Pedagogical conditions for the formation of critical thinking through the analysis of geometric interpretation of solutions to systems of linear inequalities

Abstract

The research is aimed at identifying and experimentally verifying the pedagogical conditions for the formation of critical thinking in students of mathematical specialties through the analysis of geometric interpretation of systems of linear inequalities. The relevance of the work is determined by the need to develop high-level cognitive competencies in mathematical education through the integration of visual-spatial teaching methods. The quasi-experimental study involved 118 third-year students of mathematical faculties, divided into experimental $(n=61)$ and control $(n=57)$ groups. The experimental group was trained using a specially developed methodology based on the geometric interpretation of the areas of feasible solutions to systems of linear inequalities through dynamic mathematical environments. The results showed a statistically significant increase in the level of critical thinking in the experimental group by 42,8% versus 8,7% in the control group $(p0.001)$. The development of analytical abilities was 38,4%, spatial thinking 35,2%. Correlation analysis revealed a strong positive relationship between the ability to interpret geometrically and the level of critical thinking $(r=0.71$, $p0.001)$. Delayed testing after four months confirmed the stability of the achieved results with the preservation of 84,3% of the effect. It has been established that the optimal pedagogical conditions are: integration of static and dynamic geometric representations, problem-based organization of educational activities, the use of interactive digital visualization tools, step-by-step formation of skills for the transition between algebraic and geometric forms of mathematical information representation.