Active methodologies supported by interactive digital resources for the development of mathematical reasoning and problem-solving skills in basic education
DOI:
https://doi.org/10.70577/bct4qz52Keywords:
Active Methodologies; Digital Resources; Mathematical Reasoning; Problem Solving; PLS-SEM; Basic Education.Abstract
The development of mathematical reasoning and problem-solving skills represents a central challenge in contemporary basic education, particularly in increasingly digital learning environments. Recent literature suggests that active methodologies supported by interactive digital resources may enhance higher-order cognitive processes; however, structural models explaining the mechanisms through which these practices influence mathematical performance remain limited. To analyze, through a structural equation modeling approach, the influence of active learning and technology use on mathematical reasoning and its subsequent effect on problem-solving performance among sixth- and seventh-grade students. A quantitative explanatory study was conducted with N = 130 students from public schools in Ecuador. A 20-item Likert-scale instrument (1–4) was administered, covering five dimensions: Active Learning, Technology Use, Mathematical Reasoning, Problem Solving, and Motivation. Data were analyzed using PLS-SEM with bootstrapping (5,000 resamples), assessing factor loadings, composite reliability (CR), convergent validity (AVE), discriminant validity (HTMT), structural path coefficients (β), and explained variance (R²). The model explained 63% of the variance in Problem Solving (R² = .63). Active Learning (β = .32, p < .001) and Technology Use (β = .41, p < .001) significantly predicted Mathematical Reasoning, which demonstrated a substantial effect on Problem Solving (β = .55, p < .001). Mathematical Reasoning partially mediated the relationship between pedagogical practices and performance outcomes. Motivation showed an additional significant, though smaller, effect (β = .19, p = .021). Findings indicate that the intentional integration of active methodologies and interactive digital resources enhances mathematical performance through the strengthening of conceptual reasoning processes. The study contributes an integrative explanatory model linking pedagogical innovation, educational technology, and cognitive mechanisms in basic education contexts.
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