Integration of Mathematical and Physical Thinking: Educational Strategies to Articulate the Learning of Precalculus and Physics I in Early University Education

Abstract

The integration of mathematical and physical thinking represents a crucial challenge in early university education. The fragmented teaching of Precalculus and Physics I often generates conceptual transfer difficulties, preventing students from applying mathematical foundations to the understanding of physical phenomena. This article proposes an integrative methodological framework based on scientific modeling, interdisciplinary co-teaching, and the use of interactive technologies. Through theoretical analysis and the design of instructional strategies, it outlines a learning sequence that connects content from both courses, fostering epistemological coherence and the development of representational competence. Expected results, supported by previous empirical evidence, indicate significant improvements in conceptual understanding, motivation, and interdisciplinary knowledge transfer. A projected 40% increase in conceptual performance is anticipated in the experimental group compared with traditional instruction, attributed to the coordinated use of modeling, active learning, and simulations. The conclusions emphasize that the integration between Precalculus and Physics I should be institutionalized as an academic policy promoting scientific thinking, deep understanding, and comprehensive student formation. The study provides a replicable model for higher education—especially in STEM programs—where interdisciplinary understanding constitutes an essential competence for meaningful learning and educational innovation.