Improving students' mathematical thinking in verbally solving stochastic problems: a non-calculative approach

Students often struggle with stochastic reasoning because instruction is dominated by calculational procedures that emphasize formula memorization rather than conceptual understanding and interpretation of uncertainty. This hinders the development of mathematical thinking, as students cannot provide solutions to questions without comprehension of reasoning procedures or probabilistic meaning. The study concentrated on deciding whether a non-calculational verbal method of solving problems in stochastics enhances students’ mathematical thinking. A mixed-methods quasi-experimental design was utilized with 63 undergraduate students allocated to control and experimental groups, applying pre- and post-test measures, classroom observation, assessment rubrics, think-aloud protocols, and questionnaires. Findings indicate that the experimental group performed significantly better than the control group on post-test scores. The results also showed a large effect size (Cohen’s d = 1.86) with t(61) = 7.38, p < .001, suggesting a significant improvement in mathematical thinking. The findings indicate that integrating non-calculational verbal reasoning activities can significantly improve students’ cognitive understanding of concepts.