This article extends the work of Kellam, Ling, Merisca, Brown and Ialongo (1998) by applying a mathematical model of competition between children to peer contagion in the aggressive behaviors of elementary school students. Nonlinearity in the relationship between group aggression and individual aggression at 2-year follow-up is present. Consistent…

A necessary and sufficient condition is given in this paper for the existence and uniqueness of the maximum likelihood (the so-called joint maximum likelihood) estimate of the parameters of the Partial Credit Model. This condition is stated in terms of a structural property of the pattern of the data matrix that can be easily verified on the basis…

This paper reports on studies of the deterministic and stochastic behaviours of a predator-prey system with prey-dependent response function. The first part of the paper deals with the deterministic analysis of uniform boundedness, permanence, stability and bifurcation. In the second part the reproductive and mortality factors of the prey and…

This paper presents a new hierarchical classes model, called Tucker2-HICLAS, for binary three-way three-mode data. As any three-way hierarchical classes model, the Tucker2-HICLAS model includes a representation of the association relation among the three modes and a hierarchical classification of the elements of each mode. A distinctive feature of…

Hierarchical Linear Models (HLM) have been used extensively for value-added analysis, adjusting for important student and school-level covariates such as socioeconomic status. A recently proposed alternative, the Layered Mixed Effects Model (LMEM) also analyzes learning gains, but ignores sociodemographic factors. Other features of LMEM, such as…

Biotechnological processes (BTP) are characterized by a complicated structure of organization and interdependent characteristics. Partial differential equations or systems of partial differential equations are used for their behavioural description as objects with distributed parameters. Modelling of substrate without regard to dispersion…

The author of this paper submits that a mathematics student needs to learn to conjecture and prove or disprove said conjecture. Ergo, the purpose of the paper is to submit the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method in a Bridge to…

The present study examined the influence of family and classroom environments on the development of particular individual characteristics, including level of empathy, attitude to institutional authority and perceived social reputation, and the role these characteristics may in turn play in school aggression. Participants were 1319 adolescents aged…

Children live in a highly sophisticated world composed of interlocking complex systems. An appreciation and understanding of such systems is critical for making effective decisions about everyone's lives as individuals and as community members. This article addresses one approach to introducing children of all achievement levels to introductory…

When the character Yoda first appeared on the silver screen, his movements were due to the efforts of famed muppeteer Frank Oz. In "Star Wars Episode II: Attack of the Clones," Yoda returned to the movies but this time the character was not a puppet but a digital image within a computer. This paper discusses the role, or, more aptly, the force, of…

An eighth grade algebra class used graphing calculators to simulate ecosystems. One simulation introduced mathematical chaos. The activities exposed the students to nonlinear patterns and modeling. The rate-of-change investigations related the ideas of intercept and slope to the changing equilibrium. The chaotic model intrigued them and was useful…

There is no doubt that the most important activity In schools and universities is conducting classes and lectures to their students. Preparation of timetables is a major task confronted by the management every year. A lot of time is spent on this exercise, yet the end result would be far from satisfactory. In this paper, we draw attention to the…

Math modeling is currently at the focus of educational methodologists' attention. However, little is known about the extent to which principles of the math modeling lead to methodological fallacies in educational research. The main purpose of this paper is to explore the nature and principles of math modeling and to examine its application in…

This article proposes an extension to Kintsch's Construction-Integration (CI) model of text comprehension, which changes its mathematical implementation and emphasizes the connectionist features of the model. Specifically, the extension proposed here (a) simulates the learning process in a connectionist manner by making explicit changes in the…

The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for…