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http://dx.doi.org/10.7468/jksmee.2021.35.1.37

The Conceptualizing and Practices of Mathematical Classes Based on Students' Thinking  

Lee, Seon Young (Baekseok high school)
Han, Sunyoung (Sungkyunkwan University)
Publication Information
Communications of Mathematical Education / v.35, no.1, 2021 , pp. 37-74 More about this Journal
Abstract
In this study, the student participation-centered class, which takes students' mathematical thinking as an important issues of the class, is named as student thinking-based math class. The main characteristics of student thinking-based mathematics classes were examined in terms of tasks, students engagement, and the role of teachers. According to the results of analysis of class cases practiced by five secondary mathematics teachers, student thinking-based mathematics classes were conducted in the intersection of the rich mathematics tasks, students' cognitive and social engagement, and the role of teachers' formative facilitator. The results of this study showed that the student's thinking is more important than the activity itself. And it is meaningful in that it examines the influence of the dynamic interaction of the three components of the mathematics class on the direction and outcome of the class.
Keywords
mathematical thinking; students' engagement; formative facilitator;
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1 Rimm-Kaufman, S. E., Baroody, A., Larsen, R., Curby, T. W. & Abry, T. (2015). To what extent do teacher-student interaction quality and student gender contribute to fifth graders' engagement in mathematics learning? Journal of Educational Psychology, 107(1), 170-185.   DOI
2 Rymes, B. (2009). Classroom discussion analysis: a tool for critical reflection by Betsy Rymes. 김종현 역 (2011). 말이 열리는 교실: 교실수업 개선을 위한 담화분석. 서울: 학이시습.
3 Schoenfeld, A. H. (2010). How to think: a theory of goal-oriented decision making and its educational application. 이경화 역(2013). 수학수업, 설명을 만나다. 서울: 경문사.
4 Shepard, L. A.(2000). The role of assessment in a learning culture. Educational Researcher, 29(7). 4-14   DOI
5 Smith, M. S. & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. 방정숙 역(2013). 서울: 경문사.
6 Smith, M. S. & Sherin, M. G. (2019). The 5 practices in practice. NY: Corwin mathematics publishing.
7 Stacey, K. (2006). What is mathematical thinking and why is it important? Retrieved from http://e-archives.criced.tsukuba.ac.jp/data/doc/pdf/2009/02/Kaye_Stacey.pdf
8 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, 268-275.   DOI
9 Stein, M. K., Smith, M. S. & Silver, S. A. (2009). Implementations standards-based mathematics instruction: a casebook for professional development (2nd ed.). 김남균, 조완영, 권성룡 역(2017). 수학과제가 수학수업을 만났을 때. 서울: 경문사.
10 Stockero, S. L. & Van Zoest, L. R. (2012). Characterizing pivotal teaching moments in begging matheamtics teachers' practice. Journal of Mathematics Teacher Education, 16, 125-147.   DOI
11 Sullivan, P., Clarke, D. & Clarke, B. (2013). Teaching with tasks for effective mathematics learning. 이경화, 김동원 역(2016). 수학 수업 이야기: 수학, 과제, 학습의 삼중주. 서울: 경문사.
12 Swan, M. (2008). Designing a multiple representation learning experience in secondary algebra. Educational Designer, 1(1), 1-17.
13 Swan, M. & Burkhardt, H. (2012). Designing assessment of performance in mathematics. Educational Designer, 2(5).
14 van ES, E. A., Hand, V. & Mercado, J. (2017). Making visible the relationship between teachers' noticing for equity and equitable teaching practice. In Schack et al. (Eds.), Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks, Research in Mathematics Education, DOI 10.1007/978-3-319-46753-5_15.
15 Watson, A. & Sullivan, P. (2008). Teachers learning about tasks and lessons. International Handbook of Mathematics Teacher Education, 2, 107-134.
16 Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, D.C.: National Academy Press.
17 Watson, A. & Thompson, D. R. (2015). Design Issues Related to Text-Based Tasks. In Task Design In Mathematics Education (pp. 143-190). Springer International Publishing.
18 William, D. & Thompson, M. (2007). Integrating assessment with learning: What will it take to make it work? In: Dwyer, CA, (ed). The Future of Assessment: Shaping Teaching and Learning. (pp. 53-82). New York: Routledge.
19 Hiebert, J., Carpenter, T. P., Fennema, E., & Fuson, K. C. (1997). Making sense teaching and learning mathematics with understanding. 김수환, 박영희, 이경화, 한대희 공역(2004). 어떻게 이해하지?. 서울: 경문사.
20 Jacobs, V. R., Lamb, L. L. C. & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking, Journal for research in mathematics education, 41(2), 169-202.   DOI
21 Leon, J., Medina-Garrido, E. & Munez, J. L. (2017). Teaching quality in math class: the development of a scale and the analysis of its relationship with engagement and achievement. Front. Psychol. 8:895. doi: 10.3389/fpsyg.2017.00895.   DOI
22 Li, Y. & Huang, R. (2013). How Chinese teach mathematics and improve teaching. Rouledge, New York, NY 10017
23 McMahon, B. & Portelli, J. P. (2004). Engagement for what? beyond popular discoursed of student engagement. Leadership and Policy in Schools, 3(1), 59-76.   DOI
24 Martin, D. P. & Rimm-Kaufman, S. E. (2015). Do student self-efficacy and teacher-student interaction quality contribute to emotional and social engagement in fifth grade math?, Journal of school psychology, 53, 359-373.   DOI
25 Mason, J., & Johnston-Wilder, S. (2006). Designing and using mathematical tasks. St. Albans: Tarquin Publications.
26 Munter, C. (2014). Developing visions of high-quality mathematics instruction. Journal for Research in Mathematics Education, 45(5), 584-635.   DOI
27 Bahr, D. L. & Bahr, K. (2017). Engaging all students in mathematical discussions. Teaching Children Mathematics, 23(6), 350-359.   DOI
28 Peterson, K. R., Stockero, S. L. & Zoest, L. R. (2015). Conceptualizing mathematically significant pedagogical opportunities to build on student thinking. Journal for research in mathematical education, 46(1), 88-124.   DOI
29 Hong, C. J., & Kim. G. Y. (2012). Functions in the middle school matheamtics: the cognitive demand of the mathematical tasks. School Mathematics, 14(2), 213-232.
30 Ahmed, H. O. K. (2016). Flipped learning as a new educational paradigm: an analytical critical study. European Scientific Journal, 21(10), 417-444. doi: 10.19044/esj.2016.v12n10p417   DOI
31 Black, P. & Wiliam, D. (1998). Assessment and classroom learning. Policy & Practice, 5(1), 7-74.
32 Breen, S. & O.Shea, A. (2010). Mathematical thinking and task design. Irich Mathematical Society Bulletin, 66, 39-49.   DOI
33 Chapin, S. H., O'Connor, C., & Anderson, N. C. (2013). Classroom discussions in math: a teacher's guide for using talk moves to support the common core and more, grades K-6. 김진호, 이지은, Jung Colen, 이대현, 김상미 역(2016). 수학교실토론. 서울: 경문사.
34 Choy, B. H. (2014). Teachers' productive mathematical noticing during lesson preparation. In Nicol, C., Liljedahl, P., Oesterle, S., & Allan, D. (Eds.) Proceedings of the Joint Meeting of PME 38 and PME-NA 36,Vol. 2, pp. 297-304. Vancouver, Canada: PME.
35 Choy, B. H., Dindyal, J. (2018). An approach to teach with variations: using typical problems. Avances de Investigacion en Educacion Matematica, nΩ 13, 21-38.   DOI
36 Fredricks, J. A., Wang, M. T., Linn, J. S., Hofkens, T. L., Sugn, H., Parr, A. & Allerton, J. (2016). Using qualitative methods to develop a survey measure of math and science engagement. Learning and Instruction, 43, 5-15.   DOI
37 Cohen, D. K., Raudenbush, S. W. & Ball, D. L. (2003). Resources, instruction, and research. Educational evaluation and policy analysis, 25(2), 119-142.   DOI
38 Finn, D. F. (1989). Withdrawing from school. Review of Educational Research, 59(2), 117-142.   DOI
39 Finn, J. D. & Zimmer, K. S. (2012). Student engagement: What is it? Why does it matter? In S. L. Christenson, A. L. Reschly, & C. Wylie (Eds.), Handbook of research on student engagement (pp. 97-131). New York, NY: Springer.
40 Foster, C. (2015). The Convergent-Divergent Model: an opportunity for teacher-learner development through principled task design. Educational Designer, 2(8), 1-25.
41 Hatch, J. A. (2008). Doing qualitative research in education settings. 진영은 역(2016). 교육적 상황에서 질적 연구 수행하기. 서울: 학지사.
42 Hattie, J. & Timperley, H. (2007). The power of feedback. Review of educational research, 1, 81-112.   DOI
43 Helme, S. & Clarke, D. (2001). Identifying cognitive engagement in the mathematics classroom. Mathematics Education Research Journal, 13, 133-153.   DOI
44 Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students' learning in second-grade arithmetic. American educational research journal, 30(2), 393-425.   DOI
45 Kim, M. H., & Kim, G. Y. (2013). The analysis of matheamtical tasks in the high school mathematics. School Mathematics, 15(1), 37-59.
46 Yu, J. E. & Park, M. H. (2019). Tangram task modification for exploring in elementary mathematics. Educational of Primary School Mathematics, 22(1), 95-111.
47 Kim, H. L., & Lee, K. H. (2016). Pre-service secondary mathematics teachers modification of derivative tasks, School Mathematics, 18(3), 711-731.
48 Park, Y. E., & Pang, J. S. (2016). Exploring self-study and its application to enhance instructional expertise in mathematics. Journal of educational research in mathematics, 26(3), 467-488
49 Park, J. M., Park, J, H., & Lee, J, K. (2017). A study on analysis of American CMP textbooks in terms of mathematical connectivity: Focused on equations, inequalities, and functions. Journal of the Korean School Mathematics Society, 20(3), 277-302.
50 Park, J. H. (2019). Prospective elementary mathematics teachers' difficulties on textbook task modification: focusing on fraction tasks. Journal of Educational Research in Mathematics, 29(4), 551-575.   DOI
51 Lee, D. G. (2018). A case study on student's thoughts and expressions on various types of geometric series tasks. The Mathematical Education, 57(4), 353-369.   DOI
52 Lee, S. J., & Kim, G. Y. (2019). How middle-school mathematics textbooks of Korea and the US support to develop students' statistical reasoning. Mathematical Education, 58(1), 139-160.   DOI
53 Lee, J. H. (2014). ). How do pre-service teachers disprove 0.99⋯? School Mathematics, 16(3), 491-502.
54 Kim, D. Y. & Kim, G. Y. (2014). Secondary mathematics teachers understanding and modification of mathematical tasks in textbooks. School Mathematics, 16(3), 445-469.
55 Lee, J. A. (2017). A qualitative research on middle school teachers' understanding of "student-participatory class"(Master's thesis). Seoul National University.
56 Yi., Y. B., & Hong, J. K. (2016). Primary students' mathematical thinking analysis of between abstraction of concrete materials and concretization of abstract concepts. School Mathematics, 18(1), 159-173.
57 Kim, W. (2019). A discursive approach to the development of the conceptual framework of textbook analysis, and research on teachers' recognition(Doctoral dissertation). Korea University.
58 Han, C. R., Kim, H. J. & Kwon, O. N. (2018). Teacher noticing on students' reasoning of statistical variability. Journal of the Korean School Mathematics, 21(2), 183-206.   DOI
59 Cho, H. H. & Choi, Y. G. (1999). The repreating decimal from the static and dynamic view point. School Mathematics, 1(2), 605-615.
60 Choi, H. S. (2020). Exploration of Instructional Design Changes of Pre-service Mathematics Teachers by Restructuring the Lesson Plan. Journal of KSMS, 23(1), 159-177.
61 Han, H. J., Kim, Y. G., Kim, B. E. et al. (2018). Analysis of actual conditions to student-participatory class. Sejong Educational Policy Institute, 2018-03.
62 Yang, Y. & Rick, T. E. (2013). Chinese lesson study: developing classroom instruction through collaborations in school-based teaching research group activities. In Y. Li & R. Huang (Eds.), How Chinese teach mathematics and improve teaching (pp. 51-65). New York: Routledge.