A study and research path on vectors in mathematics and physics – Københavns Universitet

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A study and research path on vectors in mathematics and physics

Defense of MSc thesis in mathematics by Louise Uglebjerg

Supervisors: Carl Winsløw and Britta Jessen

Censor:  Nicole Koefoed

Abstract:

This thesis gives a description of the development of the notion of vectors in the scientific fields of mathematics and physics respectively. It includes a description of the interaction between the notion in the two fields, because it gives some explanations why high school students struggle with the notion of vectors. Also the development of the notion of vectors in mathematics and physics in the context of high school teaching will be described. The examination of curricula, written exam problems and textbooks has revealed that the mathematical notion of vectors is divided into an algebraic and a geometric approach. Since vectors are used to model the tqo or three dimensional spaces in physics, the geometric approach is more useful in physics than the algebraic. However,  the geometric branch in mathematics does generally not include the approaches that are most useful in physics.

These findings have been used to design a study and research path on vectors. The idea was to utilise the motivations from physics and to make the applications in physics more obvious. The design was tested in a first year high school class, but did not turn out as expected. None of the students developed a notion of vectors that was useful in application to the physical problems they were asked to solve. However, the test of the design showed in other ways the relevance of working on alternative ways of teaching.