Simulation studies are the basic tools of quantitative methodologists used to obtain empirical solutions to statistical problems that may be impossible to derive through direct mathematical computations. The successful execution of many simulation studies relies on the accurate generation of correlated multivariate data that adhere to a particular…

We live in an increasingly worrying future, where researchers are looking at how we can create education for a sustainable world. In this study we investigate what such education could look like, especially for young students, reinforcing hope and an ability to act and come up with ideas of sustainable solutions with no obvious 'good' solution.…

Using the simplest possible quantum system--the qubit--the fundamental concepts of quantum physics can be introduced. This highlights the common features of many different physical systems, and provides a unifying framework when teaching quantum physics at the high school or introductory level. In a previous "TPT" article and in a…

A model solution to a proof question on an examination is explored and subjected to a detailed analysis in terms of Toulmin's scheme of argumentation. In doing so, the ways in which the scheme has been variously used in the mathematics education and philosophical literature are contrasted. The analysis raises a number of issues concerning the…

A concept of major importance in human electrophysiology studies is the process by which activation of an excitable cell results in a rapid rise and fall of the electrical membrane potential, the so-called action potential. Hodgkin and Huxley proposed a model to explain the ionic mechanisms underlying the formation of action potentials. However,…

In this research, we examine how problem solving frameworks differ between Mathematics and Software Development. Our methodology is based on the assumption that the words used frequently in a book indicate the mental framework of the author. We compared word frequencies in a sample of 139 books that discuss problem solving. The books were grouped…

In Ramsay curve item response theory (RC-IRT, Woods & Thissen, 2006) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's (1981) EM algorithm, which yields maximum marginal likelihood estimates. This method, however,…

We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…

Examined is a method of teaching based on the idea of the projective application of mathematics to simplified innovative proposals and hypotheses. (Author/MA)

The author reports research findings on the approaches used to teach mathematical concepts in technology education. Appropriate methods of teaching mathematically based concepts are recommended and discussed, and curriculum materials that employ these approaches are introduced. Findings concerning receptivity among teachers to the recommended…

Describes the construction of models of two-dimensional surfaces with negative curvature that are used to illustrate differences in the triangle sum rule for the various Big Bang Theories of the universe. (JRH)

Describes the "Two-Eight" instructional model for students who have arithmetic computational skills but lack the ability to select appropriate strategies to solve problems. Offers examples showing the replacement of the actual values used in a word problem with the simple numeric values of 2 and 8 to create a parallel, solvable problem. (DMM)

Presents the equations of motion governing the trajectory of a cricket ball subject to a linear drag force. Uses a perturbation expansion technique to solve the resulting trajectory equation for the range of a cricket ball struck into the outfield. (Author/ASK)

Students at all levels benefit from a multi-faceted approach to learning abstract material. The most commonly used technique in teaching the pure theory of international trade is a combination of geometry and algebraic derivations. Numerical simulation can provide a valuable third support to these approaches. The author describes a simple…

Mathematical modeling is defined. Examples are used to show that there are models available which illustrate both the traditional use of mathematics in the physical science and its newer use in nonphysical disciplines, and which are at a suitable level for teaching in schools. (Author/MK)