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Hermann Weyl's philosophical reflections remain a topic of considerable interest in the history and philosophy of science. In particular, Weyl's commitment to a form of idealism, as it pertains to his reading of Husserl and Fichte, has garnered much discussion. However, much less attention has been given to Weyl's later, and at that only partial, turn towards a form of empiricism (i.e. from the late 1920s onward). This lack of focus on Weyl's later philosophy has tended to obscure some of the most significant lessons that Weyl sought to draw from his decades of research in the foundations of mathematics and physics. In this paper, I develop some aspects of what I will term as Weyl's 'modest' empiricism. I will argue that Weyl's turn toward empiricism can be read in the context of a development of Helmholtz's epistemological program and his unique form of 'Kantianism'. The hope is that this reading will not only provide a better understanding of Weyl's later thought, especially his (1954) criticism of Cassirer, but that it may also provide the basis for a novel 'Weylian' account of the mathematization of nature underwriting the group-theoretic methodology of parts of modern physics., (Copyright © 2024 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

The cognitive reflection test (CRT) assesses an individual's capacity to restrain impulsive and intuitive responses and to engage in critical reflection on mathematical problems. The literature indicates that several factors influence students' performance on CRT, including gender, age, and prior knowledge of mathematics. In this study, our objective was to investigate the correlation between CRT scores and students' achievements in both mathematics and physics. We conducted our research with a sample of 150 Italian high school students, and the findings revealed a positive predictive relationship between CRT scores and students' performance in both mathematics and physics. Furthermore, we employed an ordinal logistic regression to evaluate the impact of CRT scores, gender, and school level on students' achievements in mathematics and physics. The results showed that both CRT scores and school level had statistically significant effects on predicting these achievements. In contrast, gender emerged as a statistically significant factor only in predicting students' mathematics achievements.

STEM education plays a key role in influencing and orienting students' interests towards STEM fields and careers. This influence is multifaceted, involving not only STEM content and experiences but also teachers, schools, and personal factors. The purpose of this study is to explore the factors impacting the academic performance of 951 tenth grade students in STEM subjects (physics, chemistry, biology, mathematics, and information technologies) who are attending public and private schools in two provinces of Turkey. Using a correlational research model, the study assessed how students' personal characteristics, teacher effectiveness and school characteristics affect achievement in STEM courses. Data were collected using the 'Factors Affecting STEM Achievement Questionnaire (FA-STEM-A)', a 20-item questionnaire divided into three sub-dimensions. Analyses focused on the relationships between student characteristics, teaching quality, school infrastructure and STEM performance. Structural equation modelling revealed that positive student characteristics, especially fondness for STEM subjects and confidence in STEM abilities, moderately increase achievement. In contrast, negative factors attributed to teachers and schools, such as inadequate classroom activities, lack of educator expertise, inadequate technological resources, and large class sizes, hindered student performance. These findings emphasize the important influence of both inherent student qualities and external educational conditions in determining STEM education.

A characteristic of living systems is their ability to self-organize. Using appropriate quantum mechanical and mathematical tools, we show that this ability may also be a characteristic of non-living systems, such as the electron, thus establishing an unsuspected relationship between biology and physics, whereby "biology precedes physics". Planck's constant h is not a pure number but an elementary quantum of action, a "real atom" according to Henri Poincaré. Consequently, Louis de Broglie's equation λ = h/p must be rewritten in the form h = λp or lp. This approach gives a new meaning to quantum physics: the precise equivalence lp = h = Ed combined with the conceptual tools of Laurent Nottale's scale relativity allows the reunification of physics and support the development of promising engineering applications, notably in systems biology and medicine., Competing Interests: Declaration of competing interest The authors have received no specific funding for this work, and have no conflicts of interest to declare., (Copyright © 2022. Published by Elsevier Ltd.)

Renormalization and Renormalization Group (RG) have proven to be very powerful tools in contemporary physics, with a decisive influence on how to conceive of key physical aspects, including theories themselves. While they can be tackled from a variety of standpoints, this paper focuses on a specific philosophical issue, that is, which kind of explanation can be provided by means of RG methods. After a short, historical overview to set out the physical context, we scrutinize recent debates on the topic, with a particular focus on Morrison's seminal work. With respect to her account, where RG explanation is portrayed as mathematical, non-reductive, and non-causal, our focus is on the first aspect. Our claim is that RG theory's explanatory role cannot reside exclusively in its mathematical character, independently from a physical interpretation: mathematical and physical features intersect in a highly non-trivial way to provide an explanation of physical phenomena., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

In this paper I provide a detailed history of von Neumann's "No Hidden Variables" theorem, and I argue it is a demonstration that his axiomatization mathematically captures a salient feature of the statistical transformation theory (namely, that hidden variables are incompatible). I show that this reading of von Neumann's theorem is obvious once one recalls several factors of his work. First, his axiomatization was what I call a Hilbert-style axiomatic completion; indeed, it developed from work initiated by Hilbert (and Nordheim). Second, it was responsive to specific mathematical and theoretical problems faced by Dirac and Jordan's statistical transformation theory (then called 'quantum mechanics'). Third, the axiomatization was completed across his 1927 papers and 1932 book when he identified the basic assumptions underwriting quantum mechanics, showed that these suffice for deriving the trace rule, and showed that the trace rule is incompatible with hidden variables. With this reading in mind, his claim that quantum mechanics was in "compelling logical contradiction with causality" appears as a straightforward consequence of his theorem. I conclude by reassessing the theorem's broader historical and scientific significance., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

Contribution: Visual maps that illustrate how mathematics, physics, and electrical engineering classes are connected to each other during the first two years of the electrical engineering curriculum were developed. Key terminology and differences in presentation between fields are discussed. Background: Experience has shown that engineering students struggle when they need to use an approach from their mathematics or physics courses in their first- or second-year engineering courses. In particular, students have difficulty making connections between what they learned in mathematics and physics and how it applies to engineering problems. Improving students' ability to identify the connections between fields could increase student resilience in their engineering coursework. Research Questions: 1) Can visual representations of topic connections between fields across the entry-level engineering curriculum increase student's motivation for learning topics in physics and mathematics and improve their problem solving ability? 2) Are there language barriers or other differences between fields that hinder student learning? Methodology: A multidisciplinary team of faculty members from mathematics, physics, and electrical engineering developed visual representations of the links between the core electrical engineering, physics, and mathematics concepts required to solve problems that students will see in their early electrical engineering coursework. Inconsistencies in terminology or notation were explored and documented. Findings: The developed visual aids, coined systematic approach to problem solving (SAPS) maps, describe a mechanism for linking concepts and skills across the technical courses in the first two years of the electrical engineering curriculum.

Fluid dynamics is a research area lying at the crossroads of physics and applied mathematics with an ever-expanding range of applications in natural sciences and engineering. However, despite decades of concerted research efforts, this area abounds with many fundamental questions that still remain unanswered. At the heart of these problems often lie mathematical models, usually in the form of partial differential equations, and many of the open questions concern the validity of these models and what can be learned from them about the physical problems. In recent years, significant progress has been made on a number of open problems in this area, often using approaches that transcend traditional discipline boundaries by combining modern methods of modelling, computation and mathematical analysis. The two-part theme issue aims to represent the breadth of these approaches, focusing on problems that are mathematical in nature but help to understand aspects of real physical importance such as fluid dynamical stability, transport, mixing, dissipation and vortex dynamics. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

In this autobiographical essay, Efim Liberman (1925-2011) looks back at his life summarizing his lifetime experience and drawing conclusions about the role of science and its future development and unification, with the ultimate goal to unite our understanding of nature and harmonize life. A new field of science suggested by Liberman and named Chaimatics combines biology, physics and mathematics. The main idea of Chaimatics is simple: not only measurement, but also calculation is a real physical operation and cannot be done for free-energy and time must be spent on calculation. Quantum physics arose on the basis of discovering the existence of the minimum action-Planck's constant. And this factor imposes physical limits on computation and sets the boundaries to the physical world and its observation. Explorations of the structure of the cell and the progress in the development of electronic computers have led us to the understanding of life and its place in the Universe …., (Copyright © 2022 Elsevier B.V. All rights reserved.)

Applications of unrigorous mathematics are relatively common in the history and current practice of physics but underexplored in existing philosophical work on applications of mathematics. I argue that perspicuously representing some of the most philosophically interesting aspects of these cases requires us to go beyond the most prominent accounts of the role of mathematics in scientific representations, namely versions of the mapping account. I defend an alternative, the robustly inferential conception (RIC) of mathematical scientific representations, which allows us to represent the relevant practices more naturally. I illustrate the advantages of RIC by considering one such case, Heaviside's use of his unrigorous operational calculus to produce and apply an early generalization of Ohm's law in terms of "resistance operators.", (Copyright © 2021 Elsevier Ltd. All rights reserved.)

Virtually all forms of life, from single-cell eukaryotes to complex, highly differentiated multicellular organisms, exhibit a property referred to as symmetry. However, precise measures of symmetry are often difficult to formulate and apply in a meaningful way to biological systems, where symmetries and asymmetries can be dynamic and transient, or be visually apparent but not reliably quantifiable using standard measures from mathematics and physics. Here, we present and illustrate a novel measure that draws on concepts from information theory to quantify the degree of symmetry, enabling the identification of approximate symmetries that may be present in a pattern or a biological image. We apply the measure to rotation, reflection and translation symmetries in patterns produced by a Turing model, as well as natural objects (algae, flowers and leaves). This method of symmetry quantification is unbiased and rigorous, and requires minimal manual processing compared to alternative measures. The proposed method is therefore a useful tool for comparison and identification of symmetries in biological systems, with potential future applications to symmetries that arise during development, as observed in vivo or as produced by mathematical models. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

This research aimed to reveal the effectiveness of using a Problem-Based Learning (PBL) physics pocketbook integrating augmented reality (AR) with the local wisdom of catapults in improving the mathematical and graphical representation abilities of high school students. This study is a quasi-experiment with a pretest-posttest control group design. The data collection was carried out in two stages, namely empirical testing and effectiveness testing stages. The empirical test was conducted on 276 grade XII students, while the effectiveness test was conducted on three science classes of grade XI students of State Senior High School (SMAN) 10 Yogyakarta. The three classes consisted of 36 students in the experimental class, 36 students in the Contrast Class 1, and 36 students in the Contrast 2 Class. The mathematical and graphical representation abilities were measured through a test instrument that passes the analysis of the empirical test using the QUEST program. General Linear Model (GLM) was utilized to analyze the effectiveness test, which was supported by the SPSS software. The result of the General Linear Model (GLM) analysis in the experimental class showed a significant value of 0.000 on the mathematical and graphical representation ability variables. The findings of this study indicate that the use of the developed Problem-Based Learning physics pocketbook integrating augmented reality with local wisdom is effective in increasing the mathematical and graphical representation abilities of grade XI students, with an effective contribution of 82.6% and 84.4% each.

Working with approximations is a common practice in physics. This paper presents an exploratory study of student understanding of some of the elementary aspects of approximations encountered in college physics. For this purpose, a questionnaire (a set of 14 multiple-choice questions) was developed to probe how students dealt with these aspects in a variety of contexts. The questionnaire was finalized after a trial of its pilot version on 7 students on the basis of their written scripts and interviews. After content validation by three external experts, the test was administered to a sample of 141 senior undergraduate physics students from a diverse set of colleges and national institutes. Data analysis reveals several significant student pitfalls in the topic related principally to (i) the identification of a dimensionless ratio to characterize an approximation, (ii) the notion of the order of approximation and consistent handling of a problem up to the required order, and (iii) the notion of the order of infinitesimal in calculus-based derivations. The findings are of direct pedagogic relevance.

In this article, we discuss Micro Assignment Guided Inquiry and Collaboration (MAGIC), an active learning method that draws on the merits of inquiry-based learning in STEM courses. We describe the use of Micro Assignments (MAs) consisting of a series of short, instructive guiding questions that scaffold the course material. Students work through these questions and present solutions to the class. The instructor facilitates learning as well as collaboration among the students during face-to-face interactions, providing the Guided Inquiry and Collaboration (GIC). We present a qualitative discussion about this active learning approach that achieves some of the documented benefits, such as deep student engagement with the material and familiarity with communicating arguments. This method also helps students develop the skills they need as they move from lower- to upper-level courses, such as collaborating, active reading, and breaking down involved assignments and problems into manageable steps. Through GIC and use of the MAs, the instructor guides students to become more abstract thinkers who desire evidence, evaluate arguments, and no longer follow step-by-step formulas but rather produce logical thought processes.

This study aims to investigate Kazakhstani high school students' environmental knowledge, attitude toward the environment, environmental awareness, and environmental concern, and to present the effect of various extracurricular activities on high school students' knowledge, attitude, awareness, and concern. We surveyed 124 students at various grade levels. Results indicated that Kazakhstani students did not have a strong environmental knowledge base and their awareness of environmental issues is not strong at all, but they had a strong positive environmental attitude. There was no significant relationship between knowledge, attitude, and awareness based on grades in biology, chemistry, physics, math, and geography. Gender did not influence students' environmental knowledge, attitudes, and awareness but year in school did for environmental knowledge. Kazakhstani students were most concerned about air pollution, pollution of rivers and seas, and flooding, and they were the least concerned with overpopulation, radioactive waste, extinction of species, and climate change. Extracurricular activities did prove useful with increasing students' knowledge and awareness about environmental challenges but did not impact their environmental attitude. Our results imply that what is being taught about the environment in Kazakhstani schools is not substantial enough. Educators may modify the curriculum to better address environmental issues in the classroom and add more content and activities.

Modelling roles of mathematics in physics has proved to be a difficult task, with previous models of the interplay between the two disciplines mainly focusing on mathematical modelling and problem solving. However, to convey a realistic view of physics as a field of science to our students, we need to do more than train them to become fluent in modelling and problem solving. In this article, we present a new characterisation of the roles mathematics plays in physics and physics education, taking as a premise that mathematics serves as a constitutive structure in physics analogous to language. In doing so, we aim to highlight how mathematics affects the way we conceptualise physical phenomena. To contextualise our characterisation, we examine some of the existing models and discuss aspects of the interplay between physics and mathematics that are missing in them. We then show how these aspects are incorporated in our characterisation in which mathematics serves as a foundation upon which physical theories are built, and on which we may build mathematical representations of physical information that in turn serve as a basis for further reasoning and modifications. Through reasoning processes mathematics also aids in generating new information and explanations. We have elucidated each of these roles with an example from the historical development of quantum physics. To conclude, we discuss how our new characterisation may aid the development of physics education and physics education research.

Structuralists typically appeal to some variant of the widely popular 'mapping' account of mathematical representation to suggest that mathematics is applied in modern science to represent the world's physical structure. However, in this paper, I argue that this realist interpretation of the 'mapping' account presupposes that physical systems possess an 'assumed structure' that is at odds with modern physical theory. Through two detailed case studies concerning the use of the differential and variational calculus in modern dynamics, I show that the formal structure that we need to assume in order to apply the mapping account is inconsistent with the way in which mathematics is applied in modern physics. The problem is that a realist interpretation of the 'mapping' account imposes too severe of a constraint on the conformity that must exist between mathematics and nature in order for mathematics to represent the structure of a physical system., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

When Henry Macomber published his census of owners of the first edition of the Principia in 1953, he believed the edition to be small, 'perhaps not more than 250 copies', an estimate that still enjoys currency. Lower estimates of the size of the first edition of the Principia were based partly on assessments regarding an inhospitable market for highly technical mathematical books, and partly on the presumption that the vaunted incomprehensibility of the Principia would have militated against a sizeable edition. Our preliminary census more than doubles the number of identified copies, to 387-suggesting a much larger print run than commonly assumed - as well as encourages us to believe that there existed a wider, and competent, readership of the Principia from the start. The long-standing assumption regarding the recondite nature of Newton's science as presented in the Principia , together with claims concerning the scarcity of the book, brought many scholars to assume that Newton's masterpiece exerted little influence before the 1730s. The new empirical evidence presented in our census enables a reassessment of the early diffusion of the Principia in Europe which, in turn, would necessitate a major refinement of our understanding of the contribution of Newtonianism to Enlightenment science.

Why is it that fundamental laws discovered through pure mathematics have been able to describe the behavior of our physical world with such precision? Given that the physical universe is composed of mathematical properties, some have posited that mathematics is the language of the universe, whose laws reveal what appears to be a hidden order in the natural world. Physicist S. James Gates, Jr. and science writer Margaret Wertheim explore the uncanny ability of mathematics to reveal the laws of nature., (© 2019 New York Academy of Sciences.)

We are used to thinking of mathematics as a symbolic activity. Here I argue that it may also be seen as a performative one. Making an analogy with music, I draw attention to the ways in which mathematics may not only be written down but also played out., (© 2019 New York Academy of Sciences.)

Among the relevant aspects of the family resemblance approach (FRA), our study focuses on the potential of the approach to elaborate on disciplinary identities in an interdisciplinary context, specifically regarding the interplay between physics and mathematics. We present and discuss how the FRA wheel can be used and intertwined with the framework of boundary objects and boundary crossing mechanisms (Akkerman & Bakker, "Review of Educational Research," 81, 132-169, 2011), which is well-known in STEM education for dealing with interdisciplinarity. The role of the FRA discussed in the article is dual: both practical and theoretical. It is practical in that we show how its use, in combination with the Akkerman and Bakker framework, appears effective in fostering productive discussions among prospective teachers on disciplinary identities and interdisciplinarity in historical cases. It is theoretical in that the combination of the two frameworks provides the vocabulary to characterise the 'ambiguous nature' of interdisciplinarity: like boundaries, interdisciplinarity both separates disciplines, making their identities emerge, and connects them, fostering mechanisms of crossing and transgressing the boundaries. This empirical study reveals how the theoretical elaboration took advantage of the prospective teachers' contributions. We initially presented the FRA to characterise disciplinary identities, but the prospective teachers highlighted its potential to characterise also the boundary zone and the dialogue between physics and mathematics. The data analysis showed that the combinination of the two frameworks shaped a complex learning space where there was room for very different epistemic demands of the prospective teachers: from those who feel better within the identity cores of the disciplines, to those who like to inhabit the boundary zone and others who like to re-shape boundary spaces and move dynamically across them.

The purpose of this study was to find out how the differences in perceptions and learning outcomes of physics education students of the Faculty of Teacher Training and Education Jambi University on the e-module Mathematics Physics I which were reviewed based on gender differences. The type of used research design is quantitative with survey research. The instrument used in this study was a questionnaire of perceptions and learning outcomes of the Likert type scale with 4 answer choices as a data collection tool. The data is analyzed by using descriptive statistics in terms of mean, median, mode and percentage. The data is also analyzed through statistic inferential by performing assumption tests (normality test and homogeneity test) and hypothesis testing (one-way ANOVA test followed by Tukey's further test) and simple linear regression hypothesis testing. Sampling was performed by purposive sampling technique, namely as many as 289 physics education students of the Faculty of Teacher Training and Education Jambi University. The result of this study is that there is a difference between student perceptions and learning outcomes based on gender on the E-Module Mathematics Physics I. Students with male gender are higher than female students because male students have high interest and interest in Mathematics Physics I. The results of this study are expected to contribute to educators in order to identify related perceptions and learning outcomes that students have of the learning media to further improve the quality of learning for the better.

This study aims to examine adaptability for educational games in terms of adaptation elements, components used in creating user profiles, and decision algorithms used for adaptation. For this purpose, articles and full-text papers in Web of Science, Google Scholar, and Eric databases between 2000-2021 were searched using the keywords "educational games", "serious games", "game-based learning", "adapt*", "player modeling", "user modeling". After applying the inclusion and exclusion procedures of studies accessed in the search, 26 studies were included in the study. The studies were analyzed in line with the themes determined for the components used in the adaptation of educational games. According to the results, adaptive educational game design was made for a wide variety of fields such as programming teaching, physics, mathematics, computational thinking, and logic. As for adaptive factors; It was determined that adaptations were made for the game, educational content, interface, and non-player character (NPC) behaviors. It is understood that pre-game adaptation and in-game adaptation methods are used as adaptation types. Finally, it is seen that Bayesian networks, artificial neural networks, fuzzy logic, deep learning, item response theory, and decision tree methods are preferred as decision systems in the adaptation process. The findings of this literature review can facilitate the design process by providing a roadmap for researchers interested in adaptive educational game design.

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of "geometric judgments" from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) "space" should be revisited for the purposes of life sciences., (Copyright © 2017. Published by Elsevier Ltd.)

Formative assessment (FA) is considered a powerful tool to enhance learning. However, there have been few studies addressing how the implementation of FA influences the development of inquiry skills so far. This research intends to determine the efficacy of teaching using FA in the development of students' inquiry skills. A test of inquiry skills was used as the main research instrument to identify the level of the selected inquiry skills before and after a period of teaching with or without FA in the experimental and control group respectively. In the experimental group (n=73), FA was implemented across five subjects: biology, chemistry, physics, mathematics, and informatics, while the control group (n=48) was taught without any external intervention. In both groups, mostly teacher-centred methods of teaching were applied. The research findings confirmed a low initial level of inquiry skills. Teaching using FA showed higher efficacy than teaching without FA, even without a special focus on the inquiry methods. The experimental group achieved significantly better results compared to the control group. In addition, the results confirmed higher efficacy of FA in lower performing students. Gender did not prove as a determining factor in the effective implementation of FA.

This study examines future secondary physics teachers' knowledge related to the teaching of sound waves, and specifically the topics of sound level and sound intensity. The data is comprised of future teachers' responses to a task in which they had to compose a script for an imaginary dialogue between a teacher and a group of students and to provide a commentary elaborating on their instructional choices. The topics selected for the task were chosen intentionally as they provide authentic and rich opportunities to bridge mathematics and science concepts, while challenging future teachers to consider the logarithmic measurement scale and its role in science. The task provided the participants with the beginning of a dialogue that featured student confusion about the measurement of sound level using a decibel scale. Future physics teachers were asked to extend this dialogue through describing envisioned instructional interactions that could have ensued. The instructional interchange related to the relationship between sound intensity and sound level, and particular teachers' responses to the student ideas related to the meaning of a decibel sound level scale were analysed. These responses were categorized as featuring superficial or deep, and conceptual or procedural knowledge for teaching. We describe each category using illustrative excerpts from the participants' scripts. We conclude with highlighting the affordances of scriptwriting for teachers, teacher educators, and researchers.

We present a new secondary school teaching method of quantum uncertainties of two-state systems. Intending to be a material teachable in schools, only two-state systems described by real numbers can be considered. An elementary argumentation based on school statistics leads to the identification of the uncertainty of a physical quantity in such systems with the standard deviation of two random variables. We provide a qualitative picture on the state-dependence of the uncertainty, leading to a pictorial representation in the form of four petals of a flower. When considering the product of uncertainty of two essentially different physical quantities we conclude that the general feature: "if the measurement of one of the quantities is certain, the other remains uncertain", cannot be faithfully expressed by means of an inequality, the product has no lower bound different from zero. The application of techniques used by school materials for teaching quantum physics leads to an exact formula for the state-dependence of the uncertainty valid in any two-state system described by real numbers, in full harmony with the qualitative picture. We compare the two-state case with the celebrated Heisenberg position-momentum uncertainty relation and show that these are both specific facets, but only the Heisenberg relation can be expressed by an inequality. The latter hardly provides any hint on the uncertainties of physical quantities in two-state systems. We conclude that the two-state approach is worth teaching in schools also in relation to the uncertainty relation, even if the Heisenberg relation is not part of the curriculum.

The increasing and diversifying student enrollments in introductory physics courses make reliable, valid, and usable instruments for measuring student skills and gains ever more important. In introductory physics, in addition to teaching facts about mechanics, we also seek to teach our students the skills of "thinking like a physicist," or expertise in and intuition for physical problem solving. How and when these expert, intuitive problem-solving skills emerge during a STEM education, or what the most effective teaching methods might be, are not certain. A facile survey to measure students' "physics-thinking" skills in a pretest and post-test format is therefore desirable to measure and evaluate different pedagogical approaches. Prior investigators codified these skills as "epistemic games" (e.g., order-of-magnitude estimation, evaluating extreme cases) and developed and validated the math epistemic games survey (MEGS) to measure students' ability to employ these techniques. The original survey instrument is reliable and valid but has drawbacks in its length and in students' ability to recall questions between administrations. We employed factor analysis to split the MEGS into two mutually exclusive subtests and measured them to be equivalently reliable and valid as the full-length MEGS as originally formulated. The "split MEGS" is well suited for use as a pretest and post-test instrument to measure gains in expertise in problem solving in introductory physics courses.

The framework of professional noticing describes three components (attending, interpreting, and deciding) that allow teachers to better understand the thinking of their students. Via this method, teachers attend to their classroom by observing relevant cues from students, interpret these cues based on their knowledge of student development, and decide how best to proceed in their lesson. This study utilized an open-response survey to collect data regarding the professional noticing skills, physics and mathematics content knowledge, and teaching experience of Science, Technology, Engineering, and Mathematics graduate students. Participants were given a physics and calculus problem to solve to assess their level of content knowledge and then watched a video-based scenario of a teacher and student discussing the same problems. After, participants were prompted to answer questions corresponding with the attending, interpreting, and deciding components of professional noticing. We found significant results that suggest teaching experience alone is not enough to employ professional noticing skills when attending physics scenarios, and that possessing content knowledge has a positive impact on professional noticing ability, both overall and within the components.

Secondary school students' early choices related to staying in the science track define their future decisions to choose chemistry at college. This investigation aims at analyzing the role of gender in students' causal attributions to choose or abandon chemistry when it first becomes optional in the Spanish educational system. Our analyses uncovered a relevant effect of gender in the students' decision, boys being more likely to choose physics & chemistry when they face, for the first time, the possibility of continuing or opting out the subject. Besides, students' causal attributions to the subject relationship with mathematics and to friends are affected by gender regardless of the students' level of motivation. In turn, there is a gender effect in attributions to friends and media only in the case of highly-motivated students. A multinomial logistic regression model revealed that gender is a strong predictor of the students' decision. The regression model also uncovered a significant interaction effect between gender and attributions to the subject relationship with mathematics, girls becoming less likely to choose physics & chemistry when the latter increase. Our results highlight the need of working on the students' and families' stereotypes and propose gender-balanced teaching models to close the gap between girls' and boys' attitudes, motivation, and anxiety towards mathematics in the context of physics & chemistry teaching and learning.

The Peer Assisted Learning (PAL) program at Sacramento State was established in 2012 with one section supporting introductory chemistry. The program now serves 17 courses with high rates of students who receive a D or an F or withdraw (DFW) from the course in biology, chemistry, mathematics, physics, and statistics; the program enrolls approximately 1,400 students annually. Adapting the Peer-Led Team Learning model, PAL facilitators do not teach, tutor, or even confirm answers; they ask scaffolding questions, provide encouragement, and ensure that all group members participate in problem-solving. Each PAL section is an optional credit-bearing course that supplements the targeted parent science, technology, engineering, and mathematics (STEM) course. In this article, we assess the efficacy of the program in terms of student success in the parent course. As PAL is an opt-in program, we employ propensity score matching techniques to account for confounding factors. Our analysis shows that the mean course grade point average is 1.98 for matched nonparticipants and 2.40 for matched PAL participants, indicating that the program provides an average bump of 0.42 points in the parent course. We consider data from more than 25,000 students, and our propensity score analysis uses more than 10,000 students (4,519 PAL and 5,814 non-PAL) for whom appropriate matches could be found.

The Peer Assisted Learning (PAL) program at Sacramento State was established in 2012 with one section supporting introductory chemistry. The program now serves 17 courses with high rates of students who receive a D or an F or withdraw (DFW) from the course in biology, chemistry, mathematics, physics, and statistics; the program enrolls approximately 1,400 students annually. Adapting the Peer-Led Team Learning model, PAL facilitators do not teach, tutor, or even confirm answers; they ask scaffolding questions, provide encouragement, and ensure that all group members participate in problem-solving. Each PAL section is an optional credit-bearing course that supplements the targeted parent science, technology, engineering, and mathematics (STEM) course. In this article, we assess the efficacy of the program in terms of student success in the parent course. As PAL is an opt-in program, we employ propensity score matching techniques to account for confounding factors. Our analysis shows that the mean course grade point average is 1.98 for matched nonparticipants and 2.40 for matched PAL participants, indicating that the program provides an average bump of 0.42 points in the parent course. We consider data from more than 25,000 students, and our propensity score analysis uses more than 10,000 students (4,519 PAL and 5,814 non-PAL) for whom appropriate matches could be found.

The Yuan T. Lee Foundation Science Education for All (YTLF) has implemented a science camp for students with visual impairments in central Taiwan since 2009. The implementation of the camp serves as an informal science education practice model that informs curriculum design and development, personnel preparation and organization, as well as perceptions toward students with visual impairments. This article gives an overall introduction to the implementation of the camp in addition to the ideas and the outcomes.

Quantitative reasoning and interdisciplinary skills are central to real-world environmental problem solving. Enhancing those skills for students in environmental programs will help them succeed as future environmental professionals. This paper describes an approach that uses an applied geophysical imaging course to enhance quantitative reasoning and interdisciplinary learning in an environmental geography program. To adapt the course to geography students, applied learning is emphasized through the high-impact educational practices (HEPs) of undergraduate research and service learning. Throughout the course, students learn the theories of, and utilize electrical resistivity (ER), ground penetrating radar (GPR), and electromagnetic (EM) induction methods to answer real-life environmental questions in the local community. Course evaluations indicate that the course produced positive learning outcomes consistent with the course objectives. Similarly, students appreciate the unique opportunity to learn and utilize these technologies that are not commonly found within geography programs. The teaching strategies described in this paper can benefit other faculty contemplating curricular integration for interdisciplinary learning and quantitative reasoning outcomes.

The article presents the integrated course "The History of Science and Technology" developed for the students of pedagogical universities, majoring in physics, mathematics, and computer sciences. The authors highlight the effective forms, methods and means of teaching the course. The qualitative research methods included observations, conversations with students, verbal and written surveys regarding course effectiveness; the quantitative methods applied testing of students' progress. 56 students from Poltava V. G. Korolenko National Pedagogical University studying the course "The History of Science and Technology" and 53 students from National Pedagogical Dragomanov University attending the traditional courses, such as "The History of Mathematics", "The History of Physics", "The History of Computer Science" were involved in the experiment. The results show that important components for organising science history teaching and future pedagogical activities for students are assessment, developing and using teaching aids, and solving problems referring to history. The survey of teachers showed that the effectiveness of studying the course is mostly influenced by 3 main factors: enhancing students' educational and cognitive activity in the process of introducing new material (76%); solving problems referring to history during lectures, seminars and doing homework (62%); doing individual tasks by students (56%). The efficiency of the course "The History of Science and Technology" is achieved through: revising previously studied material at the beginning of the lecture; introducing problem-based learning; team teaching; individual tasks, summative assessment. The course "The History of Science and Technology" provides students with integrated knowledge about the development of science as well as the readiness to use historical information in future pedagogical activities in the conditions of STEM-education.

The effectiveness of mathematics in physics makes people take for granted the intimate connection between both disciplines. However, history shows that this is not always the case, because mathematics has played a minor role, not only in Aristotelian physics in ancient Greece, but also in Confucian and neo-Confucian science in ancient China. The objective of this study is to discuss the role of mathematics in physics and propose a structuralistic view as an epistemological stance to interpret this role. This paper opens with a brief historical overview on the relationship between mathematics and physics, followed by a report on Taiwanese college students' work on and responses to an activity simulating Galileo's inclined plane experiment, in order to investigate in what way they analyzed the data and to what extent this activity enriched the affective, knowledge-oriented, and historical aspects of their thinking. Additionally, an investigation of a mathematician's and a physicist's beliefs was conducted to search for an epistemological stance that reveals the relationship between mathematics and physics. The study suggests that a structuralist view may be appropriate for promoting students' learning and their epistemological interpretations of mathematics and physics.

This qualitative, questionnaire and interview-based study explores how pre-service physics teachers think about the role that mathematics plays in the teaching and learning of physics at university and school level and whether these views change during their pre-service teacher education. Many of the pre-service teachers were aware of the complex relationship between these two subjects at university level, noting that success in mathematics can often mask a lack of conceptual understanding in physics and that there can be a disconnect between the physics and mathematical aspects of undergraduate courses. At school level, many stressed the importance of a focus on conceptual understanding and that technical competence in mathematics lessons does not always transfer to physics lessons. Almost all the pre-service physics teachers changed their views during the year, often in response to their classroom experiences. As they became more attuned to the difficulties students faced with respect to the mathematical challenges involved in learning physics, many took a more pragmatic position that balanced the role of mathematics in physics with acceptance that they must respond to student needs. We suggest that these changing views can be framed in terms of two "re-orientations." A disciplinary re-orientation where the role that mathematics plays in order to be successful in physics is reassessed, and a pedagogical re-orientation that attends to pragmatic, teaching considerations. We recommend that direct attention to the role of mathematics in school physics should be an integral part of pre-service physics teacher education in order to encourage these re-orientations.

We study the variation of the apparent weight of an object with height above the surface of a planet with a (buoyant) atmosphere. Interestingly, this variation depends on two competing factors--the reduced gravitational acceleration (which acts to reduce the weight with increasing height) and the reduced buoyancy force in the progressively less dense atmosphere (which acts to increase the apparent weight of an object relative to its value at the planetary surface). The relative sizes of these two competing effects are evaluated for various bodies in the Solar System. For most planets, and the one pertinent moon (Titan), the effects are quite comparable in magnitude. However, the relatively tenuous atmosphere of Mars renders the reduced buoyancy effect negligible; the apparent weight of an object thus (as generally assumed) does decrease with height. At the other extreme, the very dense atmosphere of Venus makes the reduced buoyancy effect an order of magnitude more important than the effect of reduced gravitational acceleration, so that the apparent weight of an object increases with height in the Venusian atmosphere. In addition to deriving these intrinsic results (which are admittedly somewhat esoteric in nature), studying this problem presents students at the high-school or introductory undergraduate levels with an opportunity not only to develop a deeper appreciation of the underlying physics, but also to more fully appreciate the considerable power of parametric dimensional analyses in quickly and straightforwardly obtaining (here within a factor of two) a reasonably accurate solution to a problem. The degree to which that approximate solution is sufficiently interesting (and for this particular problem it turns out that the 'sufficiently interesting' threshold is indeed met) then informs whether or not a more rigorous mathematical approach is justified.

This study sought to identify which elements contribute to success on the Automotive Service Excellence (ASE) Student Certification exam. Students at an eastern U.S. technical college who completed all of their automotive major courses and the ASE Student Certification exam during the spring 2017 semester were selected for the study. The results of this study revealed that there was a direct correlation between performance in Physics, Algebra, and Trigonometry 1 and performance on the ASE Student Certification exam. It was also revealed that students who were required to participate in remedial math and/or remedial reading courses were likely to perform at a lower level than their counterparts on the exam. Students who participated in a secondary automotive Career and Technical Education (CTE) program were also likely to perform at a lower level than their counterparts. The results of this study would be useful to administrators and faculty in postsecondary automotive preparation programs.

This paper presents yet another personal reflection on one the most important concepts in both science and the humanities: time. This elusive notion has been not only bothering philosophers since Plato and Aristotle. It goes throughout human history embracing all analytical and creative (anthropocentric) disciplines. Time has been a central theme in physical and life sciences, philosophy, psychology, music, art and many more. This theme is known with a vast body of knowledge across different theories and categories. What has been explored concerns its nature (rational, irrational, arational), appearances/qualia, degrees, dimensions and scales of conceptualization (internal, external, fractal, discrete, continuous, mechanical, quantum, local, global, etc.). Of particular interest have been parameters of time such as duration ranges, resolutions, modes (present, now, past, future), varieties of tenses (e.g. present perfect, present progressive, etc.) and some intuitive, but also fancy phenomenological characteristics such as "arrow", "stream", "texture", "width", "depth", "density", even "scent". Perhaps the most distinct characteristic of this fundamental concept is the absolute time constituting the flow of consciousness according to Husserl, the reflection of pure (human) nature without having the distinction between exo and endo. This essay is a personal reflection upon time in modern physics and phenomenological philosophy., (Copyright © 2015. Published by Elsevier Ltd.)