RUME 27
2025
Alexandria, Virginia
Reasoning About Linear Combinations and Span in a Digital Game
Page: 792
In this paper we analyze the reasoning of five students who were playing a 3-dimensional digital video game called Vector Unknown: Echelon Seas. The intention of Stage 4 of the video game is to give students experience with Numeric and Geometric representations of linear combinations of vectors in the context of a pirate throwing a grappling hook to reach an anchor. We illustrate three types of Numeric reasoning, and four types of Geometric reasoning students used to solve these puzzles. For each reasoning example, we discuss issues related to which vectors the player should choose so that the anchor is within the span of the vectors, and which scalars the player should choose so that the grappling hook ends precisely at the anchor.