The Physics-Mathematics Nexus: Theory and Empirical Implications for Physics Education

Edited by

Avraham Merzel¹ and Philipp Bitzenbauer²
¹ The Seymour Fox School of Education, The Hebrew University of Jerusalem, Jerusalem, Israel
² Institute of Physics Education, Faculty of Physics and Earth System Sciences, Leipzig University, Leipzig, Germany

Problem statement

The relationship between physics and mathematics has long been the subject of philosophical enquiry, historical analysis and educational research. Mathematics serves as the language of physics, shaping both its theoretical framework and its practical applications. However, the interplay between these two disciplines also poses persistent challenges in education. Students often struggle with linking mathematical abstractions to physical concepts, while educators often struggle with how to effectively integrate the two in the classroom. Addressing these issues requires insights from history and philosophy, theory and practice.

Historically, many groundbreaking advances in physics have been deeply rooted in mathematical thinking. Understanding the historical development of mathematical and physical ideas can illuminate their interconnectedness and improve pedagogical approaches. From a philosophical perspective, the structural conception of mathematics in physics involves complex issues of representation and applicability that go beyond simple instrumentalism. The bidirectional process of mathematization and interpretation that students must navigate raises fundamental questions about how scientific knowledge is constructed and communicated in educational settings.

In the classroom, research has highlighted the crucial role of teachers' pedagogical content knowledge in bridging physics and mathematics. Teachers who explicitly integrate both disciplines tend to foster deeper student understanding, as evidenced by studies on instructional strategies and classroom discourse. Innovative approaches such as blended learning, self-regulated and inquiry-based learning, and interactive simulations have shown significant potential for reducing cognitive barriers and supporting meaningful connections between mathematical models and physical reasoning. Recent research has also sought to diagnose the cognitive sources of students' difficulties in navigating the physics-mathematics nexus, providing valuable insights for targeted interventions.

This special issue invites contributions that explore the theoretical and empirical dimensions of integrating mathematics and physics in science education.

Focus Areas

We welcome submissions from diverse perspectives, including but not limited to:

Historical and philosophical analyses of the role of mathematics in shaping physics and its implications for teaching and learning
Theoretical frameworks that advance our understanding of how mathematical and physical knowledge are connected in learning processes
Empirical studies on students' learning challenges at the intersection of physics and mathematics, including cognitive, affective, and epistemological perspectives, the role of mathematics in teaching specific topics (e.g., quantum physics, astronomy, etc.), fostering conceptual development in physics education, and mathematics in early physics education
Research on teacher education and professional development, particularly regarding the cultivation of pedagogical content knowledge in the physicsmathematics interplay
Evidence-based Instructional innovations that address the integration of mathematics and physics, such as curriculum design, intelligent tutoring systems to foster teaching/learning mathematics in physics education, assessment strategies, and classroom interventions

Aims and Scope

By engaging with these themes, this special issue aims to advance our understanding of how mathematics and physics can be taught in a more interconnected way, enriching both student learning and instructional practices. We encourage submissions that offer new theoretical insights, empirical findings, or practical applications that contribute to the ongoing discourse in physics education.

Submission guidelines