Seeing Where Learning Breaks Down: Design and Simulation-Based Demonstration of a Python and Power BI Dashboard for Topic-Level Mastery in High-School Calculus and Trigonometry

Author

Jannathul Firdous, Shajahan Abdul Salam


Abstract

 Secondary mathematics teachers record marks question by question, but gradebooks usually keep one total per test. A total hides the topic a student has not yet mastered. This paper presents the design of a low-cost dashboard that turns item-level marks into topic-level mastery views for upper-secondary calculus and trigonometry, and demonstrates it on a simulated dataset. Marks entered in a spreadsheet are validated, pseudonymised and aggregated by a short Python (pandas) script. They are shown in Microsoft Power BI as a class heat map, a re-teach list, a student profile and a topic trend view, each linked to one classroom decision. To test the tool without using student data, we simulated two Grade 11 sections (60 students, 32 questions, four assessments, six topics) with a logistic model of performance. In it, 55 topic-specific learning gaps were deliberately planted, including a prerequisite link between limits and differentiation. The script processed 1,917 item scores in 0.13 seconds and caught all three deliberately injected data-entry errors. The topic view flagged 74.5% of the planted gaps. A total-only view, which flags every topic of a student below 60% overall, flagged 41.8%. Precision rose from 27.4% to 43.6%. Across 100 repeated simulations, mean sensitivity was 79.3% for the topic view and 42.7% for the total-only view. The advantage held at every cut-off from 45% to 75% and at every gap size tested. Fifteen of the 33 students with an overall total of 70% or more had at least one topic in the re-teach band, most often trigonometric identities. The planted link between limits and differentiation was visible in the dashboard. The design borrows the idea of leading indicators from safety-critical industries. The paper discusses privacy safeguards under Saudi Arabia's Personal Data Protection Law, the limits of simulated evidence, and a planned classroom evaluation.


Keywords

learning analytics, teacher dashboard, formative assessment, simulation, calculus, trigonometry, Power BI, Python, secondary mathematics, Saudi Arabia



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References


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