# SAIP2016

4-8 July 2016
Kramer Law building
Africa/Johannesburg timezone
The Proceedings of SAIP2016 published on 24 December 2017
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# Understanding of vector addition and subtraction by first year university students: graphical versus algebraic methods

Presented by Dr. Emanuela CARLESCHI on 5 Jul 2016 from 11:10 to 11:30
Type: Oral Presentation
Track: Track E - Physics Education

## Abstract

Vectors constitute a fundamental building block for any introductory physics course at university level. Vector concepts are used in topics such as motion, forces, linear and angular momentum, and torque, and therefore need to be properly mastered by students. The understanding of vector addition and subtraction by first year university students was investigated for both the arrow representation and the algebraic notation (using unit vectors <b>i</b> and <b>j</b>) in a generic mathematical context. In particular, students enrolled in the first semester module <i>General Physics for Earth Sciences</i> at the University of Johannesburg were given a series of tests dealing with vectors in one- and two-dimensions. Questions in these tests were structured in such a way as to probe students’ capabilities in manipulation of vectors for different relative orientations (with aligned and/or opposing <i>x</i>- and <i>y</i>-components) for both graphical and algebraic methods. Students’ performance shows that difficulties are mostly found in the use of the graphical representation. The average performance in the <i>i-j</i> format was excellent. In some of these questions the average score was higher by 60% with respect to the score in the arrow-format-type questions. Some of the trends include scores being comparatively higher for vectors in 1D than in 2D, as well as for the addition than the subtraction of vectors. For subtraction of vectors in one-dimension, the score was definitively worse when the vector to be subtracted points in the negative direction. Interestingly, there is no such trend for vectors in 2D. Having positive or negative <i>x</i>- and <i>y</i>-components does influence the solution path in the subtraction of 2D vectors. Post-test interviews were carried out in order to understand the lack of understanding and the misconceptions leading to mistakes, which will also be reported.

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## Place

Location: Kramer Law building
Address: UCT Middle Campus Cape Town
Room: 2B

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