How do Mentor Teachers Implement Mathematical Tasks?: The Perspective of Preservice Mathematics Teachers

Year 2023, , 844 - 858, 21.10.2023

Osman Bağdat

https://doi.org/10.31458/iejes.1359037

Abstract

This study aims to investigate mentor teachers’ task implementation and instructional dispositions from the perspective of preservice mathematics teachers. Twelve preservice mathematics teachers examined four mentor teachers' task selection and implementation in terms of cognitive demand and instructional dispositions that affect their cognitive demand. The data were gathered from detailed observation notes and focus group interviews of preservice teachers. The results indicated that only one teacher selected most of the tasks at a high level and maintained them without declining their cognitive demand. His instructional dispositions showed us that he displayed an approach that allowed students to explore the tasks, reason, and discuss ideas. Launching fewer problems per lesson, he enabled students to examine the tasks in depth. He discussed student-invented strategies and sometimes focused on multiple solutions and misconceptions. Instead of algorithmic solutions, he emphasized underlying concepts, multiple representations, and daily life situations. On the other hand, other teachers mostly implemented tasks at low-level, however, they had different instructional dispositions towards student explorations, classroom discussions, and utilizing multiple representations. Based on these results, this study highlights the importance of mentor teachers for the professional development of preservice teachers.

Keywords

Cognitive demand, instructional dispositions, mathematical task, mentor teachers, preservice teachers

References

• Ader, E. (2020). Investigating elementary school teachers’ development of mathematical task implementation quality. Education and Science, 45(202), 1-25. https://doi.org/10.15390/eb.2020.8544
• Arbaugh, F., & Brown, C. A. (2006). Analyzing mathematical tasks: A catalyst for change? Journal of Mathematics Teacher Education, 8(6), 499-536. https://doi.org/10.1007/s10857-006-6585-3
• Boston, M. D. (2013). Connecting changes in secondary mathematics teachers’ knowledge to their experiences in a professional development workshop. Journal of Mathematics Teacher Education, 16(1), 7-31.
• Boston, M. D., & Smith, M. S. (2009). Transforming secondary mathematics teaching: Increasing the cognitive demands of instructional tasks used in teachers' classrooms. Journal for Research in Mathematics Education, 40(2), 119-156.
• Boston, M. D., & Smith, M. S. (2011). A ‘task-centric approach’ to professional development: Enhancing and sustaining mathematics teachers’ ability to implement cognitively challenging mathematical tasks. ZDM, 43(6-7), 965-977. https://doi.org/10.1007/s11858-011-0353-2
• Butler, B. M., & Cuenca, A. (2012). Conceptualizing the roles of mentor teachers during student teaching. Action in Teacher Education, 34(4), 296-308.
• Guner, P., & Akyuz, D. (2020). Noticing student mathematical thinking within the context of lesson study. Journal of Teacher Education, 71(5), 568-583.
• Güzel, M., Bozkurt, A. & Özmantar, M. F. (2021). Analysis of the evaluations and interventions made by mathematics teachers in the activity design and implementation process. Journal of Computer and Education Research, 9 (18), 513-545. https://doi.org/10.18009/jcer.880304 Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524-549. https://doi.org/10.2307/749690
• Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393-425.
• Hong, D. S., & Choi, K. M. (2019). Challenges of maintaining cognitive demand during the limit lessons: Understanding one mathematician’s class practices. International Journal of Mathematical Education in Science and Technology, 50(6), 856-882.
• Hudson, P. (2012). How can schools support beginning teachers? A call for a timely induction and mentoring for effective teaching. Australian Journal for Teacher Education, 37(7), 71-84.
• Jackson, K., Garrison, A., Wilson, J., Gibbons, L., & Shahan, E. (2013). Exploring relationships between setting up complex tasks and opportunities to learn in concluding whole-class discussions in middle-grades mathematics instruction. Journal for Research in Mathematics Education, 44(4), 646-682.
• Loughran, J. J. (2006). Developing a pedagogy of teacher education: Understanding teaching and learning about teaching. London, England: Routledge.
• Ministry of National Education [MNE]. (2019). 5th-grade math textbook. Ankara: Ministry of Education Publications.
• Ministry of National Education [MNE]. (1998). Journal of announcements, Ankara: MNE Publication.
• National Council of Teachers of Mathematics [NCTM]. (1991). Professional standards for teaching mathematics. Reston: VA.
• Ni, Y. J., Li, X., Zhou, D., & Li, Q. (2014). Changes in instructional tasks and their influence on classroom discourse in reformed mathematics classrooms of Chinese primary schools. In Transforming Mathematics Instruction (pp. 217-230). Springer, Cham.
• Schatz-Oppenheimer, O. (2017). Being a mentor: Novice teachers’ mentors’ conceptions of mentoring prior to training. Professional Development in Education, 43(2), 274-292. https://doi.org/10.1080/19415257.2016.1152591
• Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313-340.
• 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.
• 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.
• Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based math instruction: A casebook for professional development. NY: Teachers College Press.
• Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world's teachers for improving education in the classroom. NY: Summit Books.
• Stockero, S. L., Leatham, K. R., Ochieng, M. A., Van Zoest, L. R., & Peterson, B. E. (2019). Teachers’ orientations toward using student mathematical thinking as a resource during whole-class discussion. Journal of Mathematics Teacher Education, 23(3), 237-267.
• 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, 42(5), 483-491.
• Wallin, A. J., & Amador, J. M. (2018). Supporting secondary rural teachers’ development of noticing and pedagogical design capacity through video clubs. Journal of Mathematics Teacher Education, 22(5), 515-540. https://doi.org/10.1007/s10857-018-9397-3
• 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.