Teaching Principal Component Analysis Through Multiple Representations
Impacts on Conceptual Understanding, Problem Solving and Knowledge Transfer
I. Vlădăreanu (TU Delft - Electrical Engineering, Mathematics and Computer Science)
I.E.I. Rențea – Mentor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
M.A. Migut – Mentor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Jorge Abraham Martinez Castaneda – Graduation committee member (TU Delft - Electrical Engineering, Mathematics and Computer Science)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
Machine Learning has become a prominent component of STEM curricula, yet there remains a lack of standardized pedagogical frameworks for teaching it. Principal Component Analysis represents a typical educational challenge, requiring students to simultaneously coordinate algebraic manipulation, geometric intuition, and algorithmic thinking. This study evaluates how different combinations of instructional representations affect undergraduate students’ conceptual understanding, problem-solving performance, and knowledge transfer ability. An experiment was conducted with 27 first-year Computer Science students at TU Delft. Participants were assigned to one of two experimental conditions: a traditional static representations group or a multimedia-enhanced representations group. Quantitative analysis revealed that the static group significantly outperformed the interactive group in total post-test scores and knowledge transfer. No statistically significant differences were observed in conceptual understanding or problem-solving performance. Qualitative thematic analysis indicated a disconnect between perceived and actual learning: while students preferred the interactive widgets for building geometric intuition, these features may have introduced extraneous cognitive load, provided a false sense of understanding, or students simply ran out of time because interactive exploration takes longer.