Diagnostic performance in logical mathematical reasoning varies across secondary education institutions in Chone Canton Ecuador

Logical-mathematical reasoning is essential for interpreting representations, applying procedures, justifying relationships, and solving problems; however, evidence regarding students’ performance in Ecuadorian school contexts remains limited. The aim of this study was to characterize students’ diagnostic performance in logical-mathematical reasoning and to examine differences in its distribution across the participating educational institutions. A descriptive, exploratory, non-experimental study with a quantitative approach was conducted. A total of 843 third-year upper secondary school students, aged 15 to 17 years, from 21 educational institutions in Chone Canton, Ecuador, participated in the study. Logical-mathematical reasoning was assessed using a five-task diagnostic test, with each task scored from 0 to 4 points and aggregated into an overall score ranging from 0 to 20 points. Of the participants, 76.39% were classified at the low level, 17.08% at the regular level, 5.93% at the good level, and 0.59% at the very good level; no student reached the excellent level. Statistically significant differences were identified among institutions, χ²(60) = 392.62, p_MC = 0.00001, Cramer’s V = 0.394; H(20) = 208.51, p < 0.001, ε² = 0.229. The study provides a multi-institutional baseline of logical-mathematical reasoning in a relatively understudied Ecuadorian context. The findings may support the identification of educational needs and the planning of differentiated support according to students’ initial performance. Because no comparison group or quantitative pretest–posttest measurement was available, it was not possible to evaluate changes in logical-mathematical reasoning or attribute the results to the use of GeoGebra.