The Korea Society Of Educational Studies In Mathematics

Current Issue

Journal of Educational Research in Mathematics - Vol. 29 , No. 3

[ Article ]
Journal of Educational Research in Mathematics - Vol. 29, No. 3, pp.425-452
Abbreviation: JERM
ISSN: 2288-7733 (Print) 2288-8357 (Online)
Print publication date 31 Aug 2019
Received 10 Jul 2019 Revised 12 Aug 2019 Accepted 16 Aug 2019

Learning of Teacher Community through Designing of Mathematical Induction Tasks: A Case of a Co-learning Inquiry Community
Lee, Kyeonghwa* ; Seo, Minju**, ; Lee, Eunjung*** ; Park, Mimi**** ; Song, Changgeun*****
*Professor, Center for Educational Research, Seoul National University, South Korea (
**Graduate Student, Seoul National University, South Korea (
***Lecturer, Chuncheon National University of Education, South Korea (
****Lecturer, Korea National University of Education, South Korea (
*****Graduate Student, Seoul National University, South Korea (

Correspondence to : Graduate Student, Seoul National University, South Korea,

Funding Information ▼


Mathematical induction has been known to be difficult topic for didactic transposition, especially for tasks designs, due to the formality of reasoning structures and expressions embedded in them. This study organized a co-learning inquiry community with teachers and researchers to overcome these difficulties and to lead the learning of teacher community. A series of activities consisting of tasks design, implementation, and reflection were conducted. Then the learning of teacher community was analyzed by describing which knowledge elements were developed. As a result, teacher community drew a proof-planning activity as a didactic strategy and designed tasks that enable students to recognize the recursibility of the proposition function as they rediscover the roles of inductive definitions of sequence and operations. Through this, teacher community developed the knowledge of the logical structure of mathematical induction, knowledge of students understanding and difficulties about learning mathematical induction, and knowledge of didactic strategies which support the learning process of mathematical induction.

Keywords: Mathematical induction, Tasks design, Co-learning inquiry community, Mathematical knowledge for teaching, Learning of teacher community


이 연구는 2016년 대한민국 교육부와 한국연구재단의 지원을 받아 수행된 연구임(NRF-2016S1A5A2A01024273)

1. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content Knowledge for Teaching. What Makes It Special? Journal of Teacher Education 59(5), 389-407.
2. Biza, I., Nardi, E., & Zachariades, T. (2007). Using Tasks to Explore Teacher Knowledge in Situation-Specific Contexts. Journal of Teacher Education, 10, 301-309.
3. Boero, P., Garuti, R. & Mariotti, M. A. (1996). Some dynamic mental processes underlying producing and proving conjectures. In A. Gutierrez & L. Puig (Eds.), Proceedings of the 20th Conference of International Group for the Psychology of Mathematics Education, vol. 2 (pp. 121-128). Valencia, Spain.
4. Bosch, M., & Gascón, J. (2006). Twenty-five years of the didactic transposition. ICMI Bulletin, 58, 51-63.
5. 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.
6. Broekkamp, H. & Van Hout-Wolters, B. (2007). The gap between educational research and practice: A literature review, symposium, and questionnaire. Educational Research and Evaluation, 13(3), 203-220.
7. Chevallard, Y. (1990). On mathematics education and culture: Critical afterthoughts. Educational Studies in Mathematics, 21(1), 3-27.
8. Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In Proceedings of the 4th Conference of the European Society for Research in Mathematics Education (CERME 4) (pp. 21-30).
9. Chevallard, Y. (2007). Readjusting didactics to a changing epistemology. European Educational Research Journal, 6(2), 131-134.
10. Cho, W. Y. (2011). Mathematical Content Knowledge of Secondary Mathematics Teachers. School Mathematics 13(2), 345-362.
11. Cho, W. Y. (2012). Analysis of Perspective Teachers Mathematical Content Knowledge about Differential area. School Mathematics, 14(2), 233-253.
12. Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd ed.). Thousand Oaks, CA: Sage Publications.
13. Davis, B., & Renert, M. (2013). Profound understanding of emergent mathematics: Broadening the construct of teachers’ disciplinary knowledge. Educational Studies in Mathematics, 82, 245-265.
14. Dogan, H. (2016). Amthematical induction : deductive logic perspective. European Jounarl of Science and Mathematics Education, 4(3), 315-330.
15. Elbas, F.(1983). Teacher thinking: A study of practical knowledge. New York : Nichols.
16. Ernest, P. (1984). Mathematical induction: A pedagogical discussion. Educational studies and mathematics, 15, 173-189.
17. Goodchild, S. (2008). A quest for ‘good’ research. In B. Jaworski & T. Wood (Eds.), International handbook of mathematics teacher education: Vol. 4. the mathematics teacher educator as a developing professional (pp. 201-220). Rotterdam, The Netherlands: Sense Publishers.
18. Guba, E. G., &Lincoln, Y. S. (1982). Epistemological and methodological bases of naturalistic inquiry. ECTJ, 30(4), 233-252.
19. Harel G. (2002). Development of Mathematical Induction as a Proof Scheme: A Model For DNR based Instruction. Stephen R. Campbell, Rina Zazkis (Eds.), In Learning and Teaching Number Theory: Research in Cognition and Instruction. Chapter 10, P.185. Ablex publishing, Westport CT.
20. Harel, G. & Sowder, L. (1998). Students’ Proof Schemes: Results from Exploratory Studies. In James J. Kaput & Alan H. Schoenfeld (Eds.), Research in Collegiate Mathematics Education III. CBMS Issues in Mathematics Education, Vol. 7. P. 234.
21. Jaworski, B. (2004). Insiders and Outsiders in Mathematics Teaching Development: the Design and Study of Classroom Activity. Research in Collegiate Mathematics Education III(1), 3-22.
22. Jaworski, B. (2008). Building and sustaining inquiry communities in mathematics teaching development: teachers and didacticians in collaboration. IN: Krainer, K. and Wood, T. (eds.). The International Handbook of Mathematics Teacher Education volume 3: Participants in Mathematics Teacher Education: Individuals, Teams, Communities and Networks. Rotterdam: SensePublishers.
23. Ma, L. (1999). Knowing and Teaching Elementary Mathematics. Mahwah, NJ: Lawrence Erlbaum.
24. Merseth, K. K. (2003). Windows on teaching math: Cases of middle and secondary classrooms. New York: Teachers College Press.
25. Na, G. S. (2010). Reporting the Activities of Learning Community on Elementary Mathematics Lesson. Journal of Educational Research in Mathematics, 20(3), 373-395.
26. Oh Y. Y. (2006). Exploring Teacher Change Through the Community of Practice Focused on Improving Mathematics Teaching. Journal of Educational Research in Mathematics, 16(3), 251-272.
27. Pang, J. S. & Sun W. J. (2017). An Analysis of Elementary School Teachers’Knowledge of Functional Thinking for Teaching : Focused on Mathematical Tasks and Instructional Strategies. Journal of elementary mathematics education in Korea, 21(2), 343-364.
28. Park, S. Y. (2008). Didactical analysis on the mathematical induction. Unpublished doctoral dissertation. Seoul National University.
29. Park, Y. H. (2011). Reporting the Activities of Professional Development System for Enhancing Elementary Mathematical Teaching Professionalism. J. Korean Soc. Math. Ed. Ser. E: Communications of Mathematical Education, 25(1), 47-61.
30. Polya, G. (2005). Mathematical discovery: on understanding, learning, and teaching problem solving. New York: Wiley.
31. Saldaña, J. (2012). The coding manual for qualitative researchers. Thousand Oaks, CA: Sage.
32. Schmid, E. C. (2011). Video-stimulated reflection as a professional development tool in interactive whiteboard research. ReCALL, 23(3), 252-270.
33. Sfard, A. (1988). Operational vs. structural method of teaching mathematics-Case study. Proceedings of the 12th Annual Conference on the Psychology of Mathematics Education, vol 2(pp. 560-7). Veszprem, Hungary.
34. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching.  Educational researcher, 15(2), 4-14.
35. Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. Reston, VA: NCTM.
36. Stake, R. (1995). The art of case study research, Thousand Oaks: Sage Publications.
37. Stein, M. K., Smith, M. S., Henningsen, M., & Silver, E. A. (2009). Implementing standards- based math instruction: A casebook for professional development (2nd ed.). New York, NY:Teachers College Press.
38. Stenhouse, L. (1984). Evaluating curriculum evaluation. In C. Adelman (Ed.), The politics and ethics of evaluation London: Croom Helm.
39. Stylianides, G. J., Stylianides, A. J., & Philippou, G. N. (2007). Preservice teachers’ knowledge of proof by mathematical induction. Journal of Mathematics Teacher Education, 10, 145-166.
40. Sullivan, P., Clarke, D., & Clarke, B. (2009). Converting mathematics tasks to learning opportunities: An important aspect of knowledge for mathematics teaching. Mathematics Education Research Journal, 21(1), 85-105.
41. 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. 217-237
42. Wagner, J. (1997). The Unavoidable Intervention of Educational Research: A Framework for Reconsidering Researcher-Practitioner Cooperation. Educational Researcher, 26(7), 13-22.
43. Watson, A., & Sullivan, P. (2008). Teachers learning about tasks and lessons. In The Handbook of Mathematics Teacher Education: Volume 2 (pp. 107-134). Brill Sense.
44. Wilkinson, D., & Birmingham, P. (2003). Using research instruments: A guide for researchers. London: Routledge Farmer.
45. Winsløw, C. (2011). Anthropological Theory of Didactic Phenomena: Some Examples and Principles of its Use in the Study of Mathematics Education. Un panorama de la TAD. An overview of ATD. CRM Documents, 10, 533-551.
46. Zaslavsky, O. (1995). Open-ended tasks as a trigger for mathematics teachers’ professional development. For the Learning of Mathematics, 15(3), 15-20.