Developing Students’ Critical Thinking Skills in Solving Problems in Probability Theory

Usmonova Shahzoda (Master's student of the Faculty of Mathematics at Sharof Rashidov Samarkand State University)

Academia Open
Vol. 10 No. 1 (2025): June

General Background: Critical thinking is foundational in mathematics education, especially in probabilistic reasoning, which underpins decision-making under uncertainty. Specific Background: Despite its relevance, probability theory is often taught procedurally rather than conceptually, limiting students' reasoning skills. Knowledge Gap: Existing studies rarely integrate cognitive pedagogy with probability instruction, particularly in under-researched educational contexts like Uzbekistan. Aims: This study aims to evaluate the impact of a pedagogical model—incorporating inquiry, paradox analysis, and reflection—on developing tenth-grade students’ critical thinking in probability. Results: Using a quasi-experimental design, the intervention group significantly outperformed the control group in post-test scores (83.1 vs. 70.2), with a large effect size (Cohen’s d = 1.12). Improvements were particularly strong in logical inference, assumption evaluation, and problem analysis. Novelty: This research uniquely applies metacognitive strategies to probabilistic education within a context lacking prior integrative frameworks. Implications: Findings suggest that embedding critical thinking in probability instruction not only enhances cognitive skills but also supports broader curriculum reform and teacher development. The model holds promise for adaptation across diverse educational settings, contributing to a deeper, more transferable understanding of mathematics.HIghlight : Significant Skill Gains – Students in the experimental group improved critical thinking scores by over 20 points, nearly triple the control group’s gains. Active Learning Methods – Paradox analysis, reflection, and inquiry-based tasks fostered deeper reasoning and better problem-solving in probability. Educational Reform Implications – The study supports shifting from rote teaching to metacognitive, student-centered strategies in math instruction. Keywords : Critical Thinking, Probability Theory, Inquiry Learning, Problem Solving, Metacognitive Strategy