TPACK APPROACHES TO THE EFFECTIVE USE OF IT TECHNOLOGIES ON THE EXAMPLE OF TEACHING THE CALCULATION OF DEFINITE INTEGRALS

Abstract

Introduction. The teaching of integral calculus, a fundamental component of higher mathematics essential for engineering, physics, and economics, faces a significant pedagogical challenge due to its inherent abstract nature. Contemporary educational paradigms highlight the potential of information and communication technologies to address these challenges through interactive visualization, computational automation. However, the effective integration of these technologies is not automatic; it requires a systematic approach that carefully considers technical infrastructure, instructor readiness, and methodological design. The Technological Pedagogical Content Knowledge (TPACK) framework provides a robust theoretical foundation for this integration, positing that effective technology-enhanced teaching requires an interdependent combination of technological, pedagogical, and content knowledge. Purpose. The purpose of this article is to analyze the specific pedagogical conditions necessary for the successful implementation of the TPACK framework in teaching integral calculus. It aims to delineate how digital tools can be strategically employed to move beyond substitution and towards the transformation of learning processes. Furthermore, the study seeks to provide concrete, practical examples of using widely accessible technologies-namely spreadsheet software (Excel), the online graphing calculator Desmos, and the Python programming language – to enhance the teaching and learning of definite integrals, thereby bridging the gap between abstract theory and tangible understanding. Methods. The research employs a analytical methodology, grounded in a review of recent literature on the TPACK and its application in STEM education. The practical validation of the proposed approach is demonstrated through detailed case studies. Results. The analysis confirms that the TPACK framework is a highly effective model for structuring the integration of ICT in calculus education. The practical examples demonstrate that Excel facilitates a hands-on understanding of numerical methods, allowing students to observe how parameters like step size influence approximation accuracy; Desmos provides immediate visual feedback, enabling students to connect the formal definition of an integral to its geometric meaning as an area; Python offers a powerful environment for automating symbolic calculations and for constructing algorithms, thereby developing students' computational thinking skills alongside their mathematical knowledge. Originality. The scientific novelty of this research lies in its specific, applied focus on integrating the generalized TPACK model into the particular context of teaching integral calculus in higher education. It moves beyond theoretical discussion to provide a structured, practical blueprint for implementation, complete with reproducible examples using three distinct technological approaches (spreadsheets, dynamic graphing, and programming). Conclusions. The effective use of information technologies in teaching integral calculus requires a holistic, systems-based approach grounded in the TPACK framework. Key conclusions are that technology must serve to supplement and deepen traditional methods, not replace them; that a critical investment in instructor training and support is non-negotiable for success; and that technological tools are most effective when used to facilitate visualization, exploration, and algorithmic thinking. This approach transforms digital tools from auxiliary aids into fundamental, transformative components of the educational process, making higher mathematics more accessible, engaging, and comprehensible for students.