I argue that Vygotsky’s theory of concept formation (1986) is a powerful framework within which to explore how an individual at university level constructs a new mathematical concept. In particular, this theory is able to bridge the divide between an individual’s mathematical knowledge and the body of socially sanctioned mathematical knowledge. It can also be used to explain how idiosyncratic u...

In considering supercoils formed by closed double-stranded molecules of DNA certain mathematical concepts, such as the linking number and the twist, are needed. The meaning of these for a closed ribbon is explained and also that of the writhing number of a closed curve. Some simple examples are given, some of which may be relevant to the structure of chromatin.

OBJECTIVES Numeracy, the ability to process basic mathematical concepts, may affect responses to graphical displays of health risk information. Displays of probabilistic risk information using grouped dots are easier to understand than displays using dispersed dots. However, dispersed dots may better convey the randomness with which health threats occur, so increasing perceived susceptibility. ...

Traditional methods for computing optical flow are mainly based on image brightness constancy. In the real world the brightness constancy usually does not hold. Here we present the idea of using invariant feature based on the brightness change model to estimate the optical flow. Both the mathematical derivation and the experiments show that the new model is better than brightness based optical ...

Lecture-based teaching promotes a passive interaction with students. Opportunities to modify this format are available to enhance the overall learning experience for both students and instructors. The description for a discussion-based learning format is presented as it applies to a graduate curriculum with technical (formal mathematical derivation) topics. The presented hybrid method involves ...

We introduce the mathematical concept of multifractality and describe various multifractal spectra for dynamical systems, including spectra for dimensions and spectra for entropies. We support the study by providing some physical motivation and describing several nontrivial examples. Among them are subshifts of finite type and one-dimensional Markov maps. An essential part of the article is dev...

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 ...