Browse > Article
http://dx.doi.org/10.30807/ksms.2020.23.1.004

An Analysis on Prospective Teachers' HCK : Focused on Understandings of Inverse Function Symbol  

Shin, Bomi (Chonnam National University)
Publication Information
Journal of the Korean School Mathematics Society / v.23, no.1, 2020 , pp. 67-88 More about this Journal
Abstract
This study analyzed the characteristics of prospective teachers' Horizon Content Knowledge(HCK) related to understandings of an inverse function symbol. This study aimed to deduce implications of developing HCK in terms of the means which would enhance mathematics teachers' professional development. In order to achieve the aim, this study identified features of HCK by examining the previous literature on HCK, which has conformed Ball & Bass(2009) and exploring the research in AMT, including Zazkis & Leikin(2010) which has emphasized cultivating AMT through university mathematics education. In addition, a questionnaire was developed regarding the features of HCK and taken by 57 prospective teachers. By analyzing the data obtained from the written responses the participants presented, this study delineated the specific characteristics of the teachers' HCK with regard to an inverse function symbol. Additionally, several issues in the teacher education for improving HCK were discussed, and the results of this research could inspire designing and implementing a teacher education program relevant to HCK.
Keywords
HCK(Horizon Content Knowledge); SMK(Subject Matter Knowledge); AMT(Advanced Mathematical Thinking); teachers' knowledge; inverse function; inverse function symbol;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Brown, C., & Reynolds, B. (2007). Delineating four conceptions of function: A case of composition and inverse. In T. Lamberg, & L. R. Wiest (Eds.), Proceeding of the 29th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 190-193) NV: University of Nevada.
2 Cho, Y., & Tee, F. (2018). Complementing mathematics teachers' horizon content knowledge with an elementary-on-advanced aspect. Pedagogical Research, 3(1), 1-11.
3 Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.) Advanced mathematical thinking (pp. 95-123). Dordrecht: Kluwer Academic Publishers.
4 Figueiras, L., Ribeiro, M., Carrillo, J., Fernandez, S., & Deuloffeu, J. (2011). Teachers' advanced mathematical knowledge for solving mathematics teaching challenges: A response to Zazkis and Mamolo. For the Learning of Mathematics, 31(3), 26-28.
5 Guberman, R., & Gorev, D. (2015). Knowledge concerning the mathematical horizon: A close view. Mathematics Education Research Journal, 27, 165-182.   DOI
6 Harel, G., & Kaput, J. (1991). The role of conceptual entities and their symbols in building advanced mathematical concepts. In D. Tall (Ed.) Advanced mathematical thinking (pp. 82-94). Dordrecht: Kluwer Academic Publishers.
7 Harel, G. (2013). Intellectual need. In K. Leatham (Ed.) Vital direction for mathematics education research (pp. 119-152). NY: Springer.
8 Hodgen, J. (2011). Knowing and identity: A situated theory of mathematics knowledge in teaching. In T. Rowland & K. Ruthven (Eds.) Mathematical knowledge in teaching (pp. 27-42). NY: Springer.
9 Jakobsen, A., Thames, M. H., Ribeiro, C. M. (2013). Delineating issues related to Horizon Content Knowledge for mathematics teaching. In B. Ubuz, C. Haser, & M. A. Mariotti (Eds.), Proceedings of CERME 8 (pp. 3125-3134). Turkey: ERME.
10 Ball, D., & Bass, H. (2009). With an eye on the mathematical horizon: Knowing mathematics for teaching to learners'mathematical futures. Paper presented at the 2009 Curtis Center Mathematics and Teaching Conference, LA: University of California.
11 Brousseau, G. (1998). Theory of didactical situations in mathematics. Dordrecht: Kluwer Academic Publishers.
12 Mellone, M., Jakobsen, A., & Ribeiro, C. M. (2015). Mathematics educator transformation(s) by reflecting on students' non-standard reasoning. In K. Krainer & N. Vondrova (Eds.), Proceedings of CERME 9 (pp. 2874-2880). Prague: ERME
13 Klein, F. (1932). Elementary mathematics from an advanced standpoint: Arithmetic, algebra, analysis (Vol. 1. E. R. Hedrick & C. A. Noble trans.) NY: Macmillan. (Original work published 1924).
14 Ma, L. (1996). Profound understanding of fundamental mathematics: What is it, why is it important, and how is it attained? Unpublished doctoral dissertation, Stanford: Stanford University.
15 Mamolo, A. (2010). Polysemy of symbols: Signs of ambiguity. The Montana Mathematics Enthusiast, 7(2), 247-262.
16 Montes, M., Riberiro, M., Carrillo, J., & Kilpatrick, J. (2016). Understanding mathematics from a higher standpoint as a teacher: An unpacked example. In Csikos, C., Rausch, A., & Szitanyi, J. (Eds.), Proceedings of the 40th Conference of the International Group of the Psychology of Mathematics Education, Vol. 3, (pp. 351-322). Hungary: PME.
17 Mosvold, R., & Fauskanger, J. (2014). Teachers' Beliefs about Mathematical Horizon Content Kno wledge. International Journal for Mathematics Teaching and Learning, 1-16.
18 Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57, 1-22.   DOI
19 Tall, D. (2013). How humans learn to think mathematically : Exploring the three worlds of mathematics. NY: Cambridge University Press.
20 Tall, D. (1991). The psychology of advanced mathematical thinking. In D. Tall (Ed.) Advanced mathematical thinking (pp. 3-21). Dordrecht: Kluwer Academic Publishers.
21 Wasserman, N., Weber, K., Villanueva, M., & Mejia-Ramos, J. P. (2018). Mathematics teachers' view about the limited utility of real analysis: A transport model hypothesis. The Journal of Mathematics Behavior, 50, 74-89.   DOI
22 Turner, F. & Rowland, T. (2011). The knowledge Quartet as an organising framework for developing and deepening teachers' mathematics knowledge. In T. Rowland & K. Ruthven (Eds.) Mathematical knowledge in teaching (pp. 195-212). NY: Springer.
23 Vale, C., McAndrew, A, & Krishnan, S. (2011). Connecting with the horizon: Developing teachers' appreciation of mathematical structure. Journal of Mathematics Teacher Education, 14, 193-212.   DOI
24 Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.) Advanced mathematical thinking (pp. 65-81). Dordrecht: Kluwer Academic Publishers.
25 Watson, J., Beswick, K., & Brown, N. (2006). Teachers' knowledge of their students as learners and how to intervene. In P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Eds.), Identities, cultures and learning spaces: Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia (pp. 551-558). Adelaide: MERGA.
26 William, B. (2010). How mathematicians think : Using ambiguity, contradiction, and paradox to create mathematics. Princeton: Princeton University Press.
27 Zazkis, R., & Marmur, O. (2018). Groups to the rescue: Responding to situations of contingency. In N. H. Wasserman (Ed.), Connecting abstract algebra to secondary mathematics for secondary mathematics teachers, (pp. 363-387) NY: Springer.
28 Zazkis, R., & Leizin, R. (2010). Advanced mathematical knowledge in teaching practice: Perceptions of secondary mathematics teachers. Mathematical Thinking and Learning, 12, 263-281.   DOI
29 Zazkis, R., & Mamolo, A. (2011). Reconceptualizing knowledge at the mathematical horizon. For the Learning of Mathematics, 31(2), 8-13.
30 Zazkis, R., & Zazkis, D. (2014). Script writing in the mathematics classroom: Imaginary conversations on the structure of numbers. Research in Mathematics Education, 16(1) 54-70.   DOI
31 양선아, 이수진(2019). 학교 수학과 대학 수학 사이의 연계성에 대한 중등교사의 전문성 분석-대학 수학에 대한 인식과 대수 영역에 대한 MKT를 중심으로-. 학교수학, 21(2), 419-439.
32 고희정, 고상숙(2013). 고등학교 미적분 수업에서 나타나는 초임교사의 교수를 위한 전문화된 수학 내용 지식(SCKT). 한국학교수학회논문집, 16(1), 157-185.
33 교육부(2015). 수학과 교육과정. 교육부 고시 제 2015-74호 [별책 8] 서울: 저자.
34 송근영, 방정숙(2013). 수학과 교사지식에 관한 국내 연구의 동향 분석. 한국학교수학회논문집, 16(1), 265-287.
35 이준열 외(2017). 고등학교 수학. 서울: 천재교육.
36 Adler, J., & Davis, Z. (2006). Opening another black box: Researching mathematics for teaching in mathematics teacher education, Journal for Research in Mathematics Education, 37(4), 270-296.
37 Ball, D., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.   DOI