Although estimations typically possess correct answers, these answers may be difficult to demonstrate to others. However, providing external information may increase their demonstrability. In this experiment, individuals (N = 60) and 6-person groups (N = 360) generated estimations with or without frames of reference. We hypothesized that…

In the Western Gregorian Calendar, the date of Easter Sunday is defined as the Sunday following the ecclesiastical Full Moon that falls on or next after March 21. While the pattern of dates so defined usually repeats each 19 years, there is a 0.08 day difference between the cycles. More accurately, the system has a period of 70 499 183 lunations…

The originally proposed multivariate meta-analysis approach for correlation matrices--analyze Pearson correlations, with each study's observed correlations replacing their population counterparts in its conditional-covariance matrix--performs poorly. Two refinements are considered: Analyze Fisher Z-transformed correlations, and substitute better…

A common mistake in analysis of cluster randomized trials is to ignore the effect of clustering and analyze the data as if each treatment group were a simple random sample. This typically leads to an overstatement of the precision of results and anticonservative conclusions about precision and statistical significance of treatment effects. This…

This paper uses a partial differential equation which occurs in a reduced model of large scale circulation in an ocean basin as an educational vehicle through which to demonstrate the usefulness of a set of mathematical techniques in analysing the equation. A parameter occurring in the equation does in reality vary from very small through…

This article demonstrates the use of mixed-effects logistic regression (MLR) for conducting sequential analyses of binary observational data. MLR is a special case of the mixed-effects logit modeling framework, which may be applied to multicategorical observational data. The MLR approach is motivated in part by G. A. Dagne, G. W. Howe, C. H.…

This paper, the first of a two-part article, follows the trail in history of the development of a graphical representation of the complex roots of a function. Root calculation and root representation are traced through millennia, including the development of the notion of complex numbers and subsequent graphical representation thereof. The…

This article seeks to model criminal career length using data from six different birth cohorts born between 1953 and 1978, totaling more than 58,000 males and females from England and Wales. A secondary aim of this article is to consider whether information available at the first court appearance leading to a conviction is associated with the…

As a teacher's aide this author is often asked to help children who have difficulty with mathematics. Recently she was asked to help children from three different grades with their understanding of time. Although each grade had a different activity to undertake, all of the children struggled to grasp time-concepts that adults often take for…

Before the advent of symbolism, i.e. before the end of the 16th Century, algebraic calculations were made using natural language. Through a kind of metaphorical process, a few terms from everyday life (e.g. thing, root) acquired a technical mathematical status and constituted the specialized language of algebra. The introduction of letters and…

This paper presents a new polychoric instrumental variable (PIV) estimator to use in structural equation models (SEMs) with categorical observed variables. The PIV estimator is a generalization of Bollen's (Psychometrika 61:109-121, 1996) 2SLS/IV estimator for continuous variables to categorical endogenous variables. We derive the PIV estimator…

In this paper I present a class of discrete choice models for ordinal response variables based on a generalization of the stereotype model. The stereotype model can be derived and generalized as a random utility model for ordered alternatives. Random utility models can be specified to account for heteroscedastic and correlated utilities. In the…

The different methods used for computing labile metal-ligand complexes, which are suitable for an iterative computer solution, are illustrated. The ligand function has allowed students to relegate otherwise tedious iterations to a computer, while retaining complete control over what is calculated.

This book includes two main sections: a discussion of problem solving and a section on computation with whole numbers. A primary theme of the text is that problem solving sets the stage for meaning and conceptual development with respect to numbers. The section on problem solving includes numerous problem-solving activities that have a dual…

Users of logistic regression models often need to describe the overall predictive strength, or effect size, of the model's predictors. Analogs of R[superscript 2] have been developed, but none of these measures are interpretable on the same scale as effects of individual predictors. Furthermore, R[superscript 2] analogs are not invariant to the…