Enhancing Informal Stem Learning Through Family Engagement in Cooking

Informal learning has the potential to play an important role in helping children develop a life-long interest in STEM (Science, Technology, Engineering, and Mathematics). The goal of this review is to synthesize the evidence regarding the features of effective informal learning, provide effective ways to support learning within these contexts, and illustrate that cooking is an optimal opportunity for informal STEM learning. We review evidence demonstrating that the most effective informal learning activities are authentic, social and collaborative experiences that tap into culturally-relevant practices and knowledge, although there are limitations to each. We propose that cooking provides a context for authentic, culturally-relevant learning opportunities and includes natural supports for learning and engagement. Specifically, cooking provides many opportunities to apply STEM content (e.g., measuring and chemical reactions) to an existing foundation of knowledge about food. Cooking is also a family-based learning opportunity that exists across cultures, allows for in-home mentoring, and requires no specialized materials (beyond those available in most homes). It may help overcome some limitations in informal STEM learning, namely scalability. Finally, cooking provides immediate, tangible (and edible) results, promoting interest and supporting long-term engagement.

“We Know our Students”: Teacher Views of Inquiry-Based Learning Implementation in Light of Their Working Context

Inquiry-based learning is a well-known strategy in STEM education. It aims to enhance conceptual learning, acquisition of scientific practices, and reflecting on the Nature of Science. However, evidence indicates that in practice, inquiry is often taught in a narrow, mainly experimental approach. This interpretive study analyzes teachers explicit and implicit views regarding implementing inquiry-based learning. The participants enrolled in three professional development programs. They were engaged in multiple genres of inquiry and were encouraged to design an inquiry activity. Data sources included observations, interviews, questionnaires, assignments, and reflections. Findings indicate that with regard to inquiry implementation, teachers were highly concerned about their students’ competency and their own’s working context. Teachers who discussed mostly challenges often designed a narrow-controlled inquiry, while teachers who reflected, negotiated, and challenged their initial views addressed more epistemic aspects of inquiry. Implications for supporting teachers’ development of a broader approach to inquiry learning are discussed.

Creativity in Action: Exploring Cross-Cutting Models of Self-Organization and Emergence in Science and Technology

This review presents a sequence of exemplary experience-based encounters with self-organizing systems on different levels of difficulty. Based on hands-on experiments and creative modeling it provides a viable educational road to build up a deeper understanding of self-organization principles and their comprehensive nature. Theories of self-organization describe how patterns, structures and new types of behavior emerge in energetically open systems, resulting from the local interaction of many components. As an external control instance is missing, the underlying philosophy is counterintuitive to our habits of causal thinking. This thematic and conceptual framework impacts on many STEM domains and presents a blueprint for modeling emergent structures and complex functions in natural and technological systems. It reveals unifying principles that can help in reducing, in structuring and, finally, in understanding and controlling the emerging complexity. An overview across diverse STEM domains highlights the role of this overarching concept. This cross-disciplinary approach can help in improving the dialogue and the knowledge exchange between the individual fields. Moreover, in a self-referential fashion, the modeling of self-organization provides us with fresh perspectives to reflect our own creative processes.

Enacting and Sustaining Change in Undergraduate STEM Education: A Multiple Case Study across 6 Universities

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 Mechanics of Creative Cognition: Orchestrating the Productive Interplay of Procedural and Conceptual Knowledge in STEM Education

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.

Convergence Theorems in the Sense of Vitali and Lusin for the Itô–Henstock Integral

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.

The Black–Scholes Equation with Impulses at Random Times Via Generalized Riemann Integral

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.

The Schrödinger Equation, Path Integration and Applications

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.