Developing Preservice Teachers’ Abilities to Modify Mathematical Tasks: Using Noticing-Oriented Activities

Article
  • 58 Downloads

Abstract

This study focuses on developing the abilities of preservice secondary mathematics teachers to modify mathematical tasks through noticing-oriented activities. To this end, the study designs three phases for Noticing-Oriented Task Modification Activity (NOTMA) and applies it to preservice secondary mathematics teachers. It investigates characteristics of preservice teachers’ noticing that emerged from NOTMA and analyzes their modified tasks in terms of their noticing. The results indicate that the development of preservice teachers’ noticing is linked to their progressive understanding of the mathematical and pedagogical elements involved in tasks, and this improvement influences their task modification. Based on the results, we discuss that NOTMA can be useful to develop the task modification abilities of mathematics teachers and make some suggestions for the teacher training programmes.

Keywords

Inquiry-based task Preservice secondary teacher Task modification Teacher noticing 

References

  1. Arbaugh, F., & Brown, C. A. (2005). Analyzing mathematical tasks: A catalyst for change? Journal of Mathematics Teacher Education, 8, 499–536.CrossRefGoogle Scholar
  2. Ayalon, M., & Hershkowitz, R. (2016). Teahcers’ attention to task’s potential for encouraging classroom argumentative activity. In K. Krainer & N. Vondrova (Eds.), Proceedings of the ninth congress of the European Society for Research in mathematics education (pp. 2982–2988). Prague, Czech Republic: CERME.Google Scholar
  3. Brown, S. I., & Walter, M. I. (1990). The art of problem posing (2nd Ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  4. Crespo, S., & Sinclair, N. (2008). What can it mean to pose a 'good’problem? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11, 395–415.CrossRefGoogle Scholar
  5. Freudenthal, H. (1971). Geometry between the devil and the deep sea. Educational Studies in Mathematics, 3, 413–435.CrossRefGoogle Scholar
  6. Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Dordrecht, The Netherlands: Kluwer Academic Publishers.Google Scholar
  7. 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, 169–185.CrossRefGoogle Scholar
  8. Kaur, B., & Lam, T. T. (2012). Reasoning, communication and connections in mathematics: An introduction. In B. Kaur & T. T. Lam (Eds.), Reasoning, communication and connections in mathematics: Yearbook 2012 association of mathematics educators (pp. 1–10). Singapore: World Scientific Publishing.CrossRefGoogle Scholar
  9. Kim, D., & Kim, G. Y. (2014). Secondary mathematics teachers’ understanding and modification of mathematical tasks in textbooks. School Mathematics, 16, 445–469.Google Scholar
  10. Kim, M., & Kim, G. Y. (2013). The analysis of mathematical tasks in the high school mathematics. School Mathematics, 15, 37–59.Google Scholar
  11. Lee, K. H., Lee, E. J., & Park, M. S. (2013). Task modification and knowledge utilization by Korean prospective mathematics teachers. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI study 22 (pp. 347–356). Oxford, England: University of Oxford.Google Scholar
  12. Liljedahl, P., Chernoff, E., & Zazkis, R. (2007). Interweaving mathematics and pedagogy in task design: A tale of one task. Journal of Mathematics Teacher Education, 10(4), 239–249.CrossRefGoogle Scholar
  13. Lin, F. L., Yang, K. L., Lee, K. H., Tabach, M., & Stylianides, G. (2012). Principles of task design for conjecturing and proving. In G. Hanna & M. de Villiers (Eds.), Proof and proving in mathematics education: The 19th ICMI study (pp. 305–326). New York, NY: Springer.Google Scholar
  14. Mason, J. (1998). Enabling teachers to be real teachers: Necessary levels of awareness and structure of attention. Journal of Mathematics Teacher Education, 1, 243–267.CrossRefGoogle Scholar
  15. Mason, J. (2002). Researching your own practice: The discipline of noticing. Oxon, England: Routledge.Google Scholar
  16. Mason, J. (2011). Noticing: Roots and branches. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing (pp. 35–50). New York, NY: Routledge.Google Scholar
  17. National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: Author.Google Scholar
  18. Papatistodemou, E., Potari, D., & Potta-Pantazi, D. (2014). Prospective teachers’ attention on geometrical tasks. Educational Studies in Mathematics, 86, 1–18.CrossRefGoogle Scholar
  19. Remillard, J. T., & Bryans, M. B. (2004). Teachers’ orientations toward mathematics curriculum materials: Implications for teacher learning. Journal of Research in Mathematics Education, 35(5), 352–388.CrossRefGoogle Scholar
  20. Schoenfeld, A. H. (1987). What's all the fuss about metacognition? In A. H. Schoenfeld (Ed.), Cognitive science in mathematics education (pp. 189–215). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  21. Schoenfeld, A. H. (2011). Noticing matters. a lot. now what? In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing (pp. 223–238). New York, NY: Routledge.Google Scholar
  22. Schoenfeld, A. H., & Kilpatrick, J. (2008). Toward a theory of proficiency in teaching mathematics. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education: Tools and processes in mathematics teacher education (Vol. 2, pp. 321–354). Rotterdam, The Netherlands: Sense Publishers.Google Scholar
  23. Sherin, G. M., Jacobs, V. R., & Philipp, R. A. (2011). Situating the study of teacher noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing (pp. 3–13). New York, NY: Routledge.Google Scholar
  24. Sherin, G. M., Russ, R. S., & Colestock, A. A. (2011). Accessing mathematics teachers' in-the-moment noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing (pp. 70–94). New York, NY: Routledge.Google Scholar
  25. Son, J. W., & Kim, O. K. (2015). Teachers’ selection and enactment of mathematical problems from textbooks. Mathematics Educational Research Journal, 27, 491–518.CrossRefGoogle Scholar
  26. Stephens, A. C. (2006). Equivalence and relational thinking: Preservice elementary teachers’ awareness of opportunities and misconceptions. Journal of Mathematics Teacher Education, 9, 249–278.CrossRefGoogle Scholar
  27. Thompson, D. R. (2012). Modifying textbook exercises to incorporate reasoning and communication into the primary mathematics classroom. In B. Kaur & T. Lam (Eds.), Reasoning, communication and connections in mathematics (pp. 57–74). Singapore: World Scientific Publishing Company.CrossRefGoogle Scholar
  28. Tsamir, P. (2008). Using theories as tools in mathematics teacher education. In D. Triosh & T. Wood (Eds.), Tools and processes in mathematics teacher education (pp. 211–234). Rotterdam, The Netherlands: Sense Publishers.Google Scholar
  29. Van Es, E. (2011). A framework for learning to notice student thinking. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing (pp. 134–151). New York, NY: Routledge.Google Scholar
  30. Van Es, E., & Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education, 10, 571–596.Google Scholar
  31. Watson, A., & Sullivan, P. (2008). Teachers learning about tasks and lessons. In D. Tirosh & T. Wood (Eds.), Tools and resources in mathematics teacher education (pp. 109–135). Rotterdam, The Netherlands: Sense Publishers.Google Scholar
  32. Zaslavsky, O. (2008). Meeting the challenges of mathematics teacher education through design and use of tasks that facilitate teacher learning. In B. Jaworski & T. Wood (Eds.), The mathematics teacher education as a developing professional (pp. 93–114). Rotterdam, The Netherlands: Sense Publishers.Google Scholar
  33. Zazkis, R., Liljedahl, P., & Chernoff, E. (2008). The role of examples on forming and refuting generalizations. ZDM. The International Journal on Mathematics Education, 40, 131–141.CrossRefGoogle Scholar

Copyright information

© Ministry of Science and Technology, Taiwan 2018

Authors and Affiliations

  1. 1.College of Education, Department of Mathematics EducationSeoul National UniversitySeoulRepublic of Korea

Personalised recommendations