Using scaffolds in support of teachers as task designers in geometry: a case study

References

• Battista, M. T. (2007). The development of geometric and spatial thinking. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843–908). National Council of Teachers of Mathematics.
   Google Scholar
• Boaler, J. (2015). Mathematical mind-sets: Unleashing students’ potential through creative math, inspiring messages and innovation teaching. John Wiley & Sons.
   Google Scholar
• Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52(3), 243–270. https://doi.org/10.1023/A:1024364304664
   Google Scholar
• Elementary Science Study. Attribute Games and Problems. New York: McGrawHill, 1974.
   Google Scholar
• Ezer, H. (2009). Self-study approaches and the teacher-inquirer. Sense. https://doi.org/10.1163/9789087907921
   Google Scholar
• Fischbein, E. (1987). Intuition in science and mathematics: An educational approach. Reidel.
   Google Scholar
• Fischbein, E. (1993). The interaction between the formal, the algorithmic and the intuitive components in a mathematical activity. In R. Biehler, R. W. Scholz, R. Straser, & B. Winkelmann (Eds.), Didactics of mathematics as a scientific discipline (pp. 231–245). Kluwer.
   Google Scholar
• Goodchild, S. (2014). Mathematics teaching development: Learning from developmental research in Norway. ZDM: International Journal on Mathematics Education, 46(2), 305–316. https://doi.org/10.1007/s11858-013-0567-6
   Google Scholar
• Goodchild, S., Fuglestad, A. B., & Jaworski, B. (2013). Critical alignment in inquiry-based practice in developing mathematics teaching. Educational Studies in Mathematics, 84(3), 393–412. https://doi.org/10.1007/s10649-013-9489-z
   Web of Science ®Google Scholar
• Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition (pp. 70–95). Cambridge University Press.
   Google Scholar
• Jacobs, J., & Morita, E. (2002). Japanese and American teachers’ evaluations of videotaped mathematics lessons. Journal for Research in Mathematics Education, 33(3), 154–175. https://doi.org/10.2307/749723
   Web of Science ®Google Scholar
• Jaworski, B. (2005). Learning communities in mathematics: Creating an inquiry community between teachers and didacticians. Research in Mathematics Education, 7(1), 101–119. https://doi.org/10.1080/14794800008520148
   Google Scholar
• Johnson, H. L., Coles, A., & Clarke, D. (2017). Mathematical tasks and the student: Navigating ‘tensions of intentions’ between designers, teachers, and students. ZDM: Mathematics Education, 49(6), 813–822. https://doi.org/10.1007/s11858-017-0894-0
   Web of Science ®Google Scholar
• Jones, K., & Pepin, B. (2016). Research on mathematics teachers as partners in task design. Journal of Mathematics Teacher Education, 19(2), 105–121. https://doi.org/10.1007/s10857-016-9345-z
   Google Scholar
• Kieran, C., Krainer, K., & Shaughnessy, J. M. (2013). Linking research to practice: Teachers as key stakeholders in mathematics education research. In M. A. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Third international handbook of mathematics education, volume B (pp. 361–392). Springer. https://doi.org/10.1007/978-1-4614-4684-2_12
   Google Scholar
• Kim, S., & Lee, C. (2016). Effects of robot for teaching geometry to fourth graders. International Journal of Innovation in Science and Mathematics Education, 24(2), 52–70.
   Google Scholar
• Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75–86. https://doi.org/10.1207/s15326985ep4102_1
   Web of Science ®Google Scholar
• Knott, L., Olson, J., Adams, A., & Ely, R. (2013). Task design: Supporting teachers to independently create rich tasks. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI study 22 (pp. 599–608). HAL Open Science.
   Google Scholar
• Koichu, B., & Pinto, A. (2018). Developing education research competencies in mathematics teachers through TRAIL: Teacher-researcher alliance for investigating learning. Canadian Journal of Science, Mathematics and Technology. https://doi.org/10.1007/s42330-018-0006-3
   Google Scholar
• Koichu, B., Zaslavsky, O., & Dolev, L. (2015). Effects of variations in task design on mathematics teachers’ learning experiences: A case of a sorting task. Journal of Mathematics Teacher Education, 19(4), 349–370. https://doi.org/10.1007/s10857-015-9302-2
   Google Scholar
• Kolb, D. A. (1984). Experiential learning: Experience as the source of learning and development(Vol. 1). Prentice-Hall.
   Google Scholar
• Krainer, K. (2014). Teachers as stakeholders in mathematics education research. The Mathematics Enthusiast, 11(1), 49–60. https://doi.org/10.54870/1551-3440.1291. https://scholarworks.umt.edu/tme/vol11/iss1/4
   Google Scholar
• Makar, K., & Fielding-Wells, J. (2018). Shifting more than the goal posts: Developing classroom norms of inquiry-based learning in mathematics. Mathematics Education Research Journal, 30(1), 53–63. https://doi.org/10.1007/s13394-017-0215-5
   Google Scholar
• Moss, J., Hawes, Z., Naqvi, S., & Caswell, B. (2015). Adapting Japanese lesson study to enhance the teaching and learning of geometry and spatial reasoning in early years classrooms: A case study. ZDM: International Journal on Mathematics Education, 47(3), 377–390. https://doi.org/10.1007/s11858-015-0679-2
   Google Scholar
• Ohtani, M. (2011). Teachers’ learning and lesson study: Content, community, and context. In B. Ubuz (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 63–66). PME.
   Google Scholar
• Patkin, D. (2015). Various ways of inculcating new solid geometry concepts. International Journal of Education in Mathematics, Science and Technology, 3(2), 140–154.
   Google Scholar
• Patkin, D., & Gazit, A. (2011). Effect of difference in word formulation and mathematical characteristics of story problems on mathematics preservice teachers and practising teachers. International Journal of Mathematical Education in Science and Technology, 42(1), 75–87. https://doi.org/10.1080/0020739X.2010.519790
   Google Scholar
• Retnowati, E., Ayres, P., & Sweller, J. (2010). Worked example effects in individual and group work settings. Educational Psychology, 30(3), 349–367. https://doi.org/10.1080/01443411003659960
   Web of Science ®Google Scholar
• Stavy, R., & Tirosh, D. (2000). How students (mis-)understand science and mathematics: Intuitive rules. Teachers College Press.
   Google Scholar
• Strauss, A., & Corbin, J. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Sage.
   Google Scholar
• Swan, M. (2007). The impact of task-based professional development on teachers’ practices and beliefs: A design research study. Journal of Mathematics Teacher Education, 10(4–6), 217–237. https://doi.org/10.1007/s10857-007-9038-8
   Google Scholar
• Sweller, J. (2006). The worked example effect and human cognition. Learning and Instruction, 16(2), 165–169. https://doi.org/10.1016/j.learninstruc.2006.02.005
   Web of Science ®Google Scholar
• Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics, with special reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169. https://doi.org/10.1007/BF00305619
   Google Scholar
• Tawfik, A., Law, V., Ge, X., Xing, W., & Kim, K. (2018). The effect of sustained vs. faded scaffolding on students’ argumentation in ill-structured problem solving. Computers in Human Behavior, 1–14. https://doi.org/10.1016/j.chb.2018.01.035
   Web of Science ®Google Scholar
• Taylor, J., & Bilbrey, J. (2012). Effectiveness of inquiry based and teacher directed instruction on an Alabama elementary school. Journal of Instructional Pedagogies, 8, 1–16. http://www.aabri.com.
   Google Scholar
• Taylor, L. A. (2017). How teachers become teacher researchers: Narrative as a tool for teacher identity construction. Teaching and Teacher Education, 61, 16–25. https://doi.org/10.1016/j.tate.2016.09.008
   Web of Science ®Google Scholar
• 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. https://doi.org/10.1007/s10857-014-9272-9
   Web of Science ®Google Scholar
• Tirosh, D., & Wood, T. (Eds.). (2008). The international handbook of mathematics teacher education (Vol. 2). Sense Publishers.
   Google Scholar
• Van Loon-Hillen, N., Van Gog, T., & Brand-Gruwel, S. (2010). Effects of worked examples in a primary school mathematics curriculum. Interactive Learning Environments, 18(1), 1–11. https://doi.org/10.1080/10494820802158983
   Web of Science ®Google Scholar
• Vinner, S., & Hershkowitz, R. (1983). On concept formation in geometry. Zentralblatt fur Didactic der Mathematic, 15, 20–25.
   Google Scholar
• Visnovska, J., Cobb, P., & Dean, C. (2012). Mathematics teachers as instructional designers: What does it take? In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to ‘lived’ resources: Mathematics curriculum materials and teacher development (pp. 323–341). Springer.
   Google Scholar
• Zaslavsky, O. (2008). Meeting the challenges of mathematics teacher education through design and use of tasks that facilitate teacher learning. In B. Jaworski & T. Woods (Eds.), The mathematics teacher educator as a developing professional (Vol. 4, pp. 93–114). (The International Handbook of Mathematics Teacher Education). Sense Publishers.
   Google Scholar
• Zaslavsky, O., & Sullivan, P. (2011). Constructing knowledge for teaching: Secondary mathematics tasks to enhance prospective and practicing teacher learning. Springer.
   Google Scholar