Aprendizaje basado en el pensamiento (TBL) para el desarrollo del razonamiento matemático en la resolución de problemas de álgebra

Abstract

Abstract: Learning algebra is fundamental to the development of mathematical reasoning; however, difficulties persist in the interpretation, modeling, and justification of procedures. This research aimed to implement didactic strategies based on Thinking-Based Learning to strengthen mathematical reasoning in algebraic problem-solving among third-year high school students at Unidad Educativa Fiscal Picoazá. An applied field study was conducted using an embedded mixed-methods approach with a quantitative predominance and a pre-experimental pretest-posttest design involving 22 students. The intervention comprised six sessions incorporating thinking routines, graphic organizers, and metacognitive activities. The qualitative component was addressed through systematic observation, a checklist, and reflective records. The mean score increased from 1.95 on the pretest to 5.38 on the posttest. The Shapiro-Wilk test indicated non-normality (W = 0.897; p = 0.025), and the Wilcoxon test revealed significant differences (|Z| = 4.115; p < 0.001), with a large effect size (r = 0.88). Improvements were observed that were temporally associated with the Thinking-Based Learning (TBL) intervention.