Predicting success in first year quantitative courses: an open engineering math readiness score for early levelling decisions

Mathematics readiness at entry remains critical for success in first-year engineering programs, yet many institutions lack transparent, reusable tools to diagnose risk and design levelling policies. This study develops and evaluates an open Engineering Mathematics Readiness Score (EMRS) using two publicly available datasets: the UCI Student Performance dataset in secondary-school mathematics and the international SMARVUS dataset on statistics and mathematics anxieties and related variables in university students (12,570 learners, 35 countries). We first compare several supervised learning models and then adopt a parsimonious logistic regression based primarily on prior quantitative grades, complemented by benchmark analyses with contextual and affective variables. The model achieves strong within-dataset discrimination in both development settings, with bootstrap confidence intervals and calibration analyses used to qualify uncertainty and probabilistic behaviour. Exploratory cross-dataset transfer suggests that EMRS retains useful ranking value across secondary- and university-level quantitative-course contexts, although these datasets are treated as related proxy environments rather than identical constructs and require cautious interpretation under dataset shift. Subgroup analyses by gender, school type, and country indicate that local calibration remains necessary, particularly where recall varies across subgroups. A cost-sensitive threshold analysis translates EMRS into concrete levelling-policy options, explicitly balancing the cost of missing at-risk students against the cost of over-referral. A pilot case study with 30 first-year engineering students at a Latin-American university shows that EMRS bands (high, moderate, needs remediation) align meaningfully with final outcomes in Calculus I. All code, configuration files, and an easy-to-use command-line tool (EMRS-CLI) are released as open resources, enabling institutions to compute EMRS from simple diagnostic data and to simulate levelling policies for engineering mathematics. The released EMRS-CLI should therefore be interpreted as a transparent baseline tool that supports portability with local verification, threshold tuning, and recalibration.