Strategies for teaching physics and mathematics to develop critical thinking skills in schoolchildren based on interdisciplinary connections

Maikul Kusherbayeva, Alma Abylkasymova, Sofiya Yegemberdiyeva, Bibara Kushkimbayeva, Yeskermes Mussabekov

2026

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DOI 10.3934/steme.2026045
Data confidence 70 medium
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Abstract

This study aimed to identify optimal pedagogical conditions for integrating the subject areas of physics and mathematics within educational projects aimed at fostering and enhancing critical thinking skills among schoolchildren in grades 7–9. The methodological basis of the work combined systemic, activity-based, personality-oriented, and competence-based approaches. The research, conducted at School-Lyceum No. 3 in Taraz, Republic of Kazakhstan, employed methods of systematizing approaches to define the structure of critical thinking, modeling pedagogical systems, and mathematical statistics for processing experimental data. The study revealed a multicomponent structure of critical thinking, including analytical, logical, evaluative, metacognitive, information-retrieval, and dispositional components, and identified their specific manifestations in the study of physics and mathematics. An integrated model of critical thinking development was designed and tested, consisting of four interconnected blocks: conceptual target, content information, organizational activity, and result evaluation. A pedagogical experiment involving 78 students demonstrated significant positive changes in the development of critical thinking components in the experimental group compared with the control group. The most pronounced dynamics were observed in the development of metacognitive (37.9%), logical (34.4%), and evaluative (32.8%) components. Statistical analysis confirmed the significance of differences between the groups (p < 0.01) and revealed a positive correlation between the level of critical thinking development and academic performance in physics (r = 0.67) and mathematics (r = 0.70). The study identified the pedagogical conditions for effective integration of physics and mathematics: the creation of an integrated educational environment with modern equipment; the development of coordinated curricula that take into account students' age and individual characteristics; stimulation of cognitive motivation through the demonstration of the practical significance of knowledge; and the use of active and interactive teaching methods. The practical significance of the study lies in the potential application of the developed model to improve the methodology of teaching natural sciences and mathematics in secondary schools.