[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-160108-en":3,"doc-seo-160108-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},160108,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1786009248482753345",8,"Research & Report","Learning Principal Component Analysis through an Embodied Classroom Experience","In computer science education, eigenvectors and eigenvalues are often taught in abstract linear algebra and later reinforced through PCA tasks such as image compression. Students may then treat eigenvectors as mathematical artifacts rather than as representations justified by experience. This experience paper describes an instructional sequence in a summer linear algebra course using LEGO Education SPIKE to reposition eigenvectors as learned coordinate systems.","Paper ID \\#50757  \nLearning Principal Component Analysis through an Embodied Classroom Experience  \nDr. Abbas Attarwala, California State University, Chico  \nI am currently serving as an Associate Professor in Computer Science at California State University, Chico. With 14 years of extensive teaching experience in the field of Computer Science, I have taught at both the University of Toronto and Boston University. My passion for teaching and utilizing technology in the classroom has been recognized with the prestigious Gerald and Deanne Gitner Family Award for Innovation in Teaching with Technology, which I received in 2020 at Boston University. I received the International Wildcat Outstanding Faculty of 2022-23 at California State University, Chico for my teaching.  \nProf. Jaime Raigoza, California State University, Chico  \n©American Society for Engineering Education, 2026  \nLearning Principal Component Analysis through an Embodied  \nClassroom Experience  \nAbstract  \nIn 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.  \nStudents 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.  \nFrom 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.  \n1 Introduction  \nEigenvectors and eigenvalues are foundational concepts in computer science and engineering, appearing prominently in signal processing algorithms, machine learning, and in the analysis and control of dynamical systems [1, 2] . However many students struggle to explain what eigenvectors mean beyond formal definitions and computation steps [3, 4] . In our own teaching, we repeatedly see students who can carry out eigenvector and eigenvalue calculations correctly but still experience eigenvectors as arbitrary geometric objects whose relevance is confined to textbook exercises.  \nIn instructional settings, eigenvectors are frequently re-visitted through PCA, often using static data analysis tasks such as image compression [5, 6] . Image compression using PCA effectively demonstrates variance, dimensionality reduction, and reconstruction error and correctly presents eigenvectors as an orthogonal coordinate system learned from the data. However, these activities often emphasize a retrospective use of representation: eigenvectors are learned from a fixed dataset and then used to re-express that same dataset after the fact. As a result, students can complete the activity with","cbCaibHi7ooHki7y","https://ap.wps.com/l/cbCaibHi7ooHki7y","pdf",17559909,1,19,"English","en",105,"# Introduction\n# Literature Review\n# Classroom Implementation\n## Data Collection\n## PCA Computation\n## Robot Control\n# Practical Considerations and Sensor Robustness\n# Key Pedagogical Points\n# Conclusion","[{\"question\":\"Why do students struggle to understand eigenvectors beyond formal computation?\",\"answer\":\"Many students can compute eigenvectors and eigenvalues correctly but still view eigenvectors as arbitrary geometric objects tied only to textbook exercises.\"},{\"question\":\"How does the proposed approach teach PCA differently from image-compression activities?\",\"answer\":\"It emphasizes prospective use of learned representations: students learn a coordinate system from past sensor experience and then apply it to interpret new readings in real time.\"},{\"question\":\"What is the role of the LEGO Education SPIKE robot in the learning sequence?\",\"answer\":\"Students collect paired distance sensor data from a mobile robot, apply PCA to learn orthogonal eigencoordinates, and then use those eigencoordinates as action-relevant quantities for speed and steering.\"}]","Learning Principal Component Analysis through an Embodied Classroom Experience | 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