학교수학적 지식의 성장: 고등학교 영재 학생들의 위키(Wiki) 기반 협력 문제해결 활동을 중심으로 = The growth of school mathematics: Korean secondary gifted students' collaborative problem solving using the Wiki

다국어 초록 (Multilingual Abstract)

In this study, I strive to design a collaborative learning model of Wikis, which can embed ESMCE(Educational Setting for Mathematical Creation and Errors) in collective metal space where secondary gifted students are able to work collaboratively on math problems beyond a classroom. By applying the design, this study aims to identify students' collaborative patterns in MKB(mathematical knowledge building) process and design factors of the Wiki, which facilitate educational situation to operate for collaborative mathematics problem solving in the Wiki system, and to increase understanding of the secondary gifted students' collaborative mathematics problem solving in virtual environment.
In designing this experiment, I draw on dynamics of errors as ``an organizing power of reality'' (Thom, 1992). To gradually induce students' collaboration on mathematical problem solving based on finding-error activities, I used 3 types of problems; the 1st type of ECS(Explicitly Contradictory Situation), the 2nd type of ECS, ICS(Implicitly Contradictory Situation) Participants were 14 Korean secondary gifted students, who enrolled in calculus II courses in one of gifted institutions in Korea, and their math teacher.
The findings of this study suggest that Wikis are applicable to building online Mathematical Community of Inquiry beyond classrooms for Korean secondary gifted students. The patterns emergent in students’ collaborative mathematical knowledge building process are identified as scattered form and double helix form. The double helix form consists of an axis of refutation(RFT)-agreement(AGMT) and an axis of fix(FIX)-supplement(SUPPL). I conclude that the mechanism of growing SM is solutions and refutations following the double helix form, which is very similar to the pattern of “Conjectures and Refutations”(Lakatos, 1976).
Despite that most participants had difficulty in using LaTeX for mathematical expressions, this study shows that Wikis are valuable tools for providing Korean secondary students opportunities to learn social virtue such as “humility and courage”(Lampert, 1990), which have been neglected in Korean educational environment but emphasized as precious for doing mathematics in the field of mathematics education.

국문 초록 (Abstract)

본 연구는 수학 수업에서 온라인 탐구 커뮤니티의 건설을 시도함으로써 개별화된 경쟁에 치우쳐 있는 우리나라 수학교육 환경에서도 고등학교 영재 학생들에게 수학 발전의 사회적 과정을 경험할 수 있는 기회를 제공하는 것을 목표로 하였다. 2012년 B과학고등학교에서 개설된 두 개의 미적분학 II 강좌를 수강하였던 14명의 학생들이 약 70일간 위키를 협력 문제해결 도구로 사용하여 지정된 위키 사이트에 접속하여 10개의 문제를 풀었다. 위키는 학생들의 흩어져 있는 사고과정을 공유되는 세계 내에 효과적으로 집적함으로써 상호학습이 이루어지는 것을 가능하게 하였다. 또한 학생들의 협력 문제해결의 패턴은 Lakatos(1976)의 증명과 반박과 비슷하게 ‘풀이와 반박’으로 특징지어졌는데 학생들은 이 과정을 통해 학교수학적 지식의 성장을 경험할 수 있었다. 실험 종료 후 실시된 인터뷰와 설문조사에서 담당교사와 학생들은 협력 문제해결 도구로서의 위키의 사용 경험에 대해 매우 긍정적인 반응을 보였다. 따라서 본 연구에서 위키는 수학적 지식의 사회적 측면을 경험하게 할 수 있는 가치 있는 수학교육 도구라고 평가되었다.

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