This article explores the uses of a simulation model (the two bucket story)--implemented by a stand-alone computer program, or an Excel workbook (both on the web)--that can be used for deriving bootstrap confidence intervals, and simulating various probability distributions. The strengths of the model are its generality, the fact that it provides…

The aim of this study was twofold. First, it evaluated the developmental changes on frequency of use, efficiency, and choice of counting strategies from childhood to adulthood. Second, it determined the adaptation of the counting strategies to the structural features of the task. Participants in seven age groups ranging from 5-year-old to…

The way in which computer algebra systems, such as Maple, have made the study of physical problems of some considerable complexity accessible to mathematicians and scientists with modest computational skills is illustrated by solving the multiple pendulum problem. A solution is obtained for four pendulums with no restriction on the size of the…

A structure for learning the connections among standard deviations, z-scores, and normal distributions is presented. The components of this structure are classified into intuitive or previously learned conceptual knowledge, computational knowledge, and formalized conceptual knowledge. (Contains 1 figure.)

The existing maximum likelihood theory and its computer software in structural equation modeling are established on the basis of linear relationships among latent variables with fully observed data. However, in social and behavioral sciences, nonlinear relationships among the latent variables are important for establishing more meaningful models…

In textbook treatments of enzyme inhibition kinetics, adjustment of the initial inhibitor concentration for inhibitor bound to enzyme is often neglected. For example, in graphical plots such as the Dixon plot for estimation of an inhibition constant, the initial concentration of inhibitor is usually plotted instead of the true inhibitor…

In this paper, the author looks at some classic problems in mathematics that involve motion in the plane. Many case problems like these are difficult and beyond the mathematical skills of most undergraduates, but computational approaches often require less insight into the subtleties of the problems and can be used to obtain reliable solutions.…

The authors present data from 2 feature verification experiments designed to determine whether distinctive features have a privileged status in the computation of word meaning. They use an attractor-based connectionist model of semantic memory to derive predictions for the experiments. Contrary to central predictions of the conceptual structure…

An objective method is presented to group discrete self-injurious behavior (SIB) events into bouts. Survival analysis was used to determine how long after an SIB the probability of observing a subsequent SIB remained elevated. This estimated bout length criterion time point was determined individually for 19 subjects with developmental disorders…

The paper starts from classroom situations about the study of a functional relationship with help of technological tools as a "transposition" of experimental approaches from research mathematical practices. It considers the limitation of this transposition in existing curricula and practices based on the use of non-symbolic software like dynamic…

This paper considers the problem of analysis of correlation coefficients from a multivariate normal population. A unified theorem is derived for the regression model with normally distributed explanatory variables and the general results are employed to provide useful expressions for the distributions of simple, multiple, and partial-multiple…

Assuming errors of measurement are distributed binomially, this article reviews various procedures for constructing an interval for an individual's true number-correct score; presents two general interval estimation procedures for an individual's true scale score (i.e., normal approximation and endpoints conversion methods); compares various…

Using two single-cohort longitudinal surveys, the NLS72 and the NELS88, I investigate the impact of four noncognitive traits--self-esteem, external locus of control, the importance of money/work and the importance of people/family--on wages and on the gender wage gap among these young workers. I find that gender differences in these noncognitive…

This mixed-methods study assessed the effects of Enhanced Anchored Instruction (EAI) on the math performance of adolescents with learning disabilities in math (MLD). A quasi-experimental pretest-posttest control group design with switching replications was used to measure students' computation and problem-solving skills on EAI compared to control…

Managing the pedagogical aspects of the "computational turn" that is occurring within the Humanities in general and the disciplines associated with cognitive science and neuroscience in particular, first implies facing the challenge of introducing students to computation. This paper presents what has proven to be an efficient approach to bringing…