Calculus education research on integration is coalescing around the theme that teaching integration based on quantitative reasoning is crucial for robust understanding of and usage of integrals. This paper contributes to this International Journal for Research in Undergraduate Education special issue on the teaching and learning of definite…

Two articles, Edelsbrunner and, Schneider (2013), and Nokelainen and Silander (2014) comment on Musso, Kyndt, Cascallar, and Dochy (2013). Several relevant issues are raised and some important clarifications are made in response to both commentaries. Predictive systems based on artificial neural networks continue to be the focus of current…

The use of handheld CAS technology in undergraduate mathematics courses in Australia is paradoxically shrinking under sustained disapproval or disdain from the professional mathematics community. Mathematics education specialists argue with their mathematics colleagues over a range of issues in course development and this use of CAS or even…

An error in an essential equation within the article by Williams and Zimmerman is corrected, and the algebraic inequalities are translated into questions a researcher can ask about simple or residualized difference scores. Williams and Zimmerman acknowledge the error and note that main conclusions are not affected. (SLD)

Recent empirical studies of actual research practice demonstrate that general linear models, such as regression, have become increasingly popular. The present paper explores issues related to the interpretation of regression results, with illustrations drawn from studies in the counseling psychology literature. The primary focus of this paper is…

Mathematical programing formulas are introduced as new approaches to solve the classification problem in discriminant analysis. The research literature is reviewed, and an illustration using a real-world classification problem is provided. Issues relevant to potential uses of these formulations are discussed. (TJH)

Problems in the measurement of latent variables (LVs) in structural equations causal models are presented, with examples from recent empirical studies. Main issues addressed are (1) two general types of increased operative variables; (2) criteria for indicators of LVs; and (3) disattenuation effects in LV models. (SLD)

Across conditions, differences between population parameters defined by common factor analysis and component analysis are demonstrated. Implications for data analytic and theoretical issues related to choice of analytic model are discussed. Results suggest that principal components analysis should not be used to obtain parameters reflecting latent…

An overview of the state of the art in psychological research is presented, with an emphasis on the attention given to effect sizes. The acceptance of small effect sizes for biomedical research is contrasted with the rejection of similar effect sizes for psychological research. The Binomial Effect Size Display is used to depict the practical…

A large body of data is reviewed to support a new theory of motion perception described by S. Grossberg and M. E. Rudd (1989). The Motion Boundary Contour System is used to explain classical and recent data about motion perception that have not been explained by other models. (SLD)

Summarizes the current state of the art in test construction and contrasts it with previous conceptual models, some of which are wrong or misleading. New methodologies for item selection and review are presented, with current thinking on the specification of technical characteristics of tests. (Author/SLD)

After a brief review of the contributions of factor analysis and regional analysis to the elaboration of the structures of spatial abilities, a facet design and regional model for spatial abilities are presented. A cylindrical-wedge model is proposed to represent the correlational structure of spatial ability tests. (SLD)

A short review of the different estimation procedures that have been used in association with the Rasch model is provided. These procedures include joint, conditional, and marginal maximum likelihood methods; Bayesian methods; minimum chi-square methods; and paired comparison estimation. A comparison of the marginal maximum likelihood estimation…

Criteria used in the equating process proposed in the literature are reviewed. The discussion begins by examining how equating is defined. The controversy over the best criterion, the utility of some, and whether a criterion is needed at all means that much work needs to be done in this area. (SLD)

The importance of regression diagnostics in detecting influential data points is discussed, and five statistics are recommended for the applied researcher. The suggested diagnostics were used on a dataset of 24 subjects, and effects were analyzed. Colinearity-based diagnostics and diagnostics for a variety of procedures are discussed. (SLD)