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…

This article offers an engaging student activity that allows them to make a connection between seemingly different topics of drug testing procedure, logistic model, and iterations.

This article proposes a mathematical model of Intelligent Tutoring Systems (ITS), based on observations of the behaviour of these systems. One of the most important problems of pedagogical software is to establish a common language between the knowledge areas involved in their development, basically pedagogical, computing and domain areas. A…

We report on a small scale study with six experienced teachers of mathematics in which we have applied a general theoretical model of expert practice (developed by the second author) to explore the nature of the knowledge base that enables teachers to operate effectively in the complexity of a class of 30 pupils. This model uses the notion of…

The impact of outliers on Cronbach's coefficient [alpha] has not been documented in the psychometric or statistical literature. This is an important gap because coefficient [alpha] is the most widely used measurement statistic in all of the social, educational, and health sciences. The impact of outliers on coefficient [alpha] is investigated for…

The idea of using mathematical research in the classroom to collect real data has been spoken about within education for many years. The question is, why should teachers bother with real data from their students' worlds and how do they actually put it into practice in the classroom? When using the mathematical research strategy for collecting,…