Vectors: Concepts and Technologies to Improve Comprehension by Appealing to Vectors' Geometrical Nature (In-person Session and Hybrid Session)

Target Audience: 6th-12th Grade Physics, Math, and Physical Science Teachers

Presenter: Tim Truster, University of Tennessee

The concept of vectors has been challenging for physics students because it combines spatial reasoning with trigonometry as well as introducing new concepts. Yet this fundamental concept underlies many topics in science and engineering. Students that are confused by vectors often lag behind in other later subject areas.

This workshop proposes a novel and unified teaching approach by relating a vector’s abstract nature of magnitude and direction to its geometric nature as length and unit vector. This relationship provides students with a vector object that they can touch and feel as well as a holistic definition valid in one, two, and three dimensions.  

This workshop consists of three-hour morning and three-hour afternoon session. Travel and lunch reimbursement will be provided. 

The morning session discusses contemporary teaching pedagogies on four major topics: 1) The fundamental concept of vectors as magnitude and direction linked to the objects of length and unit vector, respectively. 2) The addition of vectors through the tip-to-tail and the motivation of decomposing into components by using the distributive property. 3) The use of interaction diagrams as a bridge to drawing forces on free body diagrams. 4) The process of drawing free body diagrams without immediately separating forces into components. 

The afternoon session demonstrates technologies and multimedia related to vectors. Two examples: 1) Online interactive demos are presented for graphical vector addition and computing components. 2) Teachers will be shown how to make a coordinate system by using a transparent cube and colored arrow stickers. Also, handouts will be provided on all topics covered and some sample problems will be solved together.