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The Growth of School Mathematics: Korean Secondary Gifted Students' Collaborative Problem Solving Using The Wiki  

Lee, Seoung Woo (Seoul Science High School)
Publication Information
Journal of Educational Research in Mathematics / v.25, no.4, 2015 , pp. 717-754 More about this Journal
Abstract
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.
Keywords
Growth of School Mathematics; Collaborative Problem Solving; Double Helix; Solutions and Refutations;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 Clinkenbeard, P. R. (1991). Unfair expectations: A pilot study of middle school students' comparisons of gifted and regular classes. Journal For The Education Of The Gifted, 15(1), 56-63.   DOI
2 Cobb, P. (1994). Where Is the mind? constructivist and sociocultural perspectives on mathematical development. Educational Researcher, 23(7), 13-20.   DOI
3 Davidson, N., & Kroll, D. L. (1991). An overview of research on cooperative learning related to mathematics. Journal for Research in Mathematics Education, 22(5), 362-365.   DOI
4 Diezmann, C. M. & Watters, J. J. (2001). The collaboration of mathematically gifted students on challenging tasks. Journal For The Education Of The Gifted, 25(1), 7-31.   DOI
5 Eisner, E. W. (2001). The educational imagination: On the design and evaluation of school program. New York: Macmillan.
6 Fuks, H., & Pimentel, M. (2009). Studying response-structure confusion in VMT. In G. Stahl (Ed.), Studying Virtual Math Teams (pp. 373-398). New York, NY: Springer Science + Business Media.
7 Garrison, D. R., Anderson, T., & Archer, W. (2001). Critical thinking, cognitive presence, and computer conferencing in distance education. American Journal of Distance Education, 15(1), 7-23.   DOI
8 Garrison, D. R., & Arbaugh, J. B. (2007). Researching the community of inquiry framework: Review, issues, and future directions. The Internet and Higher Education, 10(3), 157-172.   DOI
9 Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, 35(4), 258-291.   DOI
10 Goos, M. & Galbraith, P. (1996). Do it this way! Metacognitive strategies in collaborative mathematical problem solving. Educational Studies in Mathematics, 30(3), 229-260.   DOI
11 Hurme, T. & Jarvela, S. (2005). Students' activity in computer-supported collaborative problem solving in mathematics. International Journal of Computers for Mathematical Learning, 10(1), 49-73.   DOI
12 Johnson, D. W., Johnson, R. T., & Smith, K. A. (1991). Active learning: Cooperation in the college classroom. Edina, MN: Interaction book company.
13 Kennedy, D. A., Archambault, F. X., & Hallmark, B. W. (1995). The effect of group composition on gifted and non-gifted elemenary students in cooperative learning groups. Storrs, CT: National Research Center on the Gifted and Talented, University of Connecticut.
14 Koschmann, T. (1996). Paradigm shifts and instructional technology: An introduction. In T. Koschmann (Ed.), CSCL: Theory and practice of an emerging paradigm (pp. 1-23). Mawha, NJ: Lawrence Erlbaum Associates, Publishers.
15 Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: The effects of cooperative learning and metacognitive training. American Educational Research Journal, 40(1), 281-310.   DOI
16 Krutetskii, V. A. (1976). The Psychology of Mathematical Abilities in Schoolchildren (J. Teller, Trans.). Chicago: University of Chicago Press.
17 Kulik, J. A. (2003). Grouping and tracking. In N. Colangelo & G. A. Davis (Eds.), Handbook of gifted education (pp. 268-281). Boston, MA: Allyn and Bacon.
18 Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge, UK: Cambridge University Press.
19 Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation (Learning in doing: Social, cognitive and computational perspectives). Cambridge, UK: Cambridge University Press.
20 Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29-63.   DOI
21 Lee, S. (2014). The growth of school mathematics: Korean secondary gifted students' collaborative problem solving using the Wiki. (Doctoral dissertation paper, University of Missouri- Columbia).
22 Lerman, S. (2000). The social turn in mathematics education research. In K Boaler (Ed.). Multiple perspectives on mathematics teaching and learning (pp. 19-44). Westport, CT: Alblex Publishing.
23 Li, A. K. F., & Adamson, G. (1992). Gifted secondary students' preferred learning style: Cooperative, competitive, or individualistic? Journal for the Education of the Gifted, 16(1), 46-54.   DOI
24 Litz, I. R. (2007). Student adoption of a Computer-Supported Collaborative Learning (CSCL) mathematical problem solving environment: The case of The Math Forum's Virtual Math Team (VMT) chat service. Ph.D. dissertation paper, Nova Southeastern University.
25 Matthews, M. (1993). Meaningful cooperative learning is key. Educational Leadership, 50(6), 64.
26 Moss, J., & Beatty, R. (2006). Knowledge building in mathematics: Supporting collaborative learning in pattern problems. International Journal of Computer-Supported Collaborative Learning, 1(4), 441-465.   DOI
27 Narasimhan, R. (2009). Incorporating current research, wikis, and discussion lists in a mathematics capstone course. PRIMUS, 19(1), 29-38.   DOI
28 Nason, R., & Woodruff, E. (2004). Online collaborative learning in mathematics: Some nesseary innovations. In T. S. Roberts (Ed.), Online Collborative Learning: Theory and Practice (Vol. Hershey, PA, pp. 103-131): Information Science Publishing.
29 Nason, R., & Woodruff, E. (2002). New ways of learning mathematics: Are we ready for it? Paper presented at the The International Conference on Computers in Education.
30 Nason, R., & Woodruff, E. (2003). Fostering authentic, sustained, and progressive mathematical knowledge-building activity in computer collaborative learning (CSCL) communities. Journal of Computers in Mathematics and Science Teaching, 22(4), 345-363.
31 NCTM. (1991). Professional standards for teaching mathematics. Reston, VA: The National Council of Teachers of Mathematics.
32 Neber, H., Finsterwald, M., & Urban, N. (2001). Cooperative learning with gifted and highachieving students: A review and meta-analyses of 12 studies. High Ability Studies, 12(2), 199-214.   DOI
33 Olsen, R. E. W. B., & Kagan, S. (1992). About cooperative learning. In C. Kessler (Ed.), Cooperative language learning: A teacher's resource book (pp. 1-30). Englewood Cliffs, NJ: Prentice Hall.
34 Ormrod, J. E. (2009). Human learning (5th ed.). Upper Saddle River, NJ: Pearson Prentice Hall.
35 Oxford, R. L. (1997). Cooperative learning, collaborative learning, and interaction: Three communicative strands in the language classroom. The Modern Language Journal, 81(4), 443-456.   DOI
36 Patrick, H., Bangel, N. J., Jeon, K. N., & Townsend, M. A. R. (2005). Reconsidering the issue of cooperative learning with gifted students. Journal For The Education Of The Gifted, 29(1), 90-108.   DOI
37 Reich, J., Murnane, R., & Willett, J. (2012). The State of Wiki Usage in U.S. K-12 Schools. Educational Researcher, 41(1), 7-15.   DOI
38 Peterson, E. (2009). Using a wiki to enhance cooperative learning in a real analysis course. PRIMUS, 19(1), 18-28.   DOI
39 Popper, K. (1963/2002). Conjectures and refutations: The growth of scientific knowledge. NY: Routledge Classics.
40 Reed, C. F. (2005). Mathematically gifted in the heterogeneously grouped mathematics classroom: What is a teacher to do? In S. K. Johnsen & J. Kendrick (Eds.), Math education for gifted students (pp. 17-31). Waco, TX: Prufrock Press.
41 Reynolds, B. E., Hagelgans, N. L., Schwingendorf, K. E., Vidakovic, D., Dubinsky, E., Shahin, M., et al. (1995). A practical guide to cooperative learning in collegiate mathematics (Vol. 37). Wasington, DC: The Mathematical Association of America.
42 Robinson, A. (1990a). Cooperation or exploitation? The argument against cooperative learning for talented students. Journal For The Education Of The Gifted, 14(1), 9-27.   DOI
43 Robinson, A. (1990b). Response to Slavin: Cooperation, consistency, and challenge for academically talented youth. Journal For The Education Of The Gifted, 14(1), 31-36.   DOI
44 Robinson, A. (2003). Cooperative learning and high ability students. In N. Colangelo & G. A. Davis (Eds.), Handbook of Gifted Education (3rd ed., pp. 282-292). Boston, MA: Allyn
45 Ruth, A., & Houghton, L. (2009). The wiki way of learning. Australian Journal of Educational Technology, 25(2), 135-152.
46 Sheehy, G. (2008). The Wiki as knowledge repository: Using a Wiki in a community of practice to strengthen K-12 education. emph TechTrends, 52(6), 55-60.   DOI
47 Sarmiento-Klapper, J. W. (2009). The sequential co-construction of the joint problem space. In G. Stahl (Ed.), Studying Virtual Math Teams (pp. 83-98). New York, NY: Springer Science + Business Media.
48 Scardamalia, M. (2002). Collective cognitive resposibility for the advancement of knoweldge. In B. Smith (Ed.), Liberal Education in a Knowledge Society (pp. 67-98). Peru, IL: Carus Publishing Company.
49 Scardamalia, M., & Bereiter, C. (2006). Knowledge building: Theory, pedagogy, and technology. In K. Sawyer (Ed.), Cambridge handbook of the learning sciences (pp. 97-118). New York: Cambridge University Press.
50 Schoenfeld, A. H. (1996). In fostering community of inquiry, must it matter that teacher knows "the answer"?, For the Learning of Mathematics, 16(3), 11-16.
51 Slavin, R. E. (1980). Cooperative Learning. Review of Educational Research, 50(2), 315-342.   DOI
52 Slavin, R. E. (1990a). Ability grouping, cooperative learning and the gifted. Journal of the Education of the Gifted, 14(1), 3-8.   DOI
53 Slavin, R. E. (1990b). Response to Robinson: Cooperative learning and the gifted: Who benefits? Journal For The Education Of The Gifted 14(1), 28-30.   DOI
54 Stahl, G. (2006a). Group Cognition: Computer Support for Building Collaborative Knowledge. Cambridge, MA: MIT Press.
55 Stahl, G. (2009c). Meaning making in VMT. In G. Stahl (Ed.), Studying Virtual Math Teams (pp. 505-527). New York, NY: Springer Science + Business Media.
56 Stahl, G. (2006b). Supporting group cognition in an online math community: A cognitive tool for small-group referencing in text chat. Journal of Educational Computing Research, 35(2), 103-122.   DOI
57 Stahl, G. (2009a). Introduction to part I. In G. Stahl (Ed.), Studying Virtual Math Teams(pp. 3-6). New York, NY: Springer Science + Business Media.
58 Stahl, G. (2009b). A chat about chat. In G. Stahl (Ed.), Studying Virtual Math Teams(pp. 7-16). New York, NY: Springer Science + Business Media.
59 Swan, M. (2002). Collaborative learning in mathematics: A challenge to our beliefs and practices. Chelmsford, Essex: Redlin.
60 Thom, R. (1992). Leaving mathematics for philosophy. In C. Casacuberta & M. Castellet (Eds.), Mathematical Research Today and Tomorrow: Viewpoints of Seven Fields Medalists (pp. 1-12). Berlin: Springer-Verlag.
61 Webb, N. M. & Palincsar, A. S. (1996). Group processes in the classroom. D. C. Berliner (Ed), Handbook of educational psychology (pp. 841-873). New York, NY: Macmillan.
62 Wee, J. D. (2007). Mathematical knowledge construction through the use of guided collaborative critique in a quasi-synchronous chat environment. Paper presented at the Association for Active Educational Researchers Conference (AARE 2007), Perth, Australia.
63 Wee, J. D. & Looi, C. K. (2009). A Model for Analyzing Math Knowledge Building in VMT. In G. Stahl (Ed.), Studying Virtual Math Teams (pp. 475-497). New York, NY: Springer Science + Business Media.
64 Williams, K. S., & Hardy, K. (1988). The Red Book of Mathematical Problems: Dover Publications.
65 Brandon, D. P. & Hollingshead, A. B. (1999). Collaborative learning and computer-supported groups. Communication Education, 48(2), 109-126.   DOI
66 Zemel, A., Xhafa, F., & Cakir, M. P. (2009). Combining Coding and Conversation Analysis of VMT Chats. In G. Stahl (Ed.), Studying Virtual Math Teams (Vol. 11, pp. 421-450). New York, NY: Springer.
67 이승우(2015). 학교수학이란 무엇인가? 수학교육학연구, 25(3), 381-405
68 Barbeau, E. J. (2000). Mathematical Fallcies, Flaws, and Flimflam: The Mathematical Association of America.
69 Ben-Zvi, D. (2007). Using wiki to promote collaborative learning in statistics education. Technology Innovations in Statistics Education, 1(1), 1-18.
70 Boaler, J. & Greeno, J. (2000). Identity, agency and knowing in mathematics worlds. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 171-200). Westport, CT: Alblex Publishing.
71 Brett, C., Nason, R. A., & Woodruff, E. (2002). Communities of inquiry among pre-service teachers investigating mathematics. Themes in Education, 3(1), 39-62.
72 Bruffee, K. A. (1995). Sharing our toys - Cooperative learning versus collaborative learning. Change (Jan/Feb), 12-18.   DOI
73 Carter, J. F. (2009). Lines of communication: Using a wiki in a mathematics course. PRIMUS, 19(1), 1-17.   DOI