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…

This issue brief outlines the immediate need for more accurate dropout and graduation data, while providing a snapshot of work currently underway. By drawing on two prominent methods for calculating graduation rates: the National Governors Association's endorsed longitudinal approach and the Averaged Freshman Graduation Rate (AFGR), this brief…

Despite the increasing use of the microgenetic methodology to examine change, the techniques employed to analyse microgenetic data remain fairly unsophisticated. This paper reviews the existing ways of analysing such data and describes their limitations. We use two recent studies to illustrate how modelling can avoid these problems and reveal…

We developed educational software to show graduate students how to plan molecular marker experiments. These computer simulations give the students feedback on the precision of their experiments. The objective of the software was to show students using a hands-on approach how: (1) environmental variation influences the range of the estimates of the…

An item response model is proposed for the analysis of continuous response formats in an item response theory (IRT) framework. With such formats, respondents are asked to report their response as a mark on a fixed-length graphical segment whose ends are labeled with extreme responses. An interpolation process is proposed as the response mechanism…

Calculators used widely by students, teachers, scientists, engineers and many others provide an interesting case study of a compelling technology that has helped change the way many professionals work. They not only help in enhancing problem solving skills of most individuals, but also help visualise solutions to problems in a better way. Research…