Opening Context What can a wooden stick and a measuring tape teach us about the gap between school mathematics and real engineering careers? The Atlantic Technological University Maths Enrichment Program addresses this question by bringing second-level students into authentic problem-solving scenarios beyond the standard curriculum. One representative challenge asks: how much heating oil remains in a horizontal cylindrical tank using only a dipstick and external measurements? This seemingly simple problem introduces students to applied trigonometry, geometric reasoning, and Python programming, skills explicitly sought by engineering employers but rarely integrated in traditional mathematics classrooms. Research Overview This research, published in the Physics Education Journal, examines enquiry-led, career-focused mathematics enrichment for secondary-level students across Ireland's Northwest region. Students solve a cylindrical oil tank problem through three scaffolded phases: derivation (integrating circle geometry, trigonometry, and Pythagoras to find oil cross-sectional area), implementation (translating the equation into Python code with proper edge-case handling), and visualisation (using an interactive Colab dashboard with real-time sliders and colour-coded thresholds). The activity reveals the counterintuitive non-linear relationship between oil depth and percentage full. Delivered entirely in a web browser with no installation required, the open-source notebook serves as both a teaching resource and a take-home artefact. Key Insights / Findings Two key insights emerge from this work. First, the non-linear relationship between oil depth and volume consistently surprises students—at one-quarter of the tank diameter, the tank is only approximately 15-18% full, not 25%. This counterintuitive discovery reinforces the value of precise mathematical modelling over heuristic estimation, a lesson transferable to countless engineering contexts. Second, the three-phase structure (derivation → code → visualisation) produces meaningful learning gains. Students who complete all three phases demonstrate a significantly improved ability to articulate how mathematics applies to engineering careers compared to those who receive only the final equation. The interactive visualisation phase, in particular, helps solidify abstract concepts by making the non-linear depth-volume relationship visible and manipulable in real time, transforming a purely mathematical expression into an intuitive engineering insight. Why It Matters (Impact & Relevance) This work addresses a persistent gap between school mathematics and workplace application. Employers consistently report that graduates possess theoretical knowledge but lack practical problem-solving experience. The Maths Enrichment Program directly addresses this disconnect by exposing students to engineering problems before they make career decisions, while also aiming to improve their critical thinking and problem-solving abilities. The oil tank activity demonstrates that sophisticated mathematical modelling requires no specialised equipment, only resourcefulness and deductive reasoning. This accessibility is particularly valuable for schools with limited STEM resources. Furthermore, the open-source Colab notebook enables educators nationwide to adopt the activity without cost or technical expertise. Societally, improving quantitative literacy and career awareness among secondary students contributes directly to Ireland's national priority of strengthening the STEM pipeline, particularly in the Northwest region where access to enrichment opportunities remains uneven. Wider Context / Application / Next Steps The three-phase pedagogical approach developed through this activity—derivation, implementation, and visualisation—provides a replicable template for teaching mathematically rich problems across diverse domains. Further enrichment classes are planned to cover additional practical applications where mathematical modelling transforms abstract concepts into tangible insights, drawing from areas such as structural analysis, resource optimisation, geometric design, and predictive modelling. The interactive Colab notebook format is readily adaptable to other mathematical contexts beyond liquid measurement, including any scenario where students must derive a relationship, translate it into executable code, and explore its behaviour through interactive visualisation. Each new application reinforces the same core message: mathematics is not a collection of isolated procedures but a powerful, transferable toolkit for understanding and solving real-world problems across engineering, science, and beyond.
Downes Fionn (Mon,) studied this question.