earticle

영어

Many studies have investigated teachers’ curriculum use in order to explain student achievement and opportunities to learn mathematics (Brown, 2002; Lloyd, Remillard, & Herbel-Eisenmann, 2009; Stein, Remillard, & Smith, 2007). However, little has been known about how teachers understand the roles of non-textual elements (e.g., pictures, illustrations, graphs, and mathematical figures) for effective teaching and learning. By analyzing qualitative data from 10 South Korean and 11 U.S. secondary mathematics teachers, this study explores what aspects of non-textual elements teachers consider important for teaching and learning and how teachers understand the roles of non-textual elements in their instruction. The results from this study show that both South Korean and U.S. teachers regard accuracy, aesthetics, connectivity, and contextuality as important aspects of non-textual elements for effective teaching and learning. However, their emphases on, and usages of, non-textual elements in their classrooms were largely different between South Korea and the United States. In particular, South Korean teachers tended to focus on mathematical connectivity and mathematical accuracy (with regard to the definition of a concept), emphasizing the nature of mathematics as a logical and abstract subject. U.S. teachers, however, put more emphasis on contextuality and accuracy (with regard to mathematical application and usefulness). It is also notable that both South Korean and U.S. teachers preferred simplicity to variety, despite many studies that have emphasized the importance of various mathematical experiences in student learning. Teachers' lack of understanding of the importance of variety may lead to students’ misconceptions due to the fallacy of "one-case concreteness" (Presmeg, 1997). Comparing South Korean and U.S. teachers’ perception of non-textual elements in mathematics textbooks, this study provides useful information atextbwhat criteria teachers have in selecting non-textual elements for their instruction as well as how to improve the quality of non-textual elements in mathematics textbooks for effective teaching and learning. This study also calls for further investigations of non-textual elements as well as teacher education and professional development prog nms that give attention to the importance of non-textual elements in mathematics education.

한국어

교사들의 교과 교육학적 지식의 일환으로서의 교육과정 운용과 이해에 대한 다각적 연구가 이루어져 왔음에도 불구하고, 교사들의 수학 교수에 있어서 비문자적 표상(예컨대, 그림, 삽화, 그래프, 도형 등)에 대한 이해와 활용에 대한 심층적 연구는 아직 미약하다. 본 연구는 21명의 한국과 미국 중등 수학교사들의 개별 면접을 통하여 교사들의 비문자적 표상에 대한 인식과 선택 기준 및 활용을 비교 분석하였다. 연구 결과, 양국 교사 모두 수학적 엄밀성, 심미성, 연결성, 상황성을 비문자적 표상의 중요한 요소로 인식하나, 그 의미와 활용 방식에는 다소 차이를 보였다. 또한 기존 연구에서 강조되어 온 다양성보다는 단순한 표상을 선호하는 것으로 나타나 이론과 현장 교사들의 인식 사이에 차이가 있음이 드러났다. 본 연구는 한국과 미국의 비교연구를 통해 효과적인 비문자적 표상의 특성을 규명할 뿐만 아니라 비문자적 표상에 대한 교과서 개선 방안 및 교사교육에 대한 유의미한 시사점을 제공한다는 점에서 그 의의가 있다.