The study, led by researchers at Universidad Técnica de Manabí together with collaborators from the Autonomous Decentralized Government of Chone Canton and Universidad Laica Eloy Alfaro de Manabí, was designed as a descriptive, exploratory, non-experimental investigation with a quantitative approach. Its target population consisted of 1,817 third-year upper secondary students aged 15 to 17, from which a purposive sample of 843 students—46.40 percent of the reference population—was drawn from 21 institutions. Every selected student completed the diagnostic assessment, a 100 percent participation rate within the sample, though the authors caution that because selection depended on accessibility, institutional coordination, and student availability, the results cannot be generalized beyond the schools included.

The instrument itself was a five-task diagnostic test intended to probe the multidimensional construct of logical-mathematical reasoning, which the researchers define as encompassing conceptual understanding, procedural application, interpretation of mathematical representations, and contextualized problem solving. Each task was scored on an ordinal scale from 0 to 4 points using general criteria from an analytical rubric, and the five tasks carried equal weight. Summing the scores produced an overall result between 0 and 20 points, which mapped onto five performance bands: low (0–4), regular (5–9), good (10–14), very good (15–18), and excellent (19–20). The same scoring criteria and cut-off points were applied uniformly across all 21 institutions, and the archived structure of the test and its scoring rules are documented in the study’s supplementary material.

According to the available documentation, the test and rubric were reviewed by three specialists with experience in mathematics education, instrument design, and educational assessment, and a preliminary administration was conducted with secondary students outside the final sample to check the clarity of instructions and tasks. However, the authors are unusually candid about the limits of their records: the complete original rubric was not retained, individual task-level scores were unavailable, and the database contained only aggregated overall classifications. As a result, the team could not retrospectively estimate the internal consistency of the instrument or calculate inter-rater agreement, and they explicitly state that the performance categories should be interpreted as operational classifications rather than as fully psychometrically validated measures.

The statistical machinery behind the analysis was correspondingly careful. Because no student reached the excellent level, that empty category was excluded, leaving a 21-by-4 contingency table with 84 cells and 60 degrees of freedom. Assumption checks revealed that 57.14 percent of cells had expected frequencies below 5 and 28.57 percent below 1, violating the conditions for the standard asymptotic chi-square approximation. The researchers therefore turned to a Monte Carlo simulation, generating 100,000 tables under the null hypothesis of independence while preserving the marginal totals. The resulting association between institution and performance level was emphatically significant: χ²(60) = 392.62 with a Monte Carlo p-value of 0.00001 and a Cramer’s V of 0.394, indicating a substantial relationship between which school a student attended and where they landed on the performance scale.

Because the performance categories are ordinal, the team also applied a Kruskal–Wallis test with tie correction, coding the levels from low = 1 to very good = 4. This analysis corroborated the chi-square findings, yielding H(20) = 208.51, p < 0.001, with an overall effect size of ε² = 0.229. To locate where the differences actually lived, the researchers then ran all 210 possible pairwise comparisons among the 21 institutions using Dunn’s test with tie correction, adjusting significance values with the Holm procedure to control the error inflation inherent in so many simultaneous tests. Fifty-four of the 210 comparisons remained statistically significant after adjustment, while 156 did not—a pattern suggesting that the overall variability was concentrated in specific institutional contrasts rather than spread uniformly across every pair of schools.

Those contrasts were vivid. At Colón Arteaga García, no students were classified at the low level, and participants split evenly between the regular and good levels; the school posted higher performance ranks than 18 other institutions, differing significantly from all but Bejucal and Santa Mariana de Jesús. Bejucal was the only institution with students at the very good level and outperformed 13 schools. Santa Mariana de Jesús, 5 de Mayo, San Cayetano de Chone, and Eugenio Espejo all showed percentages at the good level above the overall figure of 5.93 percent. At the other end of the spectrum, El Pueblito de Río Grande had every single participant concentrated at the low level, while Oswaldo Castro Intriago and Carlos María Castro each recorded 96.67 percent of students there, followed by Gonzalo Abad Grijalva at 96.00 percent and Aníbal Andrade Solórzano at 95.00 percent. Adjusted standardized residuals confirmed these patterns, with the largest contributions to the overall association coming from the very good level at Bejucal and the low and good levels at Colón Arteaga García.

What the study deliberately does not do is explain why these gaps exist. No data were collected on students’ sex, socioeconomic status, prior academic achievement, previous experience with digital tools, device access, connectivity, or teacher characteristics, and the hierarchical clustering of students within schools was not modeled with multilevel procedures. The authors are emphatic that the results should not be used to construct rankings of institutional quality, since unequal sample sizes and the absence of explanatory variables make causal interpretation impossible. Variables such as school climate, teacher training, and resource availability are plausible but untested explanations, and the observed differences are presented strictly as exploratory evidence of institutional heterogeneity rather than as a verdict on any school’s effectiveness.

The assessment also has a complicated relationship with technology. It was administered in person, in a session of roughly 60 minutes supported by two collaborating teachers per institution, before any GeoGebra-supported classroom activities took place. GeoGebra—the free dynamic mathematics software that integrates algebraic, graphical, geometric, and numerical representations—was subsequently used in activities guided by shared general objectives, guiding questions, and achievement criteria, with students manipulating parameters, formulating conjectures, and comparing strategies across representations. But because the study included no comparison group, no equivalent pretest–posttest measurement, and no standardized implementation checklist, the authors state plainly that the software’s effectiveness cannot be evaluated and that no changes in reasoning can be attributed to it. The GeoGebra activities serve purely as the pedagogical context that followed the diagnosis, and the documentation does not even allow the number or duration of sessions to be reconstructed uniformly across the 21 schools.

That restraint reflects a broader lesson from the literature the team reviewed. Meta-analyses of GeoGebra research, including a 2025 synthesis of two decades of studies on dynamic visualization, report favorable average outcomes for mathematics learning but reveal considerable heterogeneity tied to research design, educational level, activity duration, mathematical content, and—critically—teacher mediation. From constructivist and sociocultural perspectives, dynamic representations foster exploration and discussion only when accompanied by guiding questions, feedback, and opportunities to explain and contrast strategies, while social cognitive theory suggests that teachers’ self-efficacy, outcome expectations, and institutional support shape how such tools are actually integrated. In other words, the software is never the active ingredient on its own; the interaction among tool, task, teacher, student, and context determines the outcome.

The practical implications, the authors argue, begin with diagnosis itself. Given that 93.48 percent of tested students sat in the two lowest performance bands, the participating institutions should consider conducting initial assessments before planning instructional sequences, organizing differentiated support, and separately monitoring conceptual understanding, procedural application, interpretation of representations, and problem solving—something the present instrument, with its single overall score, could not do. Future work, they suggest, should employ experimental or quasi-experimental designs with comparison groups, instruments with documented validity and reliability, calibrated rubrics with inter-rater agreement, and multilevel models that respect the clustered structure of classroom data. Longitudinal studies could track the stability and transfer of learning, while research on teacher professional development could examine how technological self-efficacy and dialogic teaching influence the use of dynamic visualizations. For now, the study stands as a rare, methodologically transparent baseline from a region often absent from the global mathematics education literature—and as a warning that the gap between what students can do and what curricula assume is wider, and more unevenly distributed, than many had hoped.

Subject of Research: Diagnostic assessment of logical-mathematical reasoning performance among secondary school students in Chone Canton, Ecuador

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

Article References: Avellán-Avellán, L. M., Arteaga-Solórzano, R. A., Párraga-Alava, R. C., Vargas-Zambrano, P. A., Moreira-Borja, G. H., Moreira-Menéndez, H. O., Zambrano-Arteaga, R. I., & Avellán-Avellán, M. C. (2026). Diagnostic performance in logical mathematical reasoning varies across secondary education institutions in Chone Canton Ecuador. Discover Education, 5(1), Article 992. https://doi.org/10.1007/s44217-026-02186-2

Image Credits: AI Generated

DOI: 10.1007/s44217-026-02186-2

Keywords: logical-mathematical reasoning, mathematics education, diagnostic assessment, secondary education, Ecuador, GeoGebra, institutional variability, chi-square test, Kruskal-Wallis test, Monte Carlo simulation, educational inequality, Chone Canton