Provides an example of the modeling power of Mathematics, demonstrated in a piece of A-Level student coursework which was undertaken as part of the MEI Structured Mathematics scheme. A system of two masses and two springs oscillating in one dimension is found to be accurately modeled by a system of linear differential equations. (Author/ASK)

Presents a procedure, based on a Bayesian updating of the item information, for locating on the latent trait scale the scores or responses of items that follow the three-parameter logistic and monotone partial credit models. Applications are provided in terms of selecting items or score categories for criterion-referenced interpretation of mapping…

Suggests a framework for estimating the costs associated with shifting from the traditional method of financing and administering U.S. public schools to an educational voucher system. Uses certain framework components to compute "ballpark" estimates in five cost areas: accommodating additional students, record keeping, student…

Explores whether flexible nonlinear models (including neural networks and genetic algorithms) can reveal otherwise unexpected patterns of relationship in typical school-productivity data. Applying three types of algorithms alongside regression modeling to school-level data in 183 elementary schools proves the hypothesis and reveals new directions…

Suggests that mathematical modeling is "a way of life for everyone." Describes the M's of mathematics which include methods, models, and modeling; and the R's of mathematics which are reasoning, reading, 'riting and 'rithmetic. Outlines their role in promoting "the way of life" and discusses implications for the 16-19 curriculum. (Author/ASK)

Used empirical data about HIV risk behaviors from 330 female participants in a drug treatment program to explore the implications and consequences of using various statistical models to describe the association of one ordinal and one dichotomous variable in which data are incomplete for the dichotomous variable. Examined the statistical fit and…

Addresses the role that so-called emergent models can play in the process of constituting formal mathematics. Describes how the use of these models became more explicated over time and developed into the notion of emergent models. Uses the design of instructional sequence for flexible mental strategies for addition and subtraction as an example…

Explores the derivation of empirical models for the stopping distance of a car being driven at a range of speeds. Indicates that the calculation of stopping distances makes an excellent example of empirical modeling because it is a situation that is readily understood and particularly relevant to many first-year undergraduates who are learning or…

Darwinian selection by consequences was instantiated in a computational model that consisted of a repertoire of behaviors undergoing selection, reproduction, and mutation over many generations. The model in effect created a digital organism that emitted behavior continuously. The behavior of this digital organism was studied in three series of…

Spreadsheets to explore regression with an algebra 2 class in a medium-sized rural high school are presented. The use of spreadsheets can help students develop sophisticated understanding of mathematical models and use them to describe real-world phenomena.

Two simple mathematical models for how individual vehicles follow each other along a stretch of road are discussed. The resulting difference equations can be used as applications of techniques taught at A-level and first year undergraduate level, and as an introduction to the behaviour of the logistic map.

Contrasting instructional approaches were used to introduce mathematical modeling to two sets of students with weak content skills and no prior modeling experience. One group was exposed to examples of models for a particular contextual problem; the other group was asked to construct their own model for the same situation. In less than three…

This paper proposes a multidimensional generalization of Coombs' (1964) parallelogram model for "pick any/'n'" data, which result from each of a number of subjects having selected a number of objects (s)he likes most from a prespecified set of "n" objects. In the model, persons and objects are represented in a low dimensional space defined by a…

Flowing granular mixtures in rotating cylindrical drums arise in numerous industrial settings and are of great technological significance worldwide. To date, the development of a robust mathematical model for this process remains an open research problem. However, simple mathematical models may be developed that capture some of the underlying…

Students in statistics service courses are frequently exposed to dogmatic approaches for evaluating the role of randomization in statistical designs, and inferential data analysis in experimental, observational and survey studies. In order to provide an overview for understanding the inference process, in this work some key statistical concepts in…