Abstract
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.
Highlights
In Norway, vectors are part of the mathematics syllabus for the second year of upper secondary school, and students experience it as being a difficult theme (Fyhn, 2011)
This is a contrast to the traditional mathematics lessons at school, where many students participate for other reasons than intrinsic motivation
This paper focuses on students who are not familiar with vectors
Summary
In Norway, vectors are part of the mathematics syllabus for the second year of upper secondary school, and students experience it as being a difficult theme (Fyhn, 2011). The role of angles Poynter and Tall (2005) investigated teachers’ ideas about students’ difficulties in developing a vector concept They claim that «[t]he goal is to create conceptual knowledge with a relational understanding of the concepts ...» The VS builds on recommendations from Poynter and Tall (2005) because it aims to provide new insight into how students learn, and focuses on relations between the concepts vector and angle The importance of these relations is supported by Georgios, Panayotis and Athanasios (2005), who claim that the role of angles in cognitive procedures concerning vectors has been underestimated
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