The computer systems available for molecular modeling are described, along with a discussion of a molecular modeling program created and supported by computational techniques for the first-semester general chemistry course. Various exercises are listed, which direct the learner from a beginner's course in software practice to more complex…

Active student responding is often required to remedy computation skill deficits in students with learning disabilities. However, these students may find computation assignments unrewarding and frustrating, and be less likely to choose to engage in assigned computation tasks. In the current study, middle school students with learning disabilities…

The effect of person misfit to an item response theory model on a mastery/nonmastery decision was investigated. Furthermore, it was investigated whether the classification precision can be improved by identifying misfitting respondents using person-fit statistics. A simulation study was conducted to investigate the probability of a correct…

In this study, six elementary grade children with developmental dyscalculia were trained individually and in small group settings with a one-semester program stressing basic numerical knowledge and conceptual knowledge. All the children showed considerable and partly significant performance increases on all calculation components. Results suggest…

In this article, the authors describe their efforts to assess prospective K-8 teachers' knowledge of proportional reasoning. Based upon their analysis of prospective K-8 teachers' work on a mathematics performance task, they discuss the implications for preparing prospective teachers to teach proportional reasoning to their students. In general,…

In the present paper, we develop and apply a technique, based on the logic of process dissociation, for obtaining numerical estimates of item and order information. Certain variables, such as phonological similarity, are widely believed to produce dissociative effects on item and order retention. However, such beliefs rest on the questionable…

This paper presents a row-column (RC) association model in which the estimated row and column scores are forced to be in agreement with a priori specified ordering. Two efficient algorithms for finding the order-restricted maximum likelihood (ML) estimates are proposed and their reliability under different degrees of association is investigated by…

This article proposes a practical method that capitalizes on the availability of information from multiple tests measuring correlated abilities given in a single test administration. By simultaneously estimating different abilities with the use of a hierarchical Bayesian framework, more precise estimates for each ability dimension are obtained.…

Everyone is familiar with the concept that the cube and octahedron, dodecahedron and icosahedron are dual pairs, with the tetrahedron being self-dual. On the face of it, the concept seems straightforward; however, in all but the most symmetrical cases it is far from clear. By using the computer and three-dimensional graphics programs, it is…

The enumeration of small numbers of objects (approximately 4) proceeds rapidly, accurately, and with little effort via a process termed subitization. Four experiments examined whether it was possible to subitize the number of features rather than objects present in a display. Overall, the findings showed that when features are presented randomly…

A fundamental question in developmental science is how brains with and without language compute numbers. Measuring young children's verbal reactions in France (Paris) and in England (Oxford), here we show that, although there is a general arithmetic ability for small numbers that is shared by monkeys and preverbal infants, the development of such…

Preschool children are often good at counting things but seem slow to learn that there is more to counting than simply finding out how many are in a single set. Counting is useful when comparing sets and when creating new sets to match existing ones. This is part of the numerical understanding that educators wish to foster in schools. In two…

This note provides a simple method to extend the usual Leibniz rule for higher derivatives of the product of two functions to several functions, which is within the reach of freshman calculus students.

This paper discusses a result of Li and Shen which proves the existence of a unique periodic solution for the differential equation x[dots above] + kx[dot above] + g(x,t) = [epsilon](t) where k is a constant; g is continuous, continuously differentiable with respect to x , and is periodic of period P in the variable t; [epsilon](t) is continuous…

The normal equations discussed in this paper for a least-squares parabolic fit have a unique solution if and only if there are at least three different x-values in the observations. This requirement is satisfied by most real sets of quantitative observations. For particular data sets, the appropriateness of parabolic fits should be assessed with…