaching has on preservice teachers’ classroom practice. Journal of Teacher Education, 66(3),201-214.
37. Taylan, R.D. (2020). Etkinliklerin sınıf içinde uygulanması İçinde Y. Dede, M. F. Doğan ve F. Aslan Tutak (Ed.). Matematik Eğitiminde Etkinlikler ve Uygulamaları (ss.189-208). Pegem Akademi.
38. Thanheiser, E. (2015). Developing prospective teachers’ conceptions with well-designed tasks: Explaining successes and analyzing conceptual difficulties. Journal of Mathematics Teacher Education, 18(2), 141-172.
39. Ubuz, B., Erbaş, A.K., Çetinkaya, B., & Özgeldi, M. (2010). Exploring the quality of the mathematical tasks in the new Turkish elementary school mathematics curriculum guidebook: The case of algebra. ZDM-International Journal on Mathematics Education, 42(5), 483-491.
40. Ulusoy, F. (2020). Prospective teachers’ skills of attending, interpreting and responding to content-specific characteristics of mathematics instruction in classroom videos. Teaching and Teacher Education, 94, 103103.
41. Van Es, E.A., & Sherin, M.G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and teacher education, 24(2), 244-276.
42. Xu, L., & Mesiti, C. (2022). Teacher orchestration of student responses to rich mathematics tasks in the US and Japanese classrooms. ZDM Mathematics Education, 54(2), 273-286.