RUME 28
2026
Alexandria, Virginia
Preliminary Design for Pilot: Bridging Conceptual Gaps in Orthogonal Projection in Applied Linear Algebra Through Principal Component Analysis (PCA) Visualization
Page: 1335
Students often first encounter orthogonal projection in linear algebra as a procedural formula, leading to disconnects between geometric intuition, vector decomposition, and symbolic manipulation. At the pre-pilot stage, this poster introduces a preliminary classroom design leveraging Principal Component Analysis (PCA) technique as a visual means and data-driven context to bridge these gaps. Students engage with 3D and 2D PCA figures, coordinating image, vector, and symbolic reasoning through guided tasks such as vector decomposition and dot product computations. Grounded in Multiple External Representations (MERs) theory and constructivism, the approach emphasizes representational fluency and conceptual reasoning. Targeted prompts and alignment rubrics address recurring misconceptions, including “along” vs. “onto” and PCA vs. regression. The expected outcome is improved conceptual understanding of orthogonal projection and a portable instructional toolkit for instructors. This poster prepares for pilot implementation and future data collection. Pilot results will guide further refinement and broader adoption of this instructional approach in undergraduate linear algebra courses.