[논문]유리수 지수 정의에 대한 교사 이해 분석

신보미

doi:10.7468/mathedu.2021.60.1.21

[국내논문] 유리수 지수 정의에 대한 교사 이해 분석
Teachers' understanding of the definition of rational exponent 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.60 no.1, 2021년, pp.21 - 39

신보미 (전남대학교)

초록
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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 데 목적을 두었다. 이를 위해 지필검사 도구를 개발하여 현직 고등학교 교사 50명의 답변을 분석하였으며, 이를 토대로 유리수 지수 정의에 대한 교사의 이해 특징이 교사 교육에 주는 시사점 및 교수학적 쟁점을 기술하였다. 또한 이러한 시사점 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 ▼ AI-Helper

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)=rxr-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 $(-8)^{\frac{1}{3}}$ 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.

주제어

표/그림 (22)

그림 [Fig. 1] The definition of irrational exponent (Ryu et al., 2017, p. 26)
그림 [Fig. 2] The proof of f'(x) = rx^r-1 (Lang, 2001, p. 127)
표 [Table 1] Summary of the teachers' responses to Q1
표 [Table 2] Summary of the teachers' responses to Q2
그림 [Fig. 3] A case of teachers' responses in Category 2-2
그림 [Fig. 4] A case of teachers' responses with explaining x >0 in Category 2-1
그림 [Fig. 5] A case of teachers' responses in Category AB-AB1
그림 [Fig. 6] The other case of teachers' responses in Category AB-AB1
그림 [Fig. 7] A case of teachers' responses in Category A-A1
그림 [Fig. 8] A case of teachers' responses in Category B-B1
그림 [Fig. 9] A case of teachers' responses in Category B-B3
그림 [Fig. 10] The case of teacher's response in Category B-B4
그림 [Fig. 11] The case of teacher's response in Category A-B1
그림 [Fig. 12] A case of teachers' responses in Category B-A1
그림 [Fig. 13] A case of teachers' responses in Category B-B2
그림 [Fig. 14] A case of teachers' responses in Category B-A2
$[Fig. 15] The graph of y = <TEX>$x^{\frac{1}{3}}$</TEX> from Geogebra$ 그림 [Fig. 15] The graph of y = $x^{\frac{1}{3}}$ from Geogebra
$[Fig. 16] The graph of y = <TEX>$x^{\frac{1}{3}}$</TEX> from Wolfram Alpha$ 그림 [Fig. 16] The graph of y = $x^{\frac{1}{3}}$ from Wolfram Alpha
그림 [Fig. 17] A problem related to the definition of rational exponent on Mathematics I (Ko et al., 2017, p. 18)
그림 [Fig. 18] A problem related to the restriction of bases in exponential function on an American textbook (Foerster, 2003, p. 277)
그림 [Fig. 19] A table to draw the graph of y = 2^x on Mathematics I (Kim et al., 2017, p. 39)
그림 [Fig. 20] A table to draw the graph of y = 2^x on a Japanese textbook (Ohkamoto, 2017, p. 149)

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