Advertisement

Educational Studies in Mathematics

, Volume 65, Issue 3, pp 309–329 | Cite as

Reconstruction of a Collaborative Mathematical Learning Process

  • Monique PijlsEmail author
  • Rijkje Dekker
  • Bernadette Van Hout-Wolters
Article

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

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. Freudenthal, H.: 1973, Mathematics as an Educational Task, Reidel, Dordrecht.Google Scholar
  7. 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
  8. 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
  9. Pijls, M.H.J.: 2001, Whoopy Trainer (Version 1.0) [computer software], Antropi V.O.F., Almere.Google Scholar
  10. 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
  11. PRINT: (1998), Reports of meetings with teachers that participated in the project ‘Project Invoering Nieuwe Technologieën’.Google Scholar
  12. Prent: (1999), Reports of meetings with teachers that participated in the project ‘Praktische Opdrachten en Nieuwe Technologieën’.Google Scholar
  13. Roschelle, J.: 1992, ‘Learning by collaborating: Convergent conceptual change’, The Journal of the Learning Sciences 2(3), 235–276.CrossRefGoogle Scholar
  14. 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
  15. 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
  16. Teasley, S.D.: 1995, ‘The role of talk in children's peer collaborations’, Developmental Psychology 31(2), 207–220.CrossRefGoogle Scholar
  17. 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
  18. Van Hiele, P.M.: 1986, Structure and Insight, Academic Press, Orlando.Google Scholar
  19. 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
  20. Wood, T.: 1999, ‘Creating a context for argument in mathematics class’, Journal for Research in Mathematics Education 30(2), 171–191.CrossRefGoogle Scholar
  21. 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

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Monique Pijls
    • 1
    Email author
  • Rijkje Dekker
    • 1
  • Bernadette Van Hout-Wolters
    • 1
  1. 1.Graduate School of Teaching and LearningUniversiteit van AmsterdamAmsterdamThe Netherlands

Personalised recommendations