RUME 27
2025
Alexandria, Virginia
Linear Algebra Student Thinking of Magnitude, Unit Size, and Coordinates
Page: 413
This study explores how linear algebra students reason with three entities: magnitude, unit size, and coordinates in change of coordinate systems during teaching experiments. Two conceptual frameworks are employed in this study. The first framework, the coordinate system framework, was developed prior to the study and is used to frame a larger study that includes clinical interviews and teaching experiments. The second framework, the entities framework, was developed from the results of clinical interviews and is used to analyze student work from the teaching experiments. Students interacted with a GeoGebra applet that creates coordinate planes using matrices. The results present how students establish relationships among the three entities while working with the applet and how they represent their reasoning through matrix entries.