2026 ASEE Annual Conference & Exposition

In computer science education, eigenvectors and eigenvalues are typically introduced in abstract linear algebra contexts and later reinforced through practical data analysis tasks, including Principal Component Analysis (PCA) applications such as image compression.
While such PCA based activities correctly present eigenvectors as a coordinate system for re expressing data, students frequently experience them as abstract mathematical artifacts rather than as representations whose structure can be justified through physical experience.

In this experience paper, we reflect on an instructional sequence implemented in a summer linear algebra course with a small student cohort, using LEGO Education SPIKE to reposition eigenvectors as learned coordinate systems that validate, rather than replace, student intuition.

Students first collect distance sensor data from a mobile robot interacting with a physical environment and apply PCA to uncover dominant and secondary patterns of variation.
The resulting eigenvectors align with quantities students already find meaningful, such as overall distance and left right imbalance, yet emerge without being specified in advance.
In a second phase, the robot interprets new sensor readings using these learned eigencoordinates, transforming raw measurements into action relevant quantities governing forward motion and rotation.

From an instructor’s perspective, the most powerful learning moments occur when students recognize that PCA does not produce something surprising but rather justifies what they intuitively expected through a principled mathematical process.
We argue that this embodied two phase use of PCA helps students understand eigenvectors as meaningful coordinate systems grounded in experience, rather than as arbitrary geometric constructs.