Operationalising a Threshold Concept in Economics: A Pilot Study Using Multiple Choice Questions on Opportunity Cost

This paper addresses the emerging educational framework that envisions threshold concepts as mediators of learning outcomes. While the threshold concepts framework is highly appealing on a theoretical level, few researchers have attempted to measure threshold concept acquisition empirically. Achieving this would open a new arena for exploration and debate in the threshold concepts field, and provide potential results to inform teaching practice. We begin the process of operationalising threshold concepts in economics by attempting to measure students' grasp of the threshold concept of opportunity cost in an introductory economics class. We suggest two potential measures and correlate them with an array of ex ante and ex post variables, including students' expectations of success, prior misconceptions about economics and the work of economists, and actual success in the course. Results cast new light onto the factors that influence the acquisition of threshold concepts, the relationship between threshold concept acquisition and final learning outcomes, and the empirical viability of threshold concepts generally.

Threshold concepts: Impacts on teaching and learning at tertiary level

This project explored teaching and learning of hard-to-learn threshold concepts in first-year English, an electrical engineering course, leadership courses, and in doctoral writing. The project was envisioned to produce disciplinary case studies that lecturers could use to reflect on and refine their curriculum and pedagogy, thereby contributing to discussion about the relationship between theory and methodology in higher education research (Shay, Ashwin, & Case, 2009). A team of seven academics investigated lecturers’ awareness and emergent knowledge of threshold concepts and associated pedagogies and how such pedagogies can afford opportunities for learning. As part of this examination the lecturers also explored the role of threshold concept theory in designing curricula and sought to find the commonalities in threshold concepts and their teaching and learning across the four disciplines. The research highlights new ways of teaching threshold concepts to help students learn concepts that are fundamental to the disciplines they are studying and expand their educational experiences. Given that much of the international research in this field focuses on the identification of threshold concepts and debates their characteristics (Barradell, 2013; Flanagan, 2014; Knight, Callaghan, Baldock, & Meyer, 2013), our exploration of what happens when lecturers use threshold concept theory to re-envision their curriculum and teaching helps to address a gap within the field. By addressing an important theoretical and practical approach the project makes a considerable contribution to teaching and learning at the tertiary level in general and to each discipline in particular

Towards a TCT-inspired electronics concept inventory

This study reports on the initial work on the use of Threshold Concept Theory (TCT) to develop a threshold-concept inventory – a catalogue of the important concepts that underlie electronics and electrical engineering (EE) – and an assessment tool – to investigate the depth of student understanding of threshold and related concepts, independent of students’ numerical ability and knowledge mimicry in the first-year course in electrical engineering. This is both challenging and important for several reasons: there is a known issue with student retention (Tsividis, 1998; 2009); the discipline is relatively hard for students because it concerns invisible phenomena; and finally it is one that demands deep understanding from the very start (Scott, Harlow, Peter, and Cowie, 2010). Although the focus of this research was on electronic circuits, findings regarding teaching and learning of threshold concepts (TCs) will inform lecturers in three other disciplines who are part of our project on threshold concepts

Ecological thresholds and large carnivores conservation: Implications for the Amur tiger and leopard in China

The ecological threshold concept describes how changes in one or more factors at thresholds can result in a large shift in the state of an ecosystem. This concept focuses attention on limiting factors that affect the tolerance of systems or organisms and changes in them. Accumulating empirical evidence for the existence of ecological thresholds has created favorable conditions for practical application to wildlife conservation. Applying the concept has the potential to enhance conservation of two large carnivores, Amur tiger and leopard, and the knowledge gained could guide the construction of a proposed national park. In this review, ecological thresholds that result from considering a paradigm of bottom-up control were evaluated for their potential to contribute to the conservation of Amur tiger and leopard. Our review highlights that large carnivores, as top predators, are potentially affected by ecological thresholds arising from changes in climate (or weather), habitat, vegetation, prey, competitors, and anthropogenic disturbances. What's more, interactions between factors and context dependence need to be considered in threshold research and conservation practice, because they may amplify the response of ecosystems or organisms to changes in specific drivers. Application of the threshold concept leads to a more thorough evaluation of conservation needs, and could be used to guide future Amur tiger and leopard research and conservation in China. Such application may inform the conservation of other large carnivores worldwide

Threshold concept knowledge in analogue electronics: Support and assessment

In electrical engineering, as in other academic disciplines, there exist special, threshold concepts, where students often get stuck but which once grasped reveal new ways of thinking about a subject. Two surveys, student interviews and focus group discussions, and students’ assessment were directed at learning of threshold concepts and their pre-cursors. Results suggest that one of the precursor concepts, current flow, may be a threshold concept in itself. A model of precursor and threshold concepts assessment and additional student-support for learning threshold concepts is suggested

How to share a quantum secret

We investigate the concept of quantum secret sharing. In a ((k,n)) threshold scheme, a secret quantum state is divided into n shares such that any k of those shares can be used to reconstruct the secret, but any set of k-1 or fewer shares contains absolutely no information about the secret. We show that the only constraint on the existence of threshold schemes comes from the quantum "no-cloning theorem", which requires that n < 2k, and, in all such cases, we give an efficient construction of a ((k,n)) threshold scheme. We also explore similarities and differences between quantum secret sharing schemes and quantum error-correcting codes. One remarkable difference is that, while most existing quantum codes encode pure states as pure states, quantum secret sharing schemes must use mixed states in some cases. For example, if k <= n < 2k-1 then any ((k,n)) threshold scheme must distribute information that is globally in a mixed state.Comment: 5 pages, REVTeX, submitted to PR

The boundary flux. New perspectives for membrane process design

In the last decades much effort was put in understanding fouling phenomena on membranes. Many new concepts have been introduced in time, and parallel to this many parameters capable to quantify fouling issues and fouling evolution. One successful approach was the introduction of the critical flux theory. At first validated for microfiltration, the theory applied to ultrafiltration and nanofiltration, too. The possibility to measure a maximum value of the permeate flux for a given system without incurring in fouling issues was a breakthrough in membrane process design. Nevertheless, the application to the concept remains very limited: in many cases, in particular on systems where fouling is a main issue, critical fluxes were found to be very low, lower than economical feasibility permits to make membrane technology advantageous. Despite these arguments, the knowledge of the critical flux value still remains and must be considered as a good starting point for process design concerning productivity and longevity. In 2011, a new concept was introduced, that is the threshold flux. In this case, the concept evaluates the maximum permeate flow rate characterized by a low constant rate fouling regime, due to formation of a secondary, selective layer of foulant on the membrane surface. This concept, more than the critical flux, may be a new practical tool for membrane process designers. In this paper a brief review on critical and threshold flux will be reported and analyzed. In fact, critical and threshold flux concepts share many common aspects which merge perfectly into a new concept that is the boundary flux. The validation will occur mainly by the analysis of previous collected data by the authors, during the treatment of olive mill wastewater. A novel membrane process design method based on the boundary flux will then be presented