The purpose of this article is to describe findings from a study of teachers' social interaction during discussions about students' thinking. The goal of the discussions was for the teachers to interpret their students' thinking as revealed from work on non-routine, thought-revealing mathematical tasks, known as "model-eliciting…

This paper deals with a teaching approach aimed to help students become aware of targeted techniques of significance in problem solving. The teaching approach is to present a series of tasks that all can be solved by applying the same technique. Two levels of prompting are used; first for the students to realize solutions without necessarily being…

A laboratory experiment reinforces the concept of acid-base equilibria while introducing a common application of spectrophotometry and can easily be completed within a standard four-hour laboratory period. It provides students with an opportunity to use advanced data analysis techniques like data smoothing and spectral deconvolution to…

I present modifications to the traditional course entitled, "Process dynamics and control," which I renamed "Modeling, dynamics, and control of chemical and biological processes." Additions include the central dogma of biology, pharmacokinetic systems, population balances, control of gene transcription, and large­-scale…

The Trends in International Mathematics and Science studies provide country-level data for tracking changes in student achievement over time. In this paper the author has developed a method for identifying and monitoring trends in student achievement above or below any specified cut-point on these tests. The method involved the use of the Foster,…

Dichotomous item response theory (IRT) models can be viewed as families of stochastically ordered distributions of responses to test items. This paper explores several properties of such distributions. The focus is on the conditions under which stochastic order in families of conditional distributions is transferred to their inverse distributions,…

A Monte Carlo study was conducted to assess the effects of some potential confounding factors on structural equation modeling (SEM) fit indices and parameter estimates for both true and misspecified models. The factors investigated were data nonnormality, SEM estimation method, and sample size. Based on the fully crossed and balanced 3x3x4x2…

This study considers the problem of performing all pairwise comparisons of column means for a two-by-four additive nonorthogonal factorial analysis of variance (ANOVA) model where cell variances are heterogeneous. Extensions of the following procedures are considered: (1) Games-Howell (1976) procedure; (2) the C. W. Dunnett (1980) T3 and C…

The L statistic of E. B. Page (1963) tests the agreement of a single group of judges with an a priori ordering of alternative treatments. This paper extends the two group test of D. W. Leitner and C. M. Dayton (1976), an extension of the L test, to analyze difference in consensus between two unequally sized groups of judges. Exact critical values…

Most of the multivariate statistical techniques rely on the assumption of multivariate normality. The effects of non-normality on multivariate tests are assumed to be negligible when variance-covariance matrices and sample sizes are equal. Therefore, in practice, investigators do not usually attempt to remove non-normality. In this simulation…

The power of the procedure of W. Stout to detect deviations from essential unidimensionality in two-dimensional data was investigated for minor, moderate, and large deviations from unidimensionality using criteria for deviations from unidimensionality based on prior research. Test lengths of 20 and 40 items and sample sizes of 700 and 1,500 were…

A study on sampling errors of variance components was conducted within the framework of generalizability theory by P. L. Smith (1978). The study used an intuitive approach for solving the problem of how to allocate the number of conditions to different facets in order to produce the most stable estimate of the universe score variance. Optimization…

The Pearson product-moment correlation, r, is commonly applied in educational research. Almost all researchers realize that r ranges between -1.00 and +1.00, and that negative coefficients indicate that the bivariate relationship is inverse. Researchers also recognize that the Pearson r only evaluates linear relationship, and is not sensitive to…

A didactic example is provided, using a Monte Carlo method, of how differential item functioning (DIF) can be eliminated (and thus better understood) when the complete latent space is used. The main source of DIF is that the matching single criterion used in some DIF procedures, Mantel Haenszel or Simultaneous Item Bias (SIBTEST), does not account…

The psychometric objections to using essays and other subjective tests for measurement can be overcome by a many-facet Rasch model. This model enables judge-awarded grades to be transformed from their arbitrary, local, non-linear rating scale form into linear measures with explicit generalizable meaning of specifiable reliability (standard error)…