[Fig. 1] Domain map for mathematical knowledge for teaching(Ball et al., 2008, p. 403)
[Fig. 2] Teacher's knowledge of student required to design tasks and to make hypothesis about task solving paths
[Fig. 3] Task design process through discussion within the teacher-researcher community
[Fig. 4] Graph interpretation task
[Fig. 7] Interpretation task about graph which has extreme value
[Fig. 9] The final task of [Fig. 7]
[Fig. 11] The final task of [Fig. 8]
[Fig. 5] Exemplification of increasing function when f′(χ) = 0
[Fig. 8] Exemplification of functions which have extreme value
[Table 3] The change in the tasks sequence
[Table 5] Student's affective aspect perceived by teacher in the course of the revision of the task
[Table 1] Participants of the teacher-researcher community
[Table 2] Meeting date and topics
[Table 4] The change of the task
[Table 6] The change of the task
[Table 7] The change of the task
[Table 8] Focus of discussion and changes of tasks revealing changes of teacher knowledge according to focus
Supported by : 한국연구재단
- Asiala, M., Cottrill, J., Dubinsky, E., & Schwingendorf, K. E. (1997). The development of students' graphical understanding of the derivative. The Journal of Mathematical Behavior, 16(4), 399-431. https://doi.org/10.1016/S0732-3123(97)90015-8
- Aydin, S. (2014). Using example generation to explore students' understanding of the concepts of linear dependence/independence in linear algebra. International Journal of Mathematical Education in Science and Technology, 45(6), 813-826. https://doi.org/10.1080/0020739X.2013.877606
- 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. https://doi.org/10.1177/0022487108324554
- 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
- Chong, Y. O. (2011). Function. In N. H. Kim, G. S. Na, K. M. Park, K. H. Lee, Y. O. Chong, & J. G. Hong (Eds). Mathematics curriculum and textbook research (pp. 113-180). Seoul: Kyungmoonsa.
- Creswell, J. W. (2013). Qualitative Inquiry & Research Design. 질적연구방법론. (Cho H. S., Jung S. O., Kim J. S., & Kwon J. S. Trans.). Seoul: Haksisa. (Original work published 2007).
- Dahlberg, R. P. & Housman, D. L. (1997). Facilitating learning events through example generation. Educational Studies in Mathematics, 33(3), 283-299. https://doi.org/10.1023/A:1002999415887
- Edwards, A. (2001). Researching pedagogy : A sociocultural agenda. Pedagogy, Culture and Society, 9(2), 161-186. https://doi.org/10.1080/14681360100200111
- Grouws, G. A., Tarr, J. E., Chavez, O., Sears, R., Soria, V. M., & Taylan, R. D. (2013) Curriculum and implementation effects on high school students' mathematics learning from curricula representing subject-specific and integrated content organizations. Journal for Research in Mathematics Education, 44(2), 416-463. https://doi.org/10.5951/jresematheduc.44.2.0416
- Gur, H. & Barak, B. (2007). The erroneous derivative examples of eleventh grade students. Educational Sciences: Theory and Practice, 7(1), 473-479.
- Hazzan, O. & Zazkis, R. (1999). A perspective on "give an example" tasks as opportunities to construct links among mathematical concepts. Focus on Learning Problems in Mathematics, 21(4), 1-14.
- Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.
- Jeon, T. H. & Shin, J. K. (2016). An error analysis of the misconceptions occurring in the application of derivatives in 12th grade high school natural science track in Korea. CNU Journal of Educational Studies, 37(4), 125-147. https://doi.org/10.18612/cnujes.2016.37.4.125
- Kim, N. H., Na, G. S., Park, K. M., Lee, K. H., Chong, Y. O., & Hong, J. K. (2007). A Study on the Curriculum and Textbooks of Mathematical Education. Seoul: Kyungmoonsa.
- Kye, S. H. & Ha, K. C. (2010). A critical analysis on an explanation for monotonicity and local extrema of functions in korean mathematics textbooks. The Mathematical Education, 49(2), 247-257.
- Lauten, A. D., Graham, K., & Ferrini-Mundy, J. (1994). Student understanding of basic calculus concepts: Interaction with the graphics calculator. The Journal of Mathematical Behavior, 13(2), 225-237. https://doi.org/10.1016/0732-3123(94)90026-4
- Lee, C. H. & Kim, B. M. (2003). Analysis of the error-redemial effect and change of the students' misconception on the learning of linear function. School Mathemtics, 5(1), 115-133.
- Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of educational research, 60(1), 1-64. https://doi.org/10.3102/00346543060001001
- Liz, B., Dreyfus, T., Mason, J., Tsamir, P., Watson, A., & Zaslavsky, O. (2006). Exemplification in mathematics education. In Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (pp. 126-154).
- Meehan, M. (2007). Student generated examples and the transition to advanced mathematical thinking. In M. Bosch(Ed.), Proceedings of the 5th Congress of the European Society for Research in Mathematics Education. (pp. 2349-2358).
- Movshovitz-Hadar, N., Inbar, S., & Zaslavsky, O. (1986). Students' distortions of theorems. Focus on Learning Problems in Mathematics, 8(1), 49-57.
- Movshovitz-Hadar, N. & Zaslavsky, O. (1987). An empirical classification model for errors in high school mathematics. Journal for Research in Mathematics Education, 18(1), 3-14. https://doi.org/10.2307/749532
- Orhun, N. (2012). Graphical understanding in mathematics education: Derivative functions and students' difficulties. Procedia-Social and Behavioral Science, 55, 679-684. https://doi.org/10.1016/j.sbspro.2012.09.551
- Orton, A. (1983). Students' understanding of differentiation. Educational Studies in Mathematics, 14(3), 235-250. https://doi.org/10.1007/BF00410540
- Park, K. M. (2011). Derivatives and Integrals. In N. H. Kim, G. S. Na, K. M. Park, K. H. Lee, Y. O. Chong, & J. G. Hong (Eds). Mathematics curriculum and textbook research (pp. 255-311). Seoul: Kyungmoonsa.
- Park, Y. H. (2011). Reporting the activities of professional development system for enhancing elementary mathematical teaching professionalism. Communications of Mathematical Education, 25(1), 47-61. https://doi.org/10.7468/jksmee.2011.25.1.047
- Peng, A. & Luo, Z. (2009). A framework for examining mathematics teacher knowledge as used in error analysis. For the Learning of Mathematics, 29(3), 22-25.
- Pino-Fan, L. R., Godino, J. D., & Font, Vicenc (2018). Assessing key epistemic features of didactic-mathematical knowledge of prospective teachers: The case of the derivative. Journal of Mathematics Teacher Education, 21(1), 63-94. https://doi.org/10.1007/s10857-016-9349-8
- Remillard, J. T. (1999). Curriculum materials in mathematics education reform: A framework for examining teachers' curriculum development. Curriculum Inquiry, 29(3), 315-342. https://doi.org/10.1111/0362-6784.00130
- Saldana, J. (2012). The coding manual for qualitative researchers. Thousand Oaks CA: Sage.
- Shim, S. K. & Choi, J. G. (2009). An analysis on errors of students in science and engineering in extremum value of functions. Communications of Mathematical Education, 23(3), 583-597.
- Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Research, 15(2), 4-14. https://doi.org/10.2307/1175860
- Simon, M. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114-145. https://doi.org/10.2307/749205
- Simon, M. & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 91-104.
- 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. https://doi.org/10.3102/00028312033002455
- Sullivan, P., Clarke, D., & Clarke, B. (2016). Teaching with tasks for effective mathematics learning. (이경화, 김동원 역. 원저는 2013년). Springer Science & Business Media.
- Sunwoo, Jin. & Pang, J. S. (2014). An analysis of strengths and weaknesses in the study of elementary mathematics lessons via teacher learning community. Education of Primary School Mathematics, 17(3), 189-203. https://doi.org/10.7468/jksmec.2014.17.3.189
- 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.
- Tall, D. (1992). Students' difficulties in calculus. In proceedings of working group 3 on students' difficulties in calculus. ICME-7. Quebec, Canada. 13-28.
- Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25. https://doi.org/10.2307/749817
- Vinner, S. & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20(4), 356-366. https://doi.org/10.2307/749441
- Watson, A. & Mason, J. (2005). Mathematics as a constructive activity. Lawrence Erlbaum Associates.
- Woo, J. H., Chong, Y. O., Park, K. M., Lee, K. H., Kim, N. H., Na, G. S. & Yim, J. H. (2014). Resesarch methodology in mathematics education. Seoul: Kyungmoonsa.
- Zaslavsky, O. & Leikin, R. (1999). Interweaving the training of mathematics teacher educators and the professional development of mathematics teachers. In O. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education, 1, (pp. 143-158).
- Zaslavsky, O. & Leikin, R. (2004). Professional development of mathematics teacher educators: Growth through practice. Journal of Mathematics Teacher Education, 7(1), 5-32. https://doi.org/10.1023/B:JMTE.0000009971.13834.e1