The joint AAPT and APS PHYS21 report emphasizes preparing students for diverse career paths, including the need for more opportunities to learn innovation and entrepreneurship in physics. To support these changes, research is needed on students' interest and perceptions of innovation and entrepreneurship, and suggestions for integration into the undergraduate physics experience. We conducted semi-structured focus groups with 20 physics majors around several concepts related to innovation and entrepreneurship: technology, creativity, design, business, communication, and leadership. Emergent and thematic coding was used to analyze students' responses. Students have a complex view of innovation and entrepreneurship in physics perceiving creativity as closely related to physics, especially in undergraduate research, while business and leadership skills were distinct from physics and closer to engineering. These findings have implications for understanding students' perceptions of physics as a disciplinary community and field of study, and can assist departments seeking to better support students' careers.

As physics departments increasingly emphasize computational training within the physics curriculum, there is a need for educators to have guiding principles for deciding how and when to use computational approaches over analytical math and vice versa. We investigated the use of analytical and computational mathematics in professional practice by conducting ten semi-structured interviews with PhD students in the physical sciences. The interviews revealed context-rich situations where computational and analytical math were valued and used. Through an emergent and thematic coding process, key contextual features were distilled. Although analytical math was valued as a calculational tool (e.g., manipulating equations), the most prevalent use of analytical math was to develop a preliminary understanding of a problem, which included modeling systems through equations, developing simplified "toy models", understanding background concepts, and understanding how varying parameters affected system behavior. Computational tools had a complementary role of data analysis, complex numerical simulations, and visualization.

Undergraduate majors' attitudes and perceptions about physics can strongly influence their development of a physics identity, persistence, and pursuit of physics-related careers. To explore students' attitudes and perceptions, we surveyed 178 physics majors nationally. To analyze this data, we used descriptive statistics and emergent methods of qualitative analysis. While data collection is ongoing, preliminary results show themes of physics majors' value for hard-work, broadly applicable problem-solving skills, and the rewarding quest for a meaningful application of their knowledge. Furthermore, we found that students position physics as a creative and communicative endeavor when provided with opportunities to do research and lab-work that values these aspects. This rich analysis of students' attitudes and perceptions about physics can help educators better align learning opportunities with students' needs and prepare students for a long-term and broadly applicable pursuit of physics.

It is important to develop models about how mathematics is used in professional physics settings. Existing models of math use focus on mathematical modeling for problem solving. However, workplace problems often include design problems, troubleshooting, and more. To study workplace mathematics, we conducted hour-long, semi-structured interviews with employees at photonics and optics companies in Rochester, NY. We applied an emergent coding process to classify instances of math in the workplace, and present two models of mathematics use within workplace tasks. We describe a four-phase engineer task consisting of defining the problem, designing a product, testing the product, and communicating results. A common technician task replaces the design phase with manufacturing the product. Workplace math is embedded in these phases through various representations such as simulations, schematics, and machining codes. Educators should consider using diverse problem types since they require additional mathematical representations and techniques to be brought to the forefront.

Problem-solving in the undergraduate curriculum typically occurs in content-focused courses that emphasize applying a conceptual and mathematical understanding of key physics principles to given situations. This project expands the notion of problem-solving by characterizing the breadth of problem-solving activities carried out by graduate students in physics-intensive research. In 10 in-depth interviews, PhD students were asked to describe routine, difficult, and important problems they engage in. A grounded theory analysis resulted in a framework with three dimensions: problem context (e.g., experiments, software, or math), activity (e.g., design or troubleshooting), and feature that made the problem hard (e.g., complexity or insufficient resources). Problem contexts usually extended beyond theory and mathematics (e.g., experiments, data analysis, and computation). Important problem contexts blended soft and technical skills (e.g., communication and collaboration). Routine problem activities tended to be well-defined (e.g., troubleshooting) while important ones were more open-ended and had multiple solution paths (e.g., evaluating options). The results can inform curriculum development and PER with an expanded view of problem-solving.