The compatibility of the polychotomous Rasch model with dichotomization of the response continuum is discussed. It is argued that in the case of graded responses, the response categories presented to the subject are essentially an arbitrary polychotomization of the response continuum. (Author/LMO)

A neuromathematical model of information processing applied to science learning is expanded to include two coefficients representing the motivational state of the learner. The inclusion of these coefficients (which are described) permits modeling of the effects of variations in motivation on the rate and amount of information in learning tasks.…

A classification of the simple combinatorial configurations which correspond to various cases of distribution and ordering of objects into boxes is given (in French). Concrete descriptions, structured relations, translations, and formalizations are discussed. (MNS)

Presents the bivariate normal probability distribution as a method for estimating the prevalence of giftedness. The bivariate model requires the specification of two cutoff values for two selection variables and information regarding the size of the correlations between variables. The use and interpretation of bivariate estimates is discussed.…

This paper reports on the mathematical modelling of four classes of 4th-grade children as they worked on a modelling problem involving the selection of an Australian swimming team for the 2004 Olympics. The problem was implemented during the second year of the children's participation in a 3-year longitudinal program of modelling experiences…

The main purposes of this study were to investigate, by means of simulation: (1) whether the difference likelihood ratio chi-square statistic (G2-dif) for comparing item response theory (IRT) models is asymptotically distributed as a chi-square distribution; and (2) the accuracy rate of applying G2-dif in selection of nested IRT models. Two…

For thousands of years people from da Vinci to Einstein have created models to help them better understand patterns and processes in the world around them. Computers make it easier for novices to build and explore their own models and learn new scientific ideas in the process. This book introduces teachers and students to designing, creating, and…

Mathematical models can assist educators in the preparation of their educational plans. Administrators and planners of educational systems have found that their ad hoc procedures are no longer adequate to take into account the many variables impinging on their environment. Examines the potential of the Markov Chain, one model capable of predicting…

A model for the analysis of paired comparison data is presented which is metric, mathematically tractable, and has an exact algebraic solution. (Authors/MB)

The approximate nature of measurement is stressed, with examples given of elementary school mathematics problems which confuse reality with its mathematical model. Examples relating measurement to mathematical structure are given. (DT)