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Educational Studies in Mathematics

, Volume 67, Issue 1, pp 19–35 | Cite as

A climbing class’ reinvention of angles

  • Anne Birgitte FyhnEmail author
Article

Abstract

A previous study shows how a twelve-year-old girl discovers angles in her narrative from a climbing trip. Based on this research, the girl’s class takes part in one day of climbing and half a day of follow-up work at school. The students mathematise their climbing with respect to angles and they express themselves in texts and drawings. Their written and drawn expressions are categorised into three different levels: recognition, description and contextual tool. In addition, these expressions are interpreted to be narrative or analytical. All the narrative expressions were categorised as level one or below, while some of the analytical expressions were categorised as belonging to higher levels. The research findings point at how to use analytical drawings in work with analytical texts in geometry.

Keywords

Analytical drawing Angle Climbing Contextual tool Embodied cognition Flow Van Hiele Mathematising Reinvention 

Notes

Acknowledgements

Thanks a lot to teacher Frode Hansen and his class for their contribution to this work. I also would like to thank Odd Valdermo both for his support and for all his critical advice. Thanks to Therese Nøst who has contributed with advice and comments regarding climbing. Thanks to Tore Brattli for his excellent library support, Linn Sollied Madsen for language checking and Bjørn Braathen for advice as for the structure of the manuscript. Finally I would like to thank Hanne, Inger Johanne and Trine for belaying the climbing students.

Supplementary material

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References

  1. Berthelot, R., & Salin, M. H. (1998). The role of pupil’s spatial knowledge in the elementary teaching of geometry. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century (pp. 71–78). Dordrecht: Kluwer.Google Scholar
  2. Berthoz, A. (2000). The brain’s sense of movement. Cambridge, MA: Harvard University Press.Google Scholar
  3. Clements, D. H. (2003). Teaching and learning geometry. In J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 151–178). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  4. Collins (2000). English dictionary and thesaurus. Aylesbury: HarperCollins.Google Scholar
  5. Csikszentmihalyi, M. (2000). Beyond boredom and anxiety. Experiencing flow in work and play. San Francisco: Jossey-Bass (Original work published in 1975).Google Scholar
  6. Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: Reidel.Google Scholar
  7. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: Reidel.Google Scholar
  8. Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Dordrecht: Kluwer.Google Scholar
  9. Fyhn, A. (2004). How can experiences from physical activities in the snow influence geometry learning? Paper at ICME 10 (10th International Congress of Mathematics Education, Copenhagen, 4th–11th July), Topic Study Group 10 Geometry http://www.icme-organisers.dk/tsg10/articulos/Fyhn_4_revised_paper.doc.
  10. Fyhn, A. (2006). A climbing girl’s reflection about angles. Journal of Mathematical Behavior, 25, 91–102.CrossRefGoogle Scholar
  11. Gjone, G., & Nortvedt, G. (2001). Kartlegging av matematikkforståelse. Veiledning til geometri F og I. Oslo: Directorate for Primary and Secondary Education.Google Scholar
  12. Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39, 111–129.CrossRefGoogle Scholar
  13. Grønmo, L. S., Bergem, O. K., Kjærnsli, M., Lie, S., & Turmo, A. (2004). ’Hva i all verden har skjedd i realfagene? Norske elevers prestasjoner i matematikk og naturfag i TIMSS 2003’: Acta Didactica 5, Vol 5. ILS: University of Oslo.Google Scholar
  14. Henderson, D. W., & Taimina, D. (2005). Experiencing geometry. Euclidean and non-Euclidean with history. New York: Cornell University.Google Scholar
  15. Johnsen, V. (1996). Hva er en vinkel? NOMAD Nordisk Matematikkdidaktikk/Nordic Studies in Mathematics Education, 4, 25–49.Google Scholar
  16. Kjærnsli, M., Lie, S., Olsen, R. V., Roe, A., & Turmo, A. (2004). Rett spor eller ville veier? Norske elevers prestasjoner i matematikk, naturfag og lesing i PISA 2003. Oslo: Universitetsforlaget.Google Scholar
  17. Krainer, K. (1991). Consequences of a low level of acting and reflecting in geometry learning – findings of interviews on the concept of angle. Proceedings of the 15th International Conference, Psychology of Mathematics Education, Vol. 2 (254–261). Assisi, Italy.Google Scholar
  18. Krainer, K. (1993). Powerful tasks: A contribution to a high level of acting and reflecting in mathematics instruction. Educational Studies in Mathematics, 24, 65–93.CrossRefGoogle Scholar
  19. KUF, Ministry of Education and Research (1996). Læreplanverket for den 10-årige grunnskolen. Oslo: Nasjonalt Læremiddelsenter.Google Scholar
  20. Lakoff, G., & Núñez, R. (2000). Where mathematics comes from. How the embodied mind brings mathematics into being. New York: Basic Books.Google Scholar
  21. Mitchelmore, M. C., & White, P. (2000). Development of angle concepts by progressive abstraction and generalisation. Educational Studies in Mathematics, 41, 209–238.CrossRefGoogle Scholar
  22. Murphy, P., & Elwood, J. (1998). Gendered learning outside and inside school: influences on achievement. In D. Epstein, J. Elwood, V. Hey, & J. Maw (Eds.), Failing boys?: Issues in gender and achievement (pp. 162–181). Buckingham: Open University Press.Google Scholar
  23. Nemirovsky, R., Borba, M., & Dimattia, C. (2004). PME special issue: Bodily activity and imagination in mathematics learning. Educational Studies in Mathematics, 57, 303–321.CrossRefGoogle Scholar
  24. Niss, M. (1999). Aspects of the nature and the state of research in mathematics education. Educational Studies in Mathematics, 40, 1–24.CrossRefGoogle Scholar
  25. Treffers, A. (1987). Three dimensions. A model of goal and theory description in mathematics instruction – The Wiskobas Project. Dordrecht: Reidel.Google Scholar
  26. van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54, 9–35.CrossRefGoogle Scholar
  27. van Hiele, P. M. (1986). Structure and insight. A theory of mathematics education. Orlando: Academic.Google Scholar
  28. Watson, A., & Tall, D. (2002). Embodied action, effect and symbol in mathematical growth. In A. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education Norwich, UK, 369–376.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Education, 1.592University of TromsφTromsoNorway

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