From Time-Series Analysis to PCA Clustering: Exploring the Impact of Graphing Quadratic Worksheets on Mathematical Visual Thinking Skills

Ria Noviana Agus; Rina Oktaviyanthi; Usep Sholahudin

doi:10.22342/jpm.v19i1.pp119-140

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Abstract

The effectiveness of visualization tools in enhancing mathematical visual thinking skills, particularly for quadratic functions, remains underexplored. This study evaluates the impact of quadratic graph visualization worksheets on these skills using Time-Series and PCA Clustering approaches. The research involved 60 first-year Calculus students focusing on quadratic functions. A quantitative methodology was applied, with Time-Series analysis tracking score changes over time and PCA Clustering grouping students based on improvement patterns. Results revealed significant variations in score changes after using the worksheets. The highest positive score change reached 19 points, while PCA Clustering identified three student groups: minimal or negative changes (Cluster 0), moderate improvements (Cluster 1), and significant increases (Cluster 2). The findings demonstrate the potential of quadratic graph visualization worksheets to improve mathematical visual thinking skills, though the degree of enhancement varies across individuals. This research highlights the need for instructional tools that accommodate diverse learning trajectories and provides insights into the effectiveness of graph-based methods in mathematics education. It also advocates for refined analytical approaches in evaluating student learning outcomes.

Keywords

Cluster Analysis Graphing Quadratic Worksheet Mathematical Visual Thinking Skills Principal Component Analysis Time-Series Analysis

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Agus, R. N., Oktaviyanthi, R., & Sholahudin, U. (2025). From Time-Series Analysis to PCA Clustering: Exploring the Impact of Graphing Quadratic Worksheets on Mathematical Visual Thinking Skills. Mathematics Education Journal, 19(1), 119–140. https://doi.org/10.22342/jpm.v19i1.pp119-140

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Hawes, Z., & Ansari, D. (2020). What explains the relationship between spatial and mathematical skills? A review of evidence from brain and behavior. Psychonomic Bulletin and Review, 27(3), 465–482. https://doi.org/10.3758/S13423-019-01694-7

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Howell, R. A. (2021). Engaging students in education for sustainable development: The benefits of active learning, reflective practices and flipped classroom pedagogies. Journal of Cleaner Production, 325, 129318. https://doi.org/10.1016/J.JCLEPRO.2021.129318

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Iatrellis, O., Savvas, I., Fitsilis, P., & Gerogiannis, V. C. (2021). A two-phase machine learning approach for predicting student outcomes. Education and Information Technologies, 26(1), 69–88. https://doi.org/10.1007/S10639-020-10260-X

Kahu, E. R. (2013). Framing student engagement in higher education. Studies in Higher Education, 38(5), 758–773. https://doi.org/10.1080/03075079.2011.598505

Khandare, A., Agarwal, N., Bodhankar, A., Kulkarni, A., Mane, I. (2023). Analysis of python libraries for artificial intelligence. In V.E. Balas, V. B. Semwal, A. Khandare (Eds.), Intelligent Computing and Networking. Lecture Notes in Networks and Systems. Springer, Singapore. https://doi.org/10.1007/978-981-99-0071-8_13

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From Time-Series Analysis to PCA Clustering: Exploring the Impact of Graphing Quadratic Worksheets on Mathematical Visual Thinking Skills

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