8. februar 2019

# A Study and Research Path

"A Study and Research Path" - [4.3Mb]

IND's studenterserie nr. 71. Specialerapport. Matematik.

Louise Uglebjerg, 2019.

Vejleder: Carl Winsløw

## 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 interrelation 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. This has contributed to an understanding of why mathematics and physics, that historically are highly interrelated, have separated more and more over the years.

The examination of curricula, written exam problems, and textbooks have revealed that the mathematical notion of vectors is divided into an algebraic and a geometric approach. Since vectors are used to model the two 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 useful in physics.

These findings have been used to design a Study and Research Path on vectors. The idea was to combine mathematics and physics in the introduction to vectors, in order 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 it did not turn out as expected. None of the students developed a notion of vectors that was useful in the application to the physical problem they were asked to solve. However, the test of the design showed that it is highly relevant to keep working on alternative ways of teaching.