담론적 관점에서 그래프 해석에 대한 분석틀 재구성 및 적용 -우리나라 수학 교과서와 미국 CMP 교과서 중심으로-

Reconstruction and application of an analytic framework for discursive approach to interpretations of graph -The case of a Korean textbook and CMP-

Abstract

The purpose of this study is to provide implications for improvement of mathematics textbook based on discursive approach to textbook analysis that complementarily combines a communicational approach to cognition and social semiotics. For this purpose, we reconstructed an analytic framework for discursive approach to written discourses of Korean textbook and CMP, and applied it to our analysis. Results show that several characteristics in meanings were developed by the use of words and visual mediators. First, in the case of ideational meaning, there were qualitative and quantitative differences between vocabularies used and between information addressed by visual mediators. Second, in the case of structural meaning, an offer and application of procedure was emphasized in a Korean textbook, whereas expectation and selection experiences of diverse possibilities for problem solving was underlined in CMP. In the case interpersonal meaning of student-author, imperative instructions were paid attentions in a Korean textbook. In contrast, students' interdependence and active participation were stressed in CMP. Therefore, this study addressed ideas about how to analyze mathematics textbooks based on integrated meanings developed by the use of words and visual mediators. In addition, it distributes implications for improvements of Korean mathematics textbooks through the analytic framework of both mathematical meanings and interpersonal meanings of student-author.

[그림 1] 언어를 단순화하기 위한 5가지 지침(Lappan et al., 2014a) [Fig. 1] Five Guidelines for Simplifying Language (Lappan et al., 2014a)

[그림 4] 분석의 개요 [Fig. 4] Overview of analysis

[그림 5] 개념적 다이어그램 예시(김원경 외, 2018) [Fig. 5] Conceptual diagram(Kim et al., 2018)

[그림 7] 보완의 예시(김원경 외, 2018) [Fig. 7] Example of complement(Kim et al., 2018)

[그림 10] 보완 예시(Lappan et al., 2014b) [Fig. 10] Example of complement(Lappan et al., 2014b)

[그림 11] 보완 예시(Lappan et al., 2014b) [Fig. 11] Example of complement(Lappan et al., 2014b)

[그림 12] 명령법 예시(김원경 외, 2018) [Fig. 12] Examples of imperative(instructions)(Kim et al., 2018)

[그림 13] 인칭대명사 예시(Lappan et al., 2014b) [Fig. 13] Examples of personal pronoun(Lappan et al., 2014b)

[그림 2] 다섯 가지 표상(Lappan et al., 2014a) [Fig. 2] Five Representations Star(Lappan et al., 2014a)

[그림 3] 연구 절차 [Fig. 3] Research procedure

[그림 6] 내러티브 다이어그램 예시(김원경 외, 2018) [Fig. 6] Narrative diagram(Kim et al., 2018)

[그림 8] 유사와 대조의 예시(김원경 외, 2018) [Fig. 8] Examples of similarity and contrast(Kim et al., 2018)

[그림 14] 질문법과 명령법 예시(Lappan et al., 2014b) [Fig. 14] Examples of interrogative(questions) and imperative(instructions)(Lappan et al., 2014b)

[표 1] 국내∙외 교과서 단원 및 학습 목표 [Table 1] Textbook units and learning goals

[표 2] 단어와 시각적 매개체 사용을 통한 관념적 의미 분석틀 [Table 2] Analytic framework for ideational meanings by the use of words and visual mediators

[표 3] 구조적 의미 분석틀 [Table 3] Analytic framework for structural meaning

[표 4] 학생-저자 관계적 의미 분석틀 [Table 4] Analytic framework for interpersonal meaning of student-author

[표 5] 우리나라 교과서의 전문화와 대상화 [Table 5] Discursive specialisation and objectification in Korean textbook

[표 6] CMP 교과서의 전문화와 대상화 [Table 6] Discursive specialisation and objectification in CMP textbook

[표 7] 우리나라 교과서의 구조적 의미 [Table 7] Structural meaning in Korean textbook

[표 8] CMP 교과서의 구조적 의미 [Table 8] Structural meaning in CMP textbook

[표 9] 학생-저자의 관계적 의미 [Table 9] Interpersonal meaning of student-author