Finds little or no differential effects of ability grouping for high-, average-, or low-achieving students, based on data from a 1992 longitudinal study. Examination of three school inputs (class size, teacher education, and teacher experience) indicates that grouping and nongrouping schools similarly tailor resources to ability levels. (Contains…

Private universities implementing nontraditional programs for working adults typically staff these programs with part-time, adjunct, and underpaid faculty with no benefits. The model outlined suggests that a policy establishing nontraditional faculty may represent a false economy. Paying such faculty proportionately more than regular faculty would…

Describes and explains a procedure for photographing the chaotic scattering of light. (WRM)

Genetics is a difficult topic as it involves abstract concepts, which are not directly observable. Studies on using simulations to support the learning of genetics have largely been confined to the use of quantitative simulations to replace experimentation. This study describes the use of a new type of simulation built using an iconic modelling…

We first discern three different sources to describe the non-modelling-friendly environment in Taiwan: the background of mathematics teachers and students, examinations and textbooks. Under such unfriendly circumstances, how one can implement the teaching and learning of mathematical modelling is explored. In this paper, we focus on the analysis…

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…

Although differential item functioning (DIF) theory traditionally focuses on the behavior of individual items in two (or a few) specific groups, in educational measurement contexts, it is often plausible to regard the set of items as a random sample from a broader category. This article presents logistic mixed models that can be used to model…

The basic properties of a dynamic systems approach of development are illustrated by contrasting two simple equations. One equation is characteristic of dynamic systems models. The other refers to what, for the sake of simplicity, is referred to as the standard developmental approach. We give illustrations from cognitive, language and social…

A well-established approach to modeling clustered data introduces random effects in the model of interest. Mixed-effects logistic regression models can be used to predict discrete outcome variables when observations are correlated. An extension of the mixed-effects logistic regression model is presented in which the dependent variable is a latent…

In Fall 2004, Virginia Commonwealth University (VCU) piloted a modeling-based approach to college algebra. This paper describes the course and an assessment that was conducted to determine the effect of this approach on student achievement in comparison to a traditional approach to college algebra. The results show that compared with their…

This article describes an interdisciplinary course that develops essential mathematical modeling skills within an introductory biology setting. The course embodies recent recommendations regarding the need for interdisciplinary, inquiry-based mathematical preparation of undergraduates in the biological sciences. Evaluation indicates that the…

Making connections becomes increasingly important as students proceed through middle school and high school. This book shows ways of embedding connective processes in instruction in grades 9-12. Problems invite mathematical modeling, unify diverse content, call for different representations, and encourage students to look back at their work to…

Often, all of the variables in a model are latent, random, or subject to measurement error, or there is not an obvious dependent variable. When any of these conditions exist, an appropriate method for estimating the linear relationships among the variables is Least Principal Components Analysis. Least Principal Components are robust, consistent,…

Modeling, simulation, and discrete mathematics have all been identified by professional mathematics education organizations as important areas for secondary school study. This classroom study focused on the components and tools for modeling and how students use these tools to construct their understanding of contextual problems in the content area…

Researchers should investigate statistical models that can help counselors decide how to treat individual clients. This research investigated the questions, "Given an effect size (ES) from a counseling outcome study, what is the probability that a client would have a negative response to the treatment, and what is the probability that the client…