# Reconstruction of a Collaborative Mathematical Learning Process

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## Abstract

The study focused on the interaction between two secondary school students while they were working on computerized mathematical investigation tasks related to probability theory. The aim was to establish how such interaction helped the students to learn from one another, and how it may have hindered their learning process. The assumption was that interaction is beneficial for students if they can perform certain key activities, namely showing, explaining, justifying, and reconstructing their work. Both students attained mathematical level raising. However, the student who explained frequently and criticized himself attained more mathematical level raising than the student who did not explain her work frequently or criticize herself.

## Keywords

collaborative learning process model mathematical level raising computer simulation## Preview

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## References

- Boer, W., Bouwman, J., Van Dijk, B., Van der Eijk, E., Van de Giessen, C., De Goede, W. et al.: 1998,
*Moderne Wiskunde 7e Editie havo Bovenbouw Wiskunde A1 en B1-deel 1*[Modern Mathematics], Wolters-Noordhoff bv, Groningen.Google Scholar - Dekker, R.: 1994, ‘Graphs, small groups and the process of level raising’, in A. Antibi (ed.),
*Représentations graphique et symbolique de la maternelle à l'université, Tome 1*, Université Paul Sabatier, Toulouse, pp. 184–189.Google Scholar - Dekker, R. and Elshout-Mohr, M.: 1998, ‘A process model for interaction and mathematical level raising’,
*Educational Studies in Mathematics*35(3), 303–314.CrossRefGoogle Scholar - Dekker, R. and Elshout-Mohr, M.: 2004, ‘Teacher interventions aimed at mathematical level raising during collaborative learning’,
*Educational Studies in Mathematics*56(1), 39–65.CrossRefGoogle Scholar - Dekker, R., Elshout-Mohr, M. and Wood, T.: 2001, ‘Working together on assignments: Multiple analysis of learning events’, in J.V.D. Linden and P. Renshaw (eds.),
*Dialogic Learning: Shifting Perspectives to Learning, Instruction, and Teaching*, Kluwer Academic Publishers, Dordrecht, pp. 145–170.Google Scholar - Freudenthal, H.: 1973,
*Mathematics as an Educational Task*, Reidel, Dordrecht.Google Scholar - Kieran, C.: 2001, ‘The mathematical discourse of 13-year-old partnered problem solving and its relation to the mathematics that emerges’,
*Educational Studies in Mathematics*46, 187–228.CrossRefGoogle Scholar - Kieran, C. and Dreyfus, T.: 1998, ‘Collaborative versus individual problem solving: Entering another's universe of thought’, in A. Olivier and K. Newstead (eds.),
*Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education*, Vol. 3, PME, Stellenbosch, pp. 112–119.Google Scholar - Pijls, M.H.J.: 2001,
*Whoopy Trainer*(Version 1.0) [computer software], Antropi V.O.F., Almere.Google Scholar - Pijls, M.H.J., Dekker, R. and Van Hout-Wolters, B.H.A.M.: 2003, ‘Mathematical level raising through collaborative investigations with the computer’,
*The International Journal of Computers for Mathematical Learning*8(2), 191–213.CrossRefGoogle Scholar - PRINT: (1998), Reports of meetings with teachers that participated in the project ‘Project Invoering Nieuwe Technologieën’.Google Scholar
- Prent: (1999), Reports of meetings with teachers that participated in the project ‘Praktische Opdrachten en Nieuwe Technologieën’.Google Scholar
- Roschelle, J.: 1992, ‘Learning by collaborating: Convergent conceptual change’,
*The Journal of the Learning Sciences*2(3), 235–276.CrossRefGoogle Scholar - Sfard, A.: 2003, ‘Communicational conflict and learning agreement: What turns obstacles to mathematical communication into effective triggers for learning?’,
*Proceedings of the 10th European Conference for Research on Learning and Instruction*, Cooperativa Libraria Editrice Università di Padova, Padova, pp. 85–86.Google Scholar - Sfard, A. and Kieran, C.: 2001, ‘Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of student’ mathematical interactions',
*Mind, Culture, and Activity*8(1), 42–76.CrossRefGoogle Scholar - Teasley, S.D.: 1995, ‘The role of talk in children's peer collaborations’,
*Developmental Psychology*31(2), 207–220.CrossRefGoogle Scholar - Trognon, A.: 1993, ‘How does the process of interaction work when two interlocutors try to resolve a logical problem?’,
*Cognition and Instruction*11(3–4), 325–345.CrossRefGoogle Scholar - Van Hiele, P.M.: 1986,
*Structure and Insight*, Academic Press, Orlando.Google Scholar - Webb, N.M.: 1991, ‘Task-related verbal interaction and mathematics learning in small groups’,
*Journal of Research in Mathematics Education*22(5), 360–389.Google Scholar - Wood, T.: 1999, ‘Creating a context for argument in mathematics class’,
*Journal for Research in Mathematics Education*30(2), 171–191.CrossRefGoogle Scholar - Yackel, E., Rasmussen, C. and King, K.: 2000, ‘Social and sociomathematical norms in an advanced undergraduate mathematics course’,
*Journal of Mathematical Behavior*19, 275–287.CrossRefGoogle Scholar