Interest

In this article, on Descartes' famous "circle theorem," we first attempt to explain how the philosopher could have arrived at the equation that he presents without demonstration in a letter to Princess Palatine Elizabeth of Bohemia in November 1643 (a previously unpublished proof, to our knowledge). Then we report some stages of the subsequent generalization of this theorem, whose Cliffordian flavor, via the equivalence of a quadratic form and the square of a linear form, still mobilizes mathematicians today. This statement, which, over time, has undergone different extensions, Euclidean and non-Euclidean, has found, {\it in fine}, a spinor formalization. We see there the proof of what we may call, in a Bachelardian style, an "inductive value" of the truth, which extends by successive generalizations. We conclude, more briefly, with the contacts between Elizabeth and Descartes, and the perhaps symbolic meaning of these considerations on "kissing circles," as they are called in Anglo-Saxon countries, in the context of their correspondence on the soul and the body, and the question of passions.

Over the last several years, engineering identity research has gained prominence in education research circles, motivated by connections between "identity" and widely-desired outcomes such as career pursuits and selection of STEM college majors. However, quantitative research on engineering identity remains limited, with most studies focusing on qualitative research. This systematic literature review examines 85 research papers from 2007 to 2022, concentrating on survey measures related to engineering identity. Results of the review show a) a concentration of research at the postsecondary levels, with K-12 students underrepresented, and b) heavy male gender representation in survey samples. The analysis also revealed that several theoretical frameworks are frequently employed to operationalize engineering identity, but with a preference for the Engineering Identity Development Scale, the Physics Identity Scale, and the Critical Engineering Agency Framework. Drawing from our analysis, we consider the consequences of both 1) existing age and gender gaps in quantitative engineering identity research and 2) preferences of particular identity frameworks within and across age and gender categories. We discuss how these possible consequences point to focal areas in engineering identity survey-based research.

Historical post-16 data for UK A-Level Physics, Maths and Further Maths are analysed to determine the relative popularity of A-Level exam boards. A curriculum mapping of the exam board specifications is implemented and compared against first year syllabi of undergraduate physics courses at high-ranked UK universities. Gaps in curricula are identified and recommendations are made to both university module designers and A-level exam board curriculum setters, with regards to remedial action and a reconsideration of included content.

We present the design, construction and classroom use of 3D-printed experimental devices aimed at introducing dynamical systems in physics courses. Theoretical, technical and pedagogical criteria are proposed for producing low-cost, modifiable resources suitable for experimental work. Three devices are analysed as examples: a magnetic pendulum, a wooden woodpecker toy and a double pendulum. The suggested activities are organised around prediction, observation, comparison between configurations, and the elaboration of physical explanations. The main contribution of this work is to show concrete implementation possibilities in secondary education, pre-service teacher training and introductory university courses, together with a discussion of the scope and limitations of 3D printing in experimental teaching.

Undergraduate research experiences provide students with an opportunity to apply knowledge learned in the classroom to authentic scientific problems. In this work, we describe the development of a special-topics course in Plasma Physics and Engineering (PPE) at a small liberal arts college using a Course-Based Undergraduate Research Experiences (CUREs). During the first half of the semester, students learned fundamental plasma physics and dusty plasma concepts through traditional lectures and homework. During the second half, they applied this knowledge to investigate an unanswered research question: why does the levitation time of growing nanoparticles decrease in the presence of a magnetic field? Students learned and used Langmuir probe and optical emission spectroscopy diagnostics to characterize an argon plasma over a range of magnetic-field strengths. Their measurements showed a general decrease in electron density with increasing magnetic field strength, while optical emission measurements confirmed a reduction in carbonaceous nanoparticle growth-cycle time from acetylene. Using the measured plasma parameters, students estimated the nanoparticle charge and developed the hypothesis that a reduction in electron density leads to a smaller negative dust charge and consequently a weaker electric force available to levitate the particles as a function of increasing magnetic field strength between 50 and 330 Gauss. Students subsequently disseminated their results through research poster presentations at conferences. Course evaluations and E-CLASS responses also indicated positive student experiences with the laboratory and research components of the course. This work demonstrates one approach for integrating plasma physics education and authentic research in an undergraduate curriculum at a small liberal arts institution.

Multiple-choice questions are a staple of educational assessment due to their efficiency, but their diagnostic ability is inherently limited. Traditional psychometric techniques infer misconceptions by fitting models to predetermined data patterns, making them ineffective for analysing small, novel, or non-standardised samples where such prior trends are absent. To address this, we introduce a new distractor analysis method based on Information Theory, which treats the randomness in incorrect answers not as noise but as a measurable signal in student answer patterns. By examining the entropy of distractor choices alongside overall accuracy, our approach offers a sample-sized-independent framework for classifying performance. Cross-referencing low-scoring item-level response data against independently documented misconceptions on a standard mechanics inventory shows that, for items identified as most concentrated (lowest degree of randomness), a majority of incorrect responses select the exact response coded to that item's named, interview-validated misconception. Furthermore, items independently flagged elsewhere as diagnostically unreliable are exactly the items the measure identifies as having the highest degree of randomness. The pedagogically actionable cases are those with low degree of randomness in a class's incorrect answers, signalling a shared, re-teachable misconception, whereas a high degree of randomness chiefly serves as the null case against which that concentration is judged. Our analysis is intended as a fast, single-administration triage step: a practical, theory-driven complement to established distractor-analysis methods that helps instructors flag which items warrant closer, more resource-intensive investigation.

Science teachers frequently search for documentary excerpts not by describing what appears on screen, but by querying the abstract concepts they intend to teach. This use case exposes a limitation of existing language-based video moment retrieval methods, which typically assume that queries describe observable events, whereas instructional search requires retrieving concrete visual phenomena that instantiate an underlying scientific principle. We study this setting as concept-to-example video retrieval, an abstract-needle-in-a-haystack problem where compact curriculum concepts must be grounded in temporally sparse documentary evidence. To bridge this abstraction gap, we propose Concept-Driven Domain Adaptation (CDDA), a three-stage framework for adapting two-tower vision-language models to concept-level retrieval. CDDA treats concepts as intermediate semantic anchors: it first structures the textual embedding space with textbook and teacher-handbook example-concept pairs, then transfers this concept-aware geometry to documentary visuals under a frozen visual encoder, and finally jointly adapts both encoders with sparse visual concept supervision. From a geometric perspective, this staged alignment reduces text-concept and vision-concept angular gaps, thereby encouraging concept-level adaptation while preserving the pretrained model's concrete image description alignment. On a curated middle-school physics retrieval benchmark, CDDA achieves stronger pedagogically oriented concept retrieval than several competitive multimodal baselines, including Qwen3-VL-Embedding-2B, while maintaining concrete image-text matching after adaptation.