This paper explores universal relations, i.e., meta-mathematical concepts that mathematicians seem to employ in all domains of mathematical reasoning. This paper presents precise mathematical definitions for three universal relations: isomorphism (type identity), essential property , and isoonticity . Although no formal explanation is given as to how universal relations expedite mathematical re...

This paper sets out a version of the Taylor-Romer model of short-run macroeconomic equilibrium which can be used for teaching undergraduate economics principles courses.The aim is to generate a model with the proven advantages of the IS-LM framework but with a more realistic description of central bank behaviour.The paper then provides a dynamic analysis of longer-term adjustment using a phase ...

The effects on transfer of learning multiple instantiations were investigated. Undergraduate college students learned one or more artificial instantiations of a simple mathematical concept. Some students were presented with instantiations that communicated concreteness relevant to the to-be-learned concept, while others learned generic instantiations involving abstract symbols. Learning one or ...

Contemporary research has shown that remote sensing techniques can be used for estimating live fuel moisture content (FMC) from space. These remote sensing based live FMC measurements must conform to some accuracy requirements to be of any practical use in fire behavior predictions. This paper thus investigates the potential errors in live FMC estimations using two simple established techniques...

This study combines elements of the Japanese Lesson Study approach and teachers’ professional development. An explorative research design is conducted with three upper level high school teachers in the light of educational design research, whereby design activities will be cyclically evaluated. The Lesson Study team observed and evaluated two different research lesson cycles. The first one focu...

Starting from the continuum definition of helicity, we derive from first principles its different contributions for superfluid vortices. Our analysis shows that an internal twist contribution emerges naturally from the mathematical derivation. This reveals that the spanwise vector that is used to characterize the twist contribution must point in the direction of a surface of constant velocity p...

We give an overview of our philosophy of pictures in mathematics. We emphasize a bidirectional process between picture language and mathematical concepts: abstraction and simulation. This motivates a program to understand different subjects, using virtual and real mathematical concepts simulated by pictures.

In recent decades, there have been strong calls for reforms in mathematics education, and in particular for changes in classroom practices. Teachers have been encouraged to organize instruction so that students participate in more collaborative, discussion-based activities with an eye to supporting a community of learners, rather than a set of individuals working on mathematics (NCTM, 1991). Or...

We describe recent developments in research on mathematical practice and cognition and outline the nine contributions in this special issue of topiCS. We divide these contributions into those that address (a) mathematical reasoning: patterns, levels, and evaluation; (b) mathematical concepts: evolution and meaning; and (c) the number concept: representation and processing.

Recent algorithmic advances and continual increase in computational power have made it possible to simulate protein folding and dynamics on the level of ensembles. Furthermore, analyzing protein structure by using ensemble representation is intrinsic to certain experimental techniques, such as nuclear magnetic resonance. This creates a problem of how to compare an ensemble of molecules with a g...