In this paper I describe how I have used the classic buried treasure problem with prospective and practicing mathematics teachers to enhance their problem solving abilities and disposition to integrate interactive geometry software (IGS) into the learning environment. I illustrate how IGS may be used as a strategic tool to gain insight into the…

We discuss a quantum-mechanical model of two particles that interact by means of a harmonic potential and are confined to a one-dimensional box with impenetrable walls. We apply perturbation theory to the cases of different and equal masses and analyse the symmetry of the states in the latter case. We compare the approximate perturbation results…

Language is a complex adaptive system: Speakers are agents who interact with each other, and their past and current interactions feed into speakers' future behavior in complex ways. In this article, we describe the social cognitive linguistic basis for this analysis of language and a mathematical model developed in collaboration between…

Methodological implications of a person-oriented, holistic-interactionistic perspective in research on individual development are outlined, desirable properties of a mathematical model of a phenomenon are discussed, and selected methods for carrying out person-oriented research are briefly overviewed. These methods are: (1) the classificatory…

Simple slopes, regions of significance, and confidence bands are commonly used to evaluate interactions in multiple linear regression (MLR) models, and the use of these techniques has recently been extended to multilevel or hierarchical linear modeling (HLM) and latent curve analysis (LCA). However, conducting these tests and plotting the…

To help mathematics educators realise the power of computer-based applications and modelling, this paper deals with four questions: (a) What implications does technology have for the range of applications and modelling problems that can be introduced? (b) In what cases does technology facilitate the learning of applications and modelling? (c) When…

This paper discusses the requirements of Interactive Geometry Systems (IGSs) and how they can be fulfilled, explains how a geometry tool can benefit from the Internet, and presents Cinderella's Cafe. Cinderella's Cafe is a new IGS with a high mathematical background that uses the most general mathematical models whenever possible, is highly…