Bridges in mathematical problem‑solving between rural and urban schools: a quasi‑experimental study in the Ecuadorian highlands

Abstract

This study assesses the impact of a non‑routine problem‑solving instructional sequence on mathematics achievement among upper‑secondary students in Ecuador’s Andean highlands, focusing on narrowing rural–urban gaps. We implemented a quasi‑experimental design combining propensity score matching (PSM) and difference‑in‑differences (DiD) to estimate average treatment effects (ATT) and heterogeneity. The 8–10‑week intervention comprised contextualized tasks, explicit modeling scaffolds, collaborative work, and rubric‑based formative assessment. The matched sample included 96 schools (48 treated, 48 comparison) and 5,742 students. Findings show significant gains for treated schools: an ATT of 0.23 standard deviations (95% CI [0.16, 0.31]) on the problem‑solving score, and an average marginal increase of 8.9 percentage points (95% CI [6.4, 11.4]) in reaching high achievement (≥ level 3). The adjusted rural–urban gap shrank by roughly 30% over the study period, driven by larger effects in rural schools (Treatment×Post×Rural = −2.6 points; p<0.001). Mediation analyses indicate that improvements in mathematics self‑efficacy and metacognitive strategies account for about 30% of the total effect. Robustness checks—CBPS, inverse probability weighting, event‑study and placebo tests—support causal interpretation. Results suggest that problem‑oriented, context‑aware, and offline‑friendly instructional sequences can improve substantive learning outcomes and help reduce territorial inequities in upper‑secondary mathematics at manageable costs. Policy and practice should institutionalize periodic “mathematics with meaning” cycles, strengthen teacher professional development, and maintain open repositories of contextualized tasks. Future research should estimate medium‑term persistence (6–12 months) and cost‑effectiveness to inform scaling.