The theme of this year's conference is “Making Mathematics Fun, Accessible and Challenging through Technology”. Version 6 of Mathematica, released in May 2007, is instantly interactive, allowing teachers and students to easily construct live interfaces to illustrate and investigate mathematical concepts at all levels [1]. Over 2000 examples of these interactive capabilities, including a number ...

It is notoriously difficult for people to adaptively apply formal mathematical strategies learned in school to real-world contexts, even when they possess the required mathematical skills. The current study explores whether a problem context's mechanism can act as an "embodied analogy" onto which abstract mathematical concepts can be applied, leading to more frequent use of formal mathematical ...

tThe abstract nature of mathematics requires the communication of mathematical ideas through multiple representations, such as words, symbols, pictures, objects, or actions. Building representational fluency involves using mathematical representations flexibly and being able to interpret and translate among these different models and mathematical concepts. This article shares a collaborative le...

There is a huge need in general relativity for a consistent and useful mathematical theory defining the multiplication of tensor distributions in a geometric (diffeomorphism invariant) way. Significant progress has been made through the concept of Colombeau algebras, and the construction of full Colombeau algebras on differential manifolds for arbitrary tensors. Despite the fact that this goal ...

Aksentijevic (1) raises issues with our recent report (2) that bear further clarification because they reflect some fundamental confusion about the nature of random sequences. First, it is essential to distinguish statistics for individual elements (i.e., patterns of length one) vs. statistics for patterns consisting of more than one element (i.e., higher order patterns). Aksentijevic’s comment...

Protein adsorption at solid surfaces plays a key role in many natural processes and has therefore promoted a widespread interest in many research areas. Despite considerable progress in this field there are still widely differing and even contradictive opinions on how to explain the frequently observed phenomena such as structural rearrangements, cooperative adsorption, overshooting adsorption ...

1 David I. Laurenson, Mike J. Jackson, The University of Edinburgh, Kings Buildings, Mayfield Road, Edinburgh, UK, EH9 3JL Abstract  The Java language has been used in the construction of a number of learning environments to enable students to explore mathematical concepts without the barrier of mathematical manipulation. The applets are designed to be flexible for educators, and flexible in u...

A Mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences, but also in the social science (such as economics, psychology, sociology, and political science). Mathematical models can take many forms, including but not limit...

The acquiring of formal, abstract mathematical concepts by students may be said to be one of the major goals of mathematics teaching. How are such abstract concepts acquired? How does this formal knowledge interact with the students' intuitive knowledge of mathematics? How does the transition from informal mathematical knowledge to formal mathematical knowledge take place? This paper reports on...

This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and structures connected with the Frobenius integrability/nonintegrability theorems given in terms of distributions on manifolds with corresponding curvature defi...