Speaker
Description
In this talk, we will discuss a game within the video game Vector Unknown:Echelon Seas (VUES) that focuses on matrix multiplication. VUES was designed by a group of students at Arizona State University in collaboration with mathematics educators and computer scientists. The 3D video game allows students to select one of four matrices (represented by cannonballs) and one of four vectors (represented by a cannon) and fire the cannonball at a ship (represented with a target vector) to practice and interpret matrix multiplication that could be leveraged in a first-year linear algebra course. In addition to a symbolic matrix equation, players are also presented with a geometric representation of the matrix as a lattice generated by the column vectors of the chosen matrix.
We conducted several paired teaching experiments with three students from a northeastern university who had already taken linear algebra. During the paired teaching experiments we asked the students to play the game and explain their thinking as they progressed through the level and asked follow-up questions when clarification was needed. We analyzed the results qualitatively and developed a list of student strategies which we highlight during the talk. We divided these strategies into two categories depending on the information from the game the students leveraged for their reasoning: numeric and geometric. One example a student’s numeric strategy was to selective compute an part of the matrix multiplication to eliminate potential combinations of matrices and vectors by focusing on a coordinate in the target vector. Another strategy involved students leveraging the geometric supports provided to check the result of the multiplication.
In this talk, we discuss the student strategies we observed and they contributed to students not only learning about matrix multiplication computationally, but also deepening their understanding of the underlying geometric at play.