On the design of a profession-oriented course on Theoretical Mechanics for physics education students

Technical Summary: Design of a Profession-Oriented Course on Theoretical Mechanics for Physics Education Students

Problem Statement
The paper addresses a persistent "vicious circle" in the education of pre-service physics teachers at the University of Vienna. The first course in the theoretical physics sequence (Theoretical Physics 1: Classical Mechanics) is historically a major hurdle, characterized by high dropout rates, negative student attitudes, and a perception among professors that students lack necessary mathematical proficiency. Students frequently question the relevance of abstract theoretical concepts to their future profession as high school teachers, while lecturers struggle with a heterogeneous audience possessing widely varying levels of mathematical skill (as physics education students in Austria combine physics with diverse second subjects, not always mathematics). The core problem is the disconnect between the abstract, rigorous nature of university-level theoretical physics and the concrete professional needs of future teachers, leading to disengagement and poor exam performance.

Methodology
The authors employed Action Research (AR), specifically a "practical" AR approach aimed at improving teaching practice through a spiral process of planning, acting, observing, and evaluating. The study was conducted over two cycles (Summer Semesters 2022 and 2023) involving two researchers with complementary expertise: one in high school physics teaching and science education research, and the other in theoretical and computational physics.

The course design was grounded in the Model of Educational Reconstruction (MER), which guided the transformation of subject matter into instructional content through three components:

1. Clarification of Science Content: Analyzing the curriculum (Newton's laws, Kepler's problem, harmonic oscillators, Lagrangian/Hamiltonian formalisms) and identifying crucial mathematical prerequisites (e.g., complex numbers, polar coordinates, ODEs).
2. Research on Teaching and Learning: Incorporating learner perspectives, specifically addressing pre-instructional conceptions, affective variables, and the specific needs of students whose second subject is not mathematics.
3. Design of Learning Environments: Implementing constructivist strategies to foster active engagement.

Data collection involved qualitative and quantitative methods, including:

• Continuous feedback from exercise instructors and student tutors.
• Weekly team meetings to reconcile perceptions and adjust tasks.
• Moodle learning platform analytics (access counts, participation in bonus tasks, self-assessment questions).
• Standardized university evaluation questionnaires (open-ended questions).
• Semi-structured interviews with 8 students (4 per year).
• Direct observation of lectures and exercises by the authors.

Key Contributions and Design Strategies
The paper details a profession-oriented course design that bridges the gap between theoretical physics and high school teaching without sacrificing mathematical rigor. Key design contributions include:

• Contextualization via "Three Languages": Physical problems (harmonic oscillator, Kepler's problem, inertial forces) were taught using Newtonian, Lagrangian, and Hamiltonian formalisms, with a focus on the first two to ensure accessibility while demonstrating the utility of advanced formalisms.
• Mathematical Scaffolding: Specific mathematical skills (e.g., vector representations, ODE transformations) were explicitly taught as tools to solve physical problems, rather than as abstract prerequisites. The course avoided the assumption that mathematical ability is a fixed talent, instead framing it as a developable skill.
• Constructivist Implementation: The lecture format moved beyond direct instruction to include:
  • Group work during lectures to reconstruct complex derivations (e.g., deriving the trajectory in a central potential).
  • Use of GeoGebra for dynamic visualization of conic sections and trajectories, a tool familiar to Austrian high school students but rare in university settings.
  • "Bridging" activities that explicitly linked course content to high school curricula and future teaching scenarios (e.g., explaining inertial forces via accelerating streetcars).
  • Professional Learning Groups (PLGs) and bonus tasks to encourage peer interaction and self-paced learning.
• Epistemological Framing: The course emphasized that theoretical physics is grounded in experimental reality, countering the perception that it is purely abstract.

Results
The study presents findings from the 2022 and 2023 implementations (N=89 students per year):

• Engagement: Approximately one-third of enrolled students engaged regularly with learning platform activities in 2022, dropping to about one-fourth in 2023. Tutorial attendance was significantly higher in 2022 (four times that of 2023).
• Exam Performance:
  • In 2022, 68.8% of students who took the exam passed (40.0% of total enrollment).
  • In 2023, 53.6% of exam-takers passed (31.5% of total enrollment).
  • The authors correlate the higher pass rate in 2022 with higher student engagement in course activities (bonus points, tutorials, Q&A sessions).
• Student Feedback:
  • Positive: Students appreciated the bonus point system, the friendly and knowledgeable lecturers, and the explicit connection to their future profession. The use of GeoGebra and the differentiation between inertial and rotating frames were highlighted as conceptually clarifying.
  • Negative: Some students cited a fast pace, difficulty in simultaneous writing and thinking, and a lack of prior mathematical skills. In 2023, fewer students utilized the tutorial.
  • Interviews: Students rated the course highly compared to others, noting the unique atmosphere of discussion and the treatment of students as partners. The "Boltzmann's nose" example was less memorable than the practical applications regarding inertial forces.

Significance and Claims
The paper modestly claims that its primary contribution is demonstrating that a profession-oriented course for physics education students can be successfully designed and implemented without lowering professional standards. The authors assert that:

1. Motivation and Rigor are Compatible: By carefully selecting material and interweaving lecture topics with exercises, it is possible to counter negative student attitudes and professor skepticism regarding mathematical proficiency.
2. Professional Relevance is Key: Establishing close connections between course material and the students' future occupation as high school teachers is of "utmost importance" for engagement.
3. Transferability: The approach transfers findings from high school science education research (constructivism, meaningful contexts) to the university level.

The authors explicitly state that this work offers "concrete indications" of success rather than strict empirical validation, which they reserve for future work. They conclude that the "vicious circle" of disengagement can be broken through careful planning, the integration of educational research principles, and a focus on the specific professional identity of the students.