유리수 지수 정의에 대한 교사 이해 분석
Teachers’ understanding of the definition of rational exponent
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본 연구는 유리수 지수 정의에 대한 교사의 이해 특징을 분석하여 교사 교육에의 시사점을 구체화하고, 지수의 확장을 지도하는 수업에서 정의의 본질 및 그 이면의 사고를 다루기 위해 고려할 필요가 있는 교수학적 쟁점을 밝히는 데목적을 두었다. 이를 위해 지필검사 도구를 개발하여 현직 고등학교 교사 50명의 답변을 분석하였으며, 이를 토대로유리수 지수 정의에 대한 교사의 이해 특징이 교사 교육에 주는 시사점 및 교수학적 쟁점을 기술하였다. 또한 이러한시사점 및 교수학적 쟁점을 국내 교과서 전개 방식에 비추어 해석하여 수업을 통해 지수의 확장과 관련된 정의의 본질을 의미있게 다루기 위해 교사 및 교과서가 좀 더 주목할 필요가 있는 측면을 제언하였다.
Abstract
The aim of this study was to deduce implications of the growth of mathematics teachers’ specialty for effective instruction about the formulae of exponentiation with rational exponents by analyzing teachers' understanding of the definition of rational exponent. In order to accomplish the aim, this study ascertained the nature of the definition of rational exponent through examining previous literature and established specific research questions with reference to the results of the examination. A questionnaire regarding the nature of the definition was developed in order to solve the questions and was taken to 50 in-service high school teachers. By analysing the data from the written responses by the teachers, this study delineated four characteristics of the teachers’ understanding with regard to the definition of rational exponent. Firstly, the teachers did not explicitly use the condition of the bases with rational exponents while proving f`(x)=rx^{r-1}. Secondly, few teachers explained the reason why the bases with rational exponents must be positive. Thirdly, there were some teachers who misunderstood the formulae of exponentiation with rational exponents. Lastly, the majority of teachers thought that (-8)^{1over 3} equals to -2. Additionally, several issues were discussed related to teacher education for enhancing teachers’ knowledge about the definition, features of effective instruction on the formulae of exponentiation and improvement points to explanation methods about the definition and formulae on the current high school textbooks.
참고문헌 (44)
- Adler, J., "Opening another black box : Researching mathematics for teaching in mathematics teacher education", Journal for Research in Mathematics Education, 37(4), pp.270~296 (2006)[DOI]
- Bernardo, G., "The ambiguity of the sign √", Proceedings of the 6th Congress of the European Society for Research in Mathematics Education, pp.509~518 (2010), CERME
- 정윤지, "정의 지도를 위한 What-If-Not 전략의 활용 -다각형의 외각을 중심으로-", 학교수학, 20(3), pp.379~394 (2018), 대한수학교육학회[DOI]
- Choi, G. S., "Teaching geometry through Geogerba 5", Proceedings of the KSME 2014 Spring Conference on Mathematics Education, pp.433~437 (2014), KSME
- 도종훈, "고등학교 수학 교과서에 제시된 유리수 지수 a^(m", n)의 정의에 관한 소고, 2011, pp.50(1), 61~67[DOI]
- Edwards, B., "Surprises from mathematics education research : Student(mis)use of mathematical definitions", American Mathematical Monthly, 111(5), pp.411~424 (2004)[DOI]
- Even, R., "Subject matter knowledge and knowledge about students as sources of teacher presentations of the subject matter", Educational Studies in Mathematics, 29(1), pp.1~20 (1995)[DOI]
- Fan, L., "Textbook research as scientific research : Towards a common ground on issues and methods of research on mathematics textbooks", ZDM : the international journal on mathematics education, 45, pp.765~777 (2013)[DOI]
- Fischbein, E., "Didactics of Mathematics as a Scientific Discipline", pp.231~245 (1993), Kluwer
- Foerster, A. P., "Precalculus with Trigonometry" (2003), Key Curriculum Press
- Guberman, R., "Knowledge concerning the mathematical horizon : A close view", Mathematics Education Research Journal, 27, pp.165~182 (2015)[DOI]
- Kim, I. S., "Calculus" (2012), Kyungmoonsa
- Kim, W. K., "Mathematics Ⅰ" (2017), Visang
- Ko, S. E., "Mathematics Ⅰ" (2017), Sinsago
- Kwak, D. Y., "Calculus" (2001), Kyungmoonsa
- Landau, S. I., "Dictionaries : The Art and Craft of Lexicography" (2001), Cambridge University Press
- Lang, S., "Short Calculus" (2001), Springer
- Lavy, I., "Engaging in problem posing activities in a dynamic geometry setting and the development of prospective teachers’ mathematical knowledge", Journal of Mathematical Behavior, 29, pp.11~24 (2010)[DOI]
- Leikin, R., "On the content-dependence of prospective teachers’ knowledge : A case of exemplifying definitions", International Journal of Mathematical Education in Science and Technology, 41(4), pp.451~466 (2010)[DOI]
- Levenson, E., "Teachers’ knowledge of the nature of definitions : The case of the zero exponent", Journal of Mathematical Behavior, 31, pp.209~219 (2012)[DOI]
- Lewin, J., "An Interactive Introduction to Mathematical Analysis" (2003), Cambridge University Press
- Magiera, T. M., "Relationships among features of pre-service teachers' algebraic thinking", Proceedings 35th Conference of the International Group for the Psychology of Mathematics Education, 3, pp.169~176 (2011), PME
- Matić, L. J., "The use of the textbook as an artefact in the classroom : A case study in the light of a socio-didactical Tetrahedron", Journal für Mathematik-Didaktik, 37(2), pp.349~374 (2016)[DOI]
- Ministry of Education, "Mathematics curriculum", Ministry of Education, ~ (2015)
- Movshovitz-Hadar, N., "Constructing Knowledge for Teaching Secondary Mathematics", pp.117~140 (2011), Springer
- National Council of Teachers of Mathematics, "Principles and Standards for School Mathematics", NCTM, ~ (2000)
- National Council of Teachers of Mathematics, "Principles to Actions : Ensuring Mathematics Success for All", NCTM, ~ (2015)
- Ohkamoto, K., "Mathematics Ⅱ" (2017), Gikkosubang
- Remillard, J. T., "The influence of curriculum material design on opportunities for student learning", ZDM : the international journal on mathematics education, 46(5), pp.735~749 (2014)[DOI]
- Robin, M. J., "Double negative : The necessity principle, commognitive conflict, and negative number operations", Journal of Mathematical Behavior, 32, pp.649~659 (2013)[DOI]
- Ryu, H. C., "Mathematics Ⅰ" (2017), Chunjae
- Sangwin, J. C., "Textbook accounts of the rules of indices with rational exponents", International Journal of Mathematical Education in Science and Technology, 50(8), pp.1191~1209 (2019)[DOI]
- Seaman, C., "Mathematical sophistication among preservice elementary teachers", Journal of Mathematics Teacher Education, 10(3), pp.167~182 (2007)[DOI]
- Shulman, L., "Those who understand : Knowledge growth in teaching", Educational Researcher, 15(2), pp.4~14 (1986)[DOI]
- Tall, D., "How Humans Learn to Think Mathematically : Exploring the Three Worlds of Mathematics" (2013), Cambridge University Press
- "Wolfram Alpha" (2021)[URL]
- Thomas, B. G., "Calculus" (2003), Addison Wesley
- Tirosh, D., "To define or not to define : The case of ", Educational Studies in Mathematics, 33, pp.321~330 (1997)[DOI]
- Turner, F., "Mathematical Knowledge in Teaching", pp.195~212 (2011), Springer
- Verberg, D., "Calculus" (2000), Prentice Hall
- Watson, J., "Teachers’knowledge of their students as learners and how to intervene", Identities, Cultures and Learning Spaces: Proceedings of the 29th Annual Conference of the Mathematics Education Research Group of Australasia, pp.551~558 (2006), MERGA
- Woo, J. H., "A study on the definitions presented in school mathematics", The Journal of Education Research in Mathematics, 11(2), pp.363~384 (2001)
- Woo, J. H., "Revisiting 0.999… and (-8)1", 3 in school mathematics from the perspective of the algebraic permanence principle, 2008, pp.28(2), 11~16
- 양선아, "학교 수학과 대학 수학 사이의 연계성에 대한 중등교사의 전문성 분석 - 대학 수학에 대한 인식과 대수 영역에 대한 MKT를 중심으로 -", 학교수학, 21(2), pp.419~439 (2019), 대한수학교육학회[DOI]