• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.717-754
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• 2015

As a design research, this study aims to identify students' collaborative problems solving patterns using the Wiki and design factors triggering MKB(mathematical knowledge building) in virtual environment. For 70 days, 14 Korean secondary gifted students, who enrolled in calculus II courses in one of gifted institutions in Korea, solved 10 math problems together using the Wiki. In this study, I considered five design factors; motivation, practice of LaTeX, norms of participation, epistemic agency, and two types of educational settings. The primary pattern emergent in students' collaborative problem solving process is identified as 'solutions and refutations' along the double helix consisting of the constructive line and the critical line, 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 is considered to be have been neglected in Korean educational environment but is emphasized as precious for doing mathematics in the field of mathematics education.