... the effectiveness of these reforms. Physics and mathematics have historically greatly influenced each other and contributed to knowledge development in each field. In physics, mathematics is fused with physics knowledge, and physics is developed through formal and logical reasoning about symbols. It has been argued...

... that the effectiveness of formative practices still awaits further empirical verifications in ways that can go beyond merely checking correlations or comparing reformed classes with traditional courses. This is not to say that these studies are not important. Rather, the past three decades have seen a large number...

... characterize differences in means or degrees of association as small effects, medium effects, and large effects. Differences or degrees of association that are statistically significant but less than a small effect are practically negligible. The most common effect size measure for the difference in the means...

... describe Apart from these specific frameworks, there are theoretical frameworks borrowed from other fields of knowledge that try to explain human reasoning and thinking starting from very basic assumptions. These can therefore, beyond their original setting, be fruitful in describing and analysing...

... such as machine learning and natural language processing in more advanced courses. Additionally, the shared set of computational modeling techniques and practices previously discussed may allow students to access jobs beyond their home field, potentially opening up new swaths of employment to future graduates...

..., let alone strongly correlated systems such as transition metal oxides in which a metallic state is predicted for an insulating system. Few remedies have been proposed to address this issue of the XC problem, which go “beyond DFT,” such as the DFT+U method, hybrid functionals, DFT + dynamical mean...

... expert–novice finding relates to how physics principles are used. Although a means-ends analysis is a generally rational and effective strategy ( Newell and Simon, 1972 ), it is not used by experienced physics problem solvers. Why is this the case? One explanation is that experienced problem solvers have...

... and the means and media that will more effectively connect your program with the target groups. This includes designing appropriate recruitment strategies, considering language and image use, and identifying potential partners that may have access to those audiences. It is also critical to consider...

... on the systems-transfer-approach below) that incorporating systems and, in particular, fields into the teaching and learning of energy, Fiedler et al. (2022) presented a small-scale study which suggests that introducing potential energy as energy being stored in fields, effectively addressing...

..., 2019 ), all to study the contextuality and complexity of student reasoning around DC circuits. In PER as in other fields, new technologies afford new methodologies; the possibility of video recording has had a powerful effect on research in the learning sciences ( Derry et al., 2010 ). More...

... for developing conceptual understanding and that the labs uniquely developed “laboratory skills,” “laboratory resourcefulness,” and “the manipulation of laboratory materials.” We interpret this to mean: if you want to develop students' conceptual understanding with a connection to the physical world (beyond...

.... Developing a protocol—determining what will be recorded. The video collection is not immune to the effect of the researcher's subjectivity. Video recordings are limited by where the camera is pointed and the field of view. Choosing to follow the teacher with the camera results in the loss of information...

... between two measured quantities. For example, electric permittivity is a second-rank tensor property of a material that describes a cause-effect relation between applied electric field vector and electric displacement vector in a dielectric. Piezoelectric coefficient is a third-rank tensor property...

... domains of many practicing physicists, the field of education brings with it not just its own epistemological issues but also inexorably ethical ones. Instructors certainly must be more cognizant of what philosophy of physics they employ or even possess unconsciously. That means...

... to expand the notions of reasoning beyond the rational logic-based practices of deduction and induction. Nersessian advocates for the importance of recognizing creative inference due to abduction and to the potential of model-based reasoning for providing a means of specifying the nature of ampliative...

... density), and many thought there were exceptions to the rule that divergence of the magnetic field is zero always and everywhere. The authors concluded that the traditional instruction is not sufficient to fully understand the meaning and power of Maxwell's equations in electrodynamics. There are many...

... frameworks is a generative non-convergence common in emerging fields; there is a need for new theoretical tools and language that go beyond the well-mapped cognitive realm to capture the variety and impact of affective phenomena. Until PER and education research more broadly have explored...

... framework that will help students to learn more effectively and whether educational technology can improve physics learning or under which conditions collaborative learning can be combined with technological means ( Laws et al., 1999 ). In 1987, Mokros and Tinker from the Technical Education...