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.

A major goal of instruction is for students to develop competence with numbers. This study attempts to determine the effect of instructional materials that develop number concepts and connect these concepts to mental computation procedures. The study used 16 classes of eighth-grade students and a pretest-posttest design with two treatment groups.…

Presented is a method of teaching adding and subtracting as an interrelated series of patterns using a number line. Examples of the use of this method as well as the materials necessary are discussed. Applications of the method to multiplication and division are given. (CW)

Tests of computational estimation ability (CEA), strategy (CES), and mental computation ability (MCA) of (n=124) fourth, (n=143) fifth, and (n=84) sixth graders found significant relationships between CEA and MCA and between CEA and CES but not between MCA and CES. (12 references) (Author/MKR)

Presents a series of reflections in which a second-grade teacher recognizes the value of encouraging children to develop various computational processes as well as a range of different solution approaches. Uses the context of mentally calculating costs of menu items. (MKR)

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…

This article introduces a bootstrap generalization to the Modified Parallel Analysis (MPA) method of test dimensionality assessment using factor analysis. This methodology, based on the use of Marginal Maximum Likelihood nonlinear factor analysis, provides for the calculation of a test statistic based on a parametric bootstrap using the MPA…

This study examined the effects of prior knowledge, learner preference for control, and type of control (learner or program) on the achievement of middle-school students in a computer-based instructional program on adding and subtracting integers. Students were blocked by preference-for-control scores and randomly assigned to either a…

Cluster randomized trials (CRTs) have been widely used in field experiments treating a cluster of individuals as the unit of randomization. This study focused particularly on situations where CRTs are accompanied by a common complication, namely, treatment noncompliance or, more generally, intervention nonadherence. In CRTs, compliance may be…

Passive and active visuospatial working memory (VSWM) were investigated in relation to maths performance. The mental rotation task was employed as a measure of active VSWM whereas passive VSWM was investigated using a modified Corsi Blocks task and a matrix pattern task. The Raven Progressive Matrices Test measured fluid intelligence. A total of…

To address the confusion resulting from difficulties with proportional reasoning among preservice physical science students, a cube-assembly activity was used to bring a sense of concreteness to abstract ideas. The activity took students from the concrete step of assembling cubes of various sizes and directly measuring their properties to slightly…

The first part of this two-part paper [see EJ787497] described the development of a new freshman business mathematics (FBM) course at our college. In this paper, we discuss our assessment tool, the business memo, as a venue for students to apply mathematical skills, via mathematical modelling, to realistic business problems. These memos have…