2024 ASEE Annual Conference & Exposition

Engineering Statics is a fundamental engineering science course taken by many, if not most, engineering students. A basic skill of Statics is the addition of vectors (also referred to as vector resultants). Typically, textbook and exam questions on this topic are algebraic in nature, with less attention given to graphical interpretation and representation. The authors of this study are interested in investigating the relationship between students’ algebraic and graphical reasoning skills. The following research questions have been posed and are being studied:

R1. Does mastery of vector algebra imply mastery of graphical interpretations of vector addition?
R2. Do students adopt the habit of redrawing generic figures to scale when given particular parameter values?

To answer these questions, the authors draw on their common approach to testing students on this and related topics. In particular, test questions on vector addition require students to perform both the algebraic calculations as well as a corresponding sketch, to good scale and proportion. The results demonstrate that in general, a moderate number of students who do not attain the correct calculated values, nevertheless show some ability to achieve a reasonably accurate corresponding diagram. This suggests that use of graphical reasoning is a valid means to develop knowledge and skills with vectors.