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Pre-Service Secondary Mathematics Teachers' Modification of Derivative Tasks  

Kim, Ha Lim (Graduate School, Seoul National University)
Lee, Kyeong-Hwa (Seoul National University)
Publication Information
School Mathematics / v.18, no.3, 2016 , pp. 711-731 More about this Journal
Abstract
The purpose of this study is to investigate how pre-service secondary mathematics teachers modify mathematical tasks from a textbook and learning opportunities they have during the task modification. In the pursuit of this purpose, tasks was selected from derivative units in a textbook and five pre-service teachers was asked to modify the tasks. The findings from analysis are as follows. First, the cognitive demands of modified tasks were maintained or higher than those of the originals. Pre-service teachers' tendency toward conceptual understanding of derivative seems to make the result. Second, task modification provided a lot of learning opportunities for pre-service teachers. They tried to know intention of curriculum and textbook, realized the importance of predicting students' responses, and had opportunities for cooperation and reflective thinking.
Keywords
pre-service teachers; mathematical tasks; task modification; cognitive demand;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 김대영⋅김구연(2014). 중등 수학교사의 교과서 수학과제 이해 및 변형 능력, 학교수학, 16(3), 445-469.
2 김미희⋅김구연(2013). 고등학교 교과서의 수학과제 분석. 학교수학, 15(1), 37-59.
3 김민혁(2013). 수학교사의 교과서 및 교사용 지도서 활용도 조사. 학교수학, 15(3), 503-531.
4 김성희⋅방정숙(2005). 수학 교수⋅학습 과정에서 과제의 인지적 수준 분석 - 초등학교 '비와 비율' 단원을 중심으로. 수학교육학연구, 15(3), 251-272.
5 김정은⋅이수진⋅김지수(2015). 중등 수학교사의 과제 이해 및 변형 능력 : 인지적 노력 수준 중심으로. 학교수학, 17(4), 633-652.
6 방정숙(2007). 수학 과제 분석을 통한 예비 초등교사의 전문성 신장. 수학교육, 46(4), 465-482.
7 신항균⋅이광연⋅박세원⋅신범영⋅이계세⋅김정화⋅박문환⋅윤정호⋅박상의⋅서원호⋅전제동⋅이동흔(2014). 고등학교 미적분 I. 서울: 지학사.
8 강현영⋅고은성⋅김태순⋅조완영⋅이경화⋅이동환(2011). 좋은 수학수업을 위해 수학교사에게 필요한 역량과 교사교육에 대한 현직교사의 인식조사. 학교수학, 13(4), 633-649.
9 교육과학기술부(2011). 수학과 교육과정(교육과학기술부 고시 제 2011-361호 [별책8]).
10 교육부(2015). 수학과 교육과정(교육부 고시 제 2015-74호 [별책 8]).
11 우정호⋅정영옥⋅박경미⋅이경화⋅김남희⋅나귀수⋅임재훈(2006). 수학교육학 연구방법론. 서울: 경문사.
12 이현주⋅류중현⋅조완영(2015). 통합적 이해의 관점에서 본 고등학교 학생들의 미분계수 개념이해 분석. 수학교육 논문집, 29(1), 131-155.
13 이혜림⋅김구연(2013). 수학교과서 문제에 대한 예비중등교사의 이해 및 변형 능력. 수학교육학연구, 23(3), 353-371.
14 임재훈⋅박교식(2004). 학교 수학에서 접선 개념 교수 방안 연구, 수학교육학연구, 14(2), 171-185.
15 정연준(2010). 미분계수의 역사적 발달 과정에 대한 고찰. 학교수학, 12(2), 239-257.
16 조완영(2006). 고등학교 미적분에서의 수학화 교수.학습에 관한 연구, 학교수학, 8(4), 417-439.
17 Arbaugh, F., & Brown, C. A. (2005). Analyzing mathematical tasks: a catalyst for change?. Journal of Mathematics Teacher Education, 8(6), 499-536.   DOI
18 Aspinwall, L., & Miller, L. D. (2001). Diagnosing conflict factors in calculus through students' writings: One teacher's reflections. The Journal of Mathematical Behavior, 20(1), 89-107.   DOI
19 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.   DOI
20 Clarke, D., & Roche, A. (2010). Teachers' Extent of the Use of Particular Task Types in Mathematics and Choices behind That Use. Mathematics Education Research Group of Australasia.
21 Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers' practices. Educational Studies in Mathematics, 52(3), 243-270.   DOI
22 Doyle, W. (1983). Academic work. Review of educational research, 53(2), 159-199.   DOI
23 Krainer, K. (1993). Powerful tasks: A contribution to a high level of acting and reflecting in mathematics instruction. Educational Studies in Mathematics, 24(1), 65-93.   DOI
24 Lee, K., Lee, E., & Park, M. (2013). Task modification and knowledge utilization by Korean prospective mathematics teachers. Task design in mathematics education: Proceedings of ICMI Study, 22.
25 Prestage, S., & Perks, P. (2007). Developing teacher knowledge using a tool for creating tasks for the classroom. Journal of Mathematics Teacher Education, 10(4-6), 381-390.   DOI
26 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.   DOI
27 Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics teaching in the middle school, 3(4), 268-275.
28 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.   DOI
29 Steinbring, H. (1998). Elements of epistemological knowledge for mathematics teachers. Journal of Mathematics Teacher Education, 1(2), 157-189.   DOI
30 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.   DOI
31 Tall, D. (1987). Constructing the concept image of a tangent. Proceedings of PME 11, Montreal, 3, 69-75.
32 Watson, A. & Mason, J. (2005). 색다른 학교수학. (이경화 역). 서울: 경문사.
33 Yeo, J. B. W. (2007). Mathematical tasks: Clarification, classification and choice of suitable tasks for different types of learning and assessment (Tech. Rep. ME2007-01). National Institute of Education, Nanyang Technological University, Singapore.
34 Yin, R. K. (2013). Case study research: Design and methods. Thousand Oaks, CA: SAGE.
35 Zaslavsky, O. (1995). Open-ended tasks as a trigger for mathematics teachers' professional development. For the Learning of Mathematics, 15(3), 15-20.