This article provides a brief synopsis on the founding of the Institute of Physics (IPS), Singapore and the reconstitution of the Singapore National Academy of Science (SNAS).
The Kigali Amendment to the Montreal Protocol officially calls for a global phase-down of conventional hydrofluorocarbon refrigerants to reduce the climate impact of the refrigeration, heating, ventilation and air-conditioning industry. Several Asian countries, such as China, Japan and Singapore, have ratified the Kigali Amendment. Among the various options, CO 2 is recognized as a viable solution to replace conventional refrigerants, especially in supermarket applications. However, current CO 2 refrigeration systems suffer from significant throttling loss due to their high operating pressure which makes CO 2 systems less efficient as compared to conventional systems. This paper introduces different CO 2 refrigeration systems for supermarkets as well as the latest technology development to improve energy efficiency and the global refrigeration market landscape. Supermarket CO 2 refrigeration systems have already been widely adopted in Europe and several Asian countries, but China has been slow in adopting this technology despite having a tremendous and potentially expanding refrigeration market. A summary of the constraining factors and corresponding proposition of future development strategies is provided with a focus on China which can be also applied to other Asian countries.
The looming climate emergency coupled with the present-day energy crisis has led to an urgent need to decarbonize the building stock for a clean energy transition. However, the sector is not at pace with the Paris Agreement goals and requires deep systematic changes to achieve the 2050 net-zero targets. This paper presents energy sufficiency as an approach to accelerate building decarbonization that goes beyond energy efficient and renewable energy technologies and leverages lifestyle choices and practices to achieve the targeted climate goals. We synthesize the existing knowledge on sufficiency in the buildings domain encompassing empirical studies, estimating up to 48% energy savings and 54% GHG emissions reduction potential of sufficiency actions, and the possible approaches for implementation to develop a comprehensive understanding of sufficiency potential in the building sector. We also present different categories of sufficiency measures and identify the related policy and technological innovations required to implement them. Lastly, we discuss the opportunities for sufficiency-oriented building decarbonization within the national policies and roadmaps. This review intends to provide insights into the development of sufficiency-oriented strategies and policies for enabling a just energy transition in the building sector.
Researchers have argued that the use of comics in teaching mathematics is ideal for improving problem-solving skills among primary and secondary students. However, there are only a handful of studies that utilize comics, particularly in Bruneian classrooms. In this study, we share the journey of three teachers who enacted the use of comics in their respective mathematics lessons. All of them implemented their own choice and designs of different yet educationally related comics as intervention lessons, intending to scaffold the conceptual knowledge of the mathematics topics taught while encouraging collaboration and participation among their students. Their students’ perceptions on the use of comics were gathered from the surveys and/or the interviews and analyzed qualitatively. Among the overall main themes found were the students’ positive insights on the use of comics, the impact of their learning and engagement on the subject, the influence of color and image constructs of the comics, the emotions triggered by comics and the beneficial inclusivity particularly at the primary and secondary school levels.
If we want to innovate mathematics education — if we want to achieve something beyond conformity and compliance in mathematics education — these institutional norms need to be challenged. In this paper, I look at the results-first research methodology in which the institutional norms are challenged by the simple goal of increasing student thinking in the classroom. I share the specific results that emerged out of this research and use it as a specific case to argue that real innovation in mathematics education can only occur if we are willing to challenge the institutional norms that have been with us for 150 years.
The world witnessed a growing interest in inquiry-based learning in the past decade. Study and research path (SRP) is a model of such learning based on the anthropological theory of the didactic (ATD). This paper discusses the following research questions through [Formula: see text] maps of the SRPs of university freshmen using the notion of praxeology: (RQ1) how do students/pre-service teachers create SRPs in an online environment in terms of group work? (RQ2) How are the institutional conditions and constraints of each group characterized? In conclusions, the differences in media searches of the student groups lead to differences in final answers to the inquiry. Additionally, the media-milieu dialectic is closely related to the question–answer dialectic.
At the Muenster University, teaching–learning labs have been integrated into teacher education as part of a joint initiative by the German federal and state governments in order to improve the quality of teacher education. Because of the great potential in natural differentiation and the particular challenge in teaching, mathematical modeling was placed at the focus of the teaching–learning lab. The paper deals with the structure of an innovative and supportive learning environment that fosters the diagnostic competence of mathematical modeling as part of the professional competence of pre-service teachers. With the help of a newly developed test instrument, it was shown that the development of modeling-specific diagnostic competence increases significantly and with a large effect size in the teaching–learning lab for mathematical modeling, while no significant changes occur in a control group (CG).
Innovative practices in mathematics pedagogy at all levels of schooling are needed to better prepare our students to thrive amidst the demands of living in the 21st century, given that in many jurisdictions mathematics performance has been flat and students’ attitude toward mathematics has dipped. Beyond cognitive knowledge and skills, and beyond affective factors, the motivational aspect (and values in particular) is just as important too. Drawing on some recent relevant research findings, this paper presents what values associated with effective mathematics learning and with positive mathematical wellbeing look like. The need for teachers to be more aware and more confident of their values espousal is emphasized. Research on the JEDI approach to values learning is presented. Recent research on teacher strategies at orchestrating values alignment in their mathematics classroom is also reported.
With the rapid change in the society, education must evolve to adapt to the digital native students of the 21st century. A change in the current educational paradigm is thus necessary. Information and Communication Technology (ICT) is a vehicle to achieve this objective of paradigm shift in education [ 2 ]. In this paper, we propose gamification approach [ 3 ] via a virtual reality (VR) through a report of a didactic experience. A mixed method research design was adopted for this study in which students’ classification of polyhedral will be reported for the two different learning experiences using either wooden polyhedral or a VR tool within an immersive learning environment. The VR environment allows the learning of geometry in three-dimensional with a friendly interface that offers a multitude of options. It is worth highlighting the benefits of this VR tool in the teaching-learning process of geometry, making explicit the fundamental role played by ICT in meaningful learning of mathematics.
Many of the computational models in science, engineering, and social studies are agent-based models. However, despite their growing importance and potential attractiveness to students, agent-based models are not taught in elementary, middle or high school. In this paper, the author explores the feasibility of teaching agent-based models to elementary and middle school students, and the extent students can learn modeling using agent-based mathematical and computational models.
Proceedings of the Singapore National Academy of ScienceVol. 15, No. 02, pp. 77-78 (2021) Free AccessEditorial — Special Issue on STEM EducationLeo Wee Hin Tan and R. SubramaniamLeo Wee Hin TanNational University of Singapore, Singapore and R. SubramaniamNational Institute of Education, Nanyang Technological University, Singaporehttps://doi.org/10.1142/S259172262101002XCited by:0 Next AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Remember to check out the Most Cited Articles! Be inspired by these Popular Science books!Includes all-time bestsellers and new titles FiguresReferencesRelatedDetails Recommended Vol. 15, No. 02 Metrics History PDF download
The Schrödinger equation is fundamental in quantum mechanics as it makes it possible to determine the wave function from energies and to use this function in the mean calculation of variables, for example, as the most likely position of a group of one or more massive particles. In this paper, we present a survey on some theories involving the Schrödinger equation and the Feynman path integral. We also consider a Feynman–Kac-type formula, as introduced by Patrick Muldowney, with the Henstock integral in the description of the expectation of random walks of a particle. It is well known that the non-absolute integral defined by R. Henstock “fixes” the defects of the Feynman integral. Possible applications where the potential in the Schrödinger equation can be highly oscillating, discontinuous or delayed are mentioned in the end of the paper.
In this paper, we formulate a version of convergence theorem using double Lusin condition and a version of Vitali convergence theorem for the Itô–Henstock integral of an operator-valued stochastic process with respect to a [Formula: see text]-Wiener process.
In T. L. Gill and W. W. Zachary, Functional Analysis and the Feynman Operator Calculus (Springer, New York, 2016), the topology of [Formula: see text] was replaced with a new topology and denoted by [Formula: see text]. This space was then used to construct Lebesgue measure on [Formula: see text] in a manner that is no more difficult than the same construction on [Formula: see text]. More important for us, a new class of separable Banach spaces [Formula: see text], [Formula: see text], for the HK-integrable functions, was introduced. These spaces also contain the [Formula: see text] spaces and the Schwartz space as continuous dense embeddings. This paper extends the work in T. L. Gill and W. W. Zachary, Functional Analysis and the Feynman Operator Calculus (Springer, New York, 2016) from [Formula: see text] to [Formula: see text].
As a reaction to the growing economical, ecological and societal demands on education innumerous efforts and programs have been initiated throughout the educational chain to improve the quality of teaching and learning in the STEM field. On that background we sketch a framework to foster creative engagement in learning to promote scientific inquiry and modeling processes. In the theoretical part the article presents a dualistic perspective on the grounding of creative cognition in concrete experience, highlighting the productive and reflexive interplay of procedural and conceptual knowing. Their entanglement is pivotal to successful knowledge construction and application in science and technology. The ‘mechanics’ of creativity is elaborated exemplarily in a project based learning sequence that starts from investigating and modeling elastic forces as a basic paradigm of creative model construction. The creative part refers to conceptual expansions of the elastic spring model that assist in modeling emergent mechanical properties in hard and soft condensed matter. With additional moderate instructional input this knowledge is productive in creating basic models of the self-organized dynamics of biomolecular systems that orchestrate life at the cellular level. The sequence demonstrates how the interplay of hands-on experience and conceptual modeling can promote near and far transfer.
It is well known that the derivative of the primitive of 1-dimensional Henstock integral exists almost everywhere. Point-interval pairs used in the derivative are Henstock point-interval pairs, which are consistent with point-interval pairs used in the Henstock integral. Note that “almost everywhere” is a set of points, more precisely, the derivative does not exist on a set of points with measure zero. We can transform a set of Henstock point-interval pairs to a set of points with measure zero because of Vitali’s covering theorem. For 1-dimensional McShane integrals, [Formula: see text]-dimensional McShane and Henstock integrals, covering theorems of Vitali’s type cannot be applied. In this paper, we shall discuss differentiation of [Formula: see text]-dimensional McShane and Henstock integrals.
University teaching in STEM has come under increased scrutiny as internationally, a recognition of the importance of a STEM-literate future workforce is becoming clear. In STEM faculties, where change has been historically difficult and the tension between teaching and research more pronounced, this represents a significant challenge. Although there have been no widespread success stories or single models for pedagogical change in STEM in higher education, there have been unique ‘pockets’ of excellence; faculties, groups or individuals that are making a significant difference. In this study, we adopt a multiple case study approach to identify emergent themes underlying ‘pockets of excellence’ at six Australian universities. We argue that the four themes correspond to critical factors; a ‘champion’, support for the champion from the leadership team or a mentor, a critical mass of supporters, and an institutional culture that values the contribution. We find that although change can occur with some of these present, for it to be lasting, all must be emphasised to some degree.
The classical pricing theory requires that the simple sets of outcomes are extended, using the Kolmogorov Extension Theorem, to a sigma-algebra of measurable sets in an infinite-dimensional sample space whose elements are continuous paths; the process involved are represented by appropriate stochastic differential equations (using Itô calculus); a suitable measure for the sample space can be found by means of the Girsanov and Radon–Nikodym Theorems; the derivative asset valuation is determined by means of an expression using Lebesgue integration. It is known that if we replace Lebesgue’s by the generalized Riemann integration to obtain the expectation, the same result can be achieved by elementary methods. In this paper, we consider the Black–Scholes PDE subject to impulse action. We replace the process which follows a geometric Brownian motion by a process which has additional impulsive displacements at random times. Instead of constants, the volatility and the risk-free interest rate are considered as continuous functions which can vary in time. Using the Feynman–Ka[Formula: see text] formulation based on generalized Riemann integration, we obtain a pricing formula for a European call option which copes with many discontinuities. This paper seeks to develop techniques of mathematical analysis in derivative pricing theory which are less constrained by the standard assumption of lognormality of prices. Accordingly, the paper is aimed primarily at analysis rather than finance. An example is given to illustrate the main results.
In V. Boonpogkrong, On measurability of [Formula: see text], Thai J. Math. (accepted) we have proved that [Formula: see text] is measurable in a setting of a dyadic Henstock integral, where dimension sets are subsets of the dyadic rational. In this paper, we replace “dyadic rational” by “countable dense set” and use a setting of Henstock integral, where dimension sets are subsets of this fixed countable dense set. The collection of measurable sets in this new setting is smaller than that in the old setting. We still can prove that [Formula: see text] is measurable.
