Julia Hofmann

Making sense of mathematical expressions is a central component of expertlike reasoning in physics. Previous research has shown that sensemaking strategies can be successfully integrated into university instruction and that students benefit from explicit support in using such strategies. However, it remains largely unexplored to what extent the amount of practice influences students’ learning. In the present study, we investigate dose-effect relationships for sensemaking tasks with limiting case analysis. The study was conducted during a two-week preparatory course for incoming undergraduate physics students at a German university. The course focuses on the repetition of important mathematical concepts and prepares students for the demands of the first semester of physics studies. Limiting case analysis was systematically embedded in daily exercises that students solved in recitation sessions. A total of N = 103 students participated in the study and were randomly assigned to one of five intervention groups, each with a different number of limiting case tasks (0–8 tasks). The study employed a pre-post design to assess perceived usefulness, instructional integration, competence, and performance regarding the analysis of limiting cases. The results show that students’ perceived competence increased with the number of tasks, with effect sizes up to d = 0.88 . Students’ performance also showed an increase in effect size for a greater number of tasks with effect sizes up to d = 1.07 . The observed patterns in the target variables are compatible with a sigmoidal dose-effect relationship. Overall, this proof-of-concept study provides the first empirical evidence for dose-effect relationships in the context of sensemaking strategies in physics and demonstrates the feasibility of dose-effect study designs in undergraduate physics education research. The study highlights the importance of explicitly integrating sensemaking strategies into undergraduate physics and indicates that increased and targeted practice can foster both students’ confidence and their ability to apply such strategies.

A deep understanding of mathematical equations and their physical meaning is an important skill for physicists and therefore a central learning goal in university physics education. However, many students approach mathematical expressions in physics in a purely procedural manner, using them as calculation tools without critically evaluating their physical plausibility. Making sense of equations, that is, being able to interpret and evaluate equations within a physical context, is essential for the development of expertlike reasoning in physics. Frequently employed strategies that assist in the sensemaking process are dimensional, covariational, special, and limiting case analysis. Despite their importance, these strategies are rarely taught or practiced explicitly in university physics courses. The present intervention study systematically implemented sensemaking strategies within a university course for first-year physics students covering topics of electro- and magnetostatics as well as electrodynamics. Traditional exercises were enriched with tasks requiring students to critically evaluate the plausibility of self-derived equations. The tasks were integrated into recitation sessions and homework assignments. A total of N = 67 physics students participated in the study. A quasiexperimental pre-post design with two groups was employed to evaluate the effectiveness of the intervention approach. Results show that students highly valued all four strategies equally and reported an increased perceived competence in their application after the intervention. Significant improvements in performance were observed for dimensional ( d = 0.67 ) as well as for special case analysis ( d = 0.50 ). Students’ performance in analyzing covariations only showed a tendency favoring the intervention group. No intervention-related impact on the performance of limiting case analysis was found, suggesting that this strategy may require more extensive practice. The findings underscore the importance and usefulness of explicitly teaching strategies to support students’ sensemaking of physics equations.

The current dropout rate in physics studies in Germany is about 60%, with the majority of dropouts occurring in the first year. Consequently, the physics study entry phase poses a significant challenge for many students. Students’ stress perceptions can provide more profound insights into the processes and challenges during that period. In a panel study featuring 67 measuring points involving up to 128 participants at each point, we investigated students’ stress perceptions with the perceived stress questionnaire (PSQ), identified underlying sources of stress, and assessed self-estimated workloads across two different cohorts. This examination occurred almost every week during the first semester, and for one cohort also in the second semester, yielding a total of 3241 PSQ data points and 5823 stressors. The PSQ data indicate a consistent stress trajectory across all three groups studied that is characterized by significant dynamics between measuring points, spanning from M = 20.1 , S D = 15.9 to M = 63.6 , S D = 13.4 on a scale from 0 to 100. Stress levels rise in the first weeks of the lecture, followed by stable, elevated stress levels until the exams and a relaxation phase afterward during the lecture-free time and Christmas vacation. In the first half of the lecture period, students primarily indicated the weekly exercise sheets, the physics lab course, and math courses as stressors; later on, preparation for exams and the exams themselves emerged as the most important stressors. Together with the students’ self-estimated workloads that correlate with the PSQ scores, we can create a coherent picture of stress perceptions among first-year physics students, which builds the basis for supportive measures and interventions. Published by the American Physical Society 2024