Examined role of spontaneous gesture in 2- to 4-year-olds' counting and assessment of counting accuracy. Found that correspondence of children's speech and gesture varied systematically across age. Children adhered to one-to-one correspondence principle in gesture prior to speech. Counting accuracy related to correspondence of speech and gesture,…

Two experiments examined preschoolers' performance on test relying on the uniqueness principle for using evidence from a miscount in inferring a counterfactual cardinal number, with subtests probing associated number-skills. All the 5-year-olds and half the preschoolers passed the test. Results suggest that a crucial preschool step is to start…

Fit indexes were compared with respect to a specific type of model misspecification. Simple structure was violated with some secondary loadings that were present in the true models that were not specified in the estimated models. The c2 test, Comparative Fit Index, Goodness-of-Fit Index, Incremental Fit Index, Nonnormed Fit Index, root mean…

A bias-corrected estimator of noncentrality parameters of covariance structure models is discussed. The approach represents an application of the bootstrap methodology for purposes of bias correction, and utilizes the relation between average of resample conventional noncentrality parameter estimates and their sample counterpart. The…

The choice of constraints used to identify a simple factor model can affect the shape of the likelihood. Specifically, under some nonzero constraints, standard errors may be inestimable even at the maximum likelihood estimate (MLE). For a broader class of nonzero constraints, symmetric normal approximations to the modal region may not be…

Variants of adaptive Bayesian procedures for estimating the 5% point on a psychometric function were studied by simulation. Bias and standard error were the criteria to evaluate performance. The results indicated a superiority of (a) uniform priors, (b) model likelihood functions that are odd symmetric about threshold and that have parameter…

Students should be encouraged to focus on a big mathematical idea and to look for connections between problems and solution strategies. This unified view suggests that the students are developing computational fluency with fractions.

Through a large-scale simulation study, this article compares item parameter estimates obtained by the marginal maximum likelihood estimation (MMLE) and marginal Bayes modal estimation (MBME) procedures in the 3-parameter logistic model. The impact of different prior specifications on the MBME estimates is also investigated using carefully…

If the goal is to promote mathematical thinking and help children become flexible problem solvers, then it is important to show students multiple representations of a problem. Because it is important to help students develop both counting-based and collections-based conceptions of number, teachers should be showing students both number line…

A computational experiment is devised for advanced inorganic laboratory course that allows the students to explore the structure and bonding patterns of ethene and some heavier analogues. The HOMO-LUMO gaps, double bond dissociation energetics, and optimized geometries of ethene, disilene, and digermene are explored.

Students in the classroom should be provided with engaging activities for improving their computational fluency, making effective use of time, and as a medium of self-motivation. Games such as Contig, the 24 Game, and Number Jumbler are useful for practicing basic facts and computational fluency of mathematics.

Establishing an instrument's factorial invariance provides the empirical foundation to compare an individual's score across time or to examine the pattern of correlations between variables in differentiated age groups. In the recently published Woodcock-Johnson Tests of Cognitive Ability (WJ COG) and Achievement (WJ ACH) Third Edition (III) the…

This article presents a formula for weighted kappa in terms of rater means, rater variances, and the rater covariance that is particularly helpful in emphasizing that weighted kappa is an absolute agreement measure in the sense that it is sensitive to differences in rater's marginal distributions. Specifically, rater mean differences will decrease…

We focus on a major difficulty in solving combinatorial problems, namely, on the verification of a solution. Our study aimed at identifying undergraduate students' tendencies to verify their solutions, and the verification strategies that they employ when solving these problems. In addition, an attempt was made to evaluate the level of efficiency…

This study investigated the development of the many-to-one counting strategy in 4- year-old children. In the first experiment, 52 children participated. Their development with respect to two kinds of tasks, a hidden-items task and a needed-items task, was studied over four sessions. Children (n = 28) who accurately used the many-to-one strategy in…