We used a random-assignment experiment in Los Angeles Unified School District to evaluate various non-experimental methods for estimating teacher effects on student test scores. Having estimated teacher effects during a pre-experimental period, we used these estimates to predict student achievement following random assignment of teachers to…

Many arithmetic problems can be solved in two ways: by a calculation involving several steps, and by direct retrieval of the answer. With practice on particular problems, memory retrieval tends to supplant calculation--an important aspect of skill learning. We asked how the distribution of practice on particular problems affects this kind of…

This paper analyzes the sum score based (SSB) formulation of the Rasch model, where items and sum scores of persons are considered as factors in a logit model. After reviewing the evolution leading to the equality between their maximum likelihood estimates, the SSB model is then discussed from the point of view of pseudo-likelihood and of…

A new method is introduced to study the behaviour of the falling spherical ball in a viscous liquid using the well known Stokes' law. Experimental results are compared with those obtained by numerical calculations. Upper limits on the size and mass of the spherical balls of different materials used in the experiment are presented. (Contains 5…

Item response theory-likelihood ratio-differential item functioning (IRT-LR-DIF) is used to evaluate the degree to which items on a test or questionnaire have different measurement properties for one group of people versus another, irrespective of group-mean differences on the construct. Usually, the latent distribution is presumed normal for both…

Four methods for estimating a dynamic factor model, the direct autoregressive factor score (DAFS) model, are evaluated and compared. The first method estimates the DAFS model using a Kalman filter algorithm based on its state space model representation. The second one employs the maximum likelihood estimation method based on the construction of a…

A method is presented to calculate accurate approximations to the half-life values of elimination systems modelled by one compartment. The major advantage of this method is that only algebraic mathematical operations are required. The results will be of value not only to students beginning the study of elimination kinetics, but also to…

Differential item functioning (DIF) occurs when an item has different measurement properties for members of one group versus another. Likelihood-ratio (LR) tests for DIF based on item response theory (IRT) involve statistically comparing IRT models that vary with respect to their constraints. A simulation study evaluated how violation of the…

Several types of parameterizations of attribute correlations in cognitive diagnosis models use the reduced reparameterized unified model. The general approach presumes an unconstrained correlation matrix with K(K - 1)/2 parameters, whereas the higher order approach postulates K parameters, imposing a unidimensional structure on the correlation…

The main purpose of this research is to evaluate the performance of a Bayesian approach for estimating unknown change points using Monte Carlo simulations. The univariate and bivariate unknown change point mixed models were presented and the basic idea of the Bayesian approach for estimating the models was discussed. The performance of Bayesian…

Partial-interval (PIR), whole-interval (WIR), and momentary time sampling (MTS) estimates were compared against continuous measures of safety performance for three postural behaviors: feet, back, and shoulder position. Twenty-five samples of safety performance across five undergraduate students were scored using a second-by-second continuous…

We study different ways of determining the mean distance (r[subscript n]) between a reference point and its nth neighbour among random points distributed with uniform density in a D-dimensional Euclidean space. First, we present a heuristic method; though this method provides only a crude mathematical result, it shows a simple way of estimating…

Just as the tree bridges the worlds of earth and air-light, transforming energies so that there is a flow of nutrients between these two worlds, so too teachers can be seen as bridges or mediators between the world of learners and the world of mathematics. In this speech, the author suggests that one of the principal roles for mathematics…

Formulas to determine the necessary sample sizes for parametric tests of group comparisons are available from several sources and appropriate when population distributions are normal. However, in the context of nonnormal population distributions, researchers recommend Yuen's trimmed mean test, but formulas to determine sample sizes have not been…

Computational models will play an important role in our understanding of human higher-order cognition. How can a model's contribution to this goal be evaluated? This article argues that three important aspects of a model of higher-order cognition to evaluate are (a) its ability to reason, solve problems, converse, and learn as well as people do;…