What happens when a climber falls? Young climbers mathematise a climbing situation

Anne Birgitte Fyhn 1 *
More Detail
1 Department of Education, UiT – The Arctic University of Norway, Tromsø, Norway
* Corresponding Author
EUR J SCI MATH ED, Volume 5, Issue 1, pp. 28-42. https://doi.org/10.30935/scimath/9495
OPEN ACCESS   1085 Views   937 Downloads
Download Full Text (PDF)


Students in Norway and other countries experience vectors as a difficult topic. Four young skilled climbers, who all did well in mathematics at school, participated in the Vector Study (VS). They participated for free and each lesson lasted until the students decided it was over. The idea was to investigate how climbing may function as a basis for students’ development of a vector concept. The teaching goal was the parallelogram law of vector addition. The students investigated what happens when a climber falls. They discussed the situation, and they tested it out in practice. They also performed a supporting activity, a rope-pulling situation, which provides insight into what happens in the climbing situation. The students’ development is analysed by identifying a) Bishop’s six basic activities, b) the role of angles, and c) manipulation of mental objects. The analysis reveals that relations between a vector’s magnitude and direction was central in the students’ investigations. It is important that students develop two aspects of vectors before the parallelogram law of addition is introduced. These are a) relations between angles and vectors, and b) the zero vector.


Fyhn, A. B. (2017). What happens when a climber falls? Young climbers mathematise a climbing situation. European Journal of Science and Mathematics Education, 5(1), 28-42. https://doi.org/10.30935/scimath/9495


  • Andersen, T., Jasper, P., Natvig, B. and Viken F. (2007). Giga. Matematikk R1. Programfag i studiespesialiserende utdanningsprogram. Oslo, Norway: N.W. Damm & søn AS.
  • Bishop, A. J. (1988). Mathematics Education in its Cultural Context. Educational Studies in Mathematics, 19, 179-191.
  • Dawson, S. (2015). Learning mathematics does not (necessarily) mean constructing the right knowledge. For the learning of mathematics, 35 (3), 17-22.
  • Dewey, J. (1998). How we think. A restatement of the relation of reflective thinking to the educative process. Boston/New York: Houghton Mifflin Company. Original work published 1933.
  • Eriksen, T. Hylland (2001). Kultur, kommunikasjon og makt [Culture, communication and power]. In T. Hylland Eriksen (Ed.). Flerkulturell forståelse [Multicultural understanding]. Second edition (pp. 53-66). Oslo, Norway: Universitetsforlaget.
  • Freudenthal, H. (1973). Mathematics as an Educational Task. Dordrecht, Netherlands: D. Reidel.
  • Freudenthal, H. (1983). Didactical Phenomenology of Mathematical Structures. Dordrecht, Netherlands: D. Reidel.
  • Freudenthal, H. (1991). Revisiting Mathematics Education. China Lectures. Dordrecht, Netherlands: Kluwer Academic Publishers.
  • Fyhn, A. (2006). A climbing girl’s reflections about angles, Journal of mathematical behaviour, 25, 91-102.
  • Fyhn, A. B. (2008). A climbing class’ reinvention of angles, Educational studies in mathematics, 67 (1), 19-35.
  • Fyhn, A. B. (2009). Video: Vectors in climbing, NDLA Norsk Digital Læringsarena [Norwegian Digital Learning Arena]. http://ndla.no/nb/node/46170?from_fag=56, (accessed May 2016).
  • Fyhn, A. B. (2011). Introduksjon til vektorer i norske matematikklæreverk og i en klatrefilm. NOMAD Nordic Studies in Mathematics Education, 16 (3), 5-24.
  • Fyhn, A. B., Nutti, Y. Jannok, Eira, E. J. Sara., Børresen, T., Sandvik, S. O. and Hætta, O. E. (2015a). Ruvden as a basis for the teaching of mathematics: A Sámi mathematics teacher’s experiences. In E. S. Huaman and B. Sriraman (Eds.), Indigenous Universalities and Peculiarities of Innovation. Advances in Innovation Education (pp. 169-186). Rotterdam/Boston/Taipei: Sense Publishers.
  • Fyhn, A. B., Dunfjeld, M., Dunfjeld Aagård, A., Eggen, P. & Larsen, T. M. (2015b). Muligheter og utfordringer ved sørsamisk ornamentikk i matematikkfaget [Possibilities and challenges with including south Sámi ornamentation in school mathematics], Tangenten, 26 (4), 5-11.
  • Fyhn, A. B., Harbrecht, J. and Kristiansen, J. (under review a). Utforskende mathematikk på musikklinja [Investigative mathematics in the music program]. Under review by Tangenten – tidsskrift for matematikk i skolen. Bergen, Norway: Caspar.
  • Fyhn, A. B., Teig, V. T. and Pedersen, S. S. (under review b). Grunnleggende matematisering i småskolen [Basic mathematisation in lower grades]. Under review by Tangenten – tidsskrift for matematikk i skolen. Bergen, Norway: Caspar.
  • Gay, G. (2016). Cultural diversity and multicultural education. Curriculum Inquiry, 49 (1), 48-70.
  • Georgios, P., Panayotis, S. and Athanasios, G. (2005). The role of angle in understanding the vectors. Paper presentation at The 4th Mediterranean Conference on Mathematics Education, January 28-30. Palermo, Italy: http://www.math.uoa.gr/me/faculty/spirou/THE%20ROLE%20OF%20ANGLE%20IN%20THE%20UNDERSTANDING%20OF%20VECTORS.pdf, (accessed June 2016)
  • Harel, G. and Trgalová, J. (1996). Higher Mathematics Education. In A. B. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick and C. Laborde (Eds.) International handbook of mathematics education (pp. 675-700). Dordrecht, Netherlands: Kluwer Academic Publishers.
  • Hayfa, N. (2006). Impact of language on conceptualization of the vector. For the learning of mathematics, 26 (2), 36-40.
  • Van Hiele, P. M. (1986). Structure and Insight. A Theory of Mathematics Education. Orlando, Florida: Academic Press.
  • Klausen, A. M. (1992). Kultur, mønster og kaos. [Culture, pattern and chaos] Oslo, Norway: Ad Notam Gyldendal A/S.
  • Maracci, M. (2006). On students’ conceptions in vector space theory. In J. Novotná, H. Moraová, M. Krátká and N. Stehlíková (Eds.) Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, Vol 4, pp. 129-136.
  • Poynter, A. and Tall, D. (2005). What do mathematics and physics teachers think that students will find difficult? A challenge to accepted practices of teaching. Proceedings of the sixth British Congress of Mathematics Education, 128-135. http://www.bsrlm.org.uk/IPs/ip25-1/BSRLM-IP-25-1-17.pdf, (accessed June 2016).
  • Rosenbloom, P. C. (1969). Vectors and symmetry. Educational Studies in Mathematics, 2, 405-414.
  • Sandoval, I. and Possani, E. (2016). An analysis of different representations for vectors and planes in ³. Educational Studies in Mathematics, 92, 109-127.
  • Yin, R. K. (2009). Case Study Research. Design and Methods (4th ed.). Thousand Oaks, California: Sage Publications Inc.