In this paper, we describe a design experiment aimed at helping students to explore and develop concepts of infinite processes and objects. Our approach is based on the design and development of a computational microworld, which afforded students the means to construct a range of representational models (symbolic, visual and numeric) of…

Cognitive mechanisms underlying repetition priming in picture naming were decomposed in several experiments. Sets of encoding manipulations meant to selectively prime or reduce priming in object identification or word production components of picture naming were combined factorially to dissociate processes underlying priming in picture naming.…

The abstract nature of mathematics requires the communication of mathematical ideas through multiple representations, such as words, symbols, pictures, objects, or actions. Building representational fluency involves using mathematical representations flexibly and being able to interpret and translate among these different models and mathematical…

The current mantra in education is "technology, technology, technology." Many teachers and prospective teachers become frustrated with their lack of knowledge regarding the "appropriate" use of technology in the classroom. Prospective teachers need training in their education to understand how technology can be used "appropriately" in the…

Most college algebra courses are offered in the spirit of preparing the students to move on toward calculus. In reality, only a vanishingly small fraction of the million students a year who take these courses ever get to calculus. This article builds a strong case for the need to change the focus in college algebra to one that better meets the…

This article describes several methods from discrete mathematics used to simulate and solve an interesting problem occurring at a holiday gift exchange. What is the probability that two people will select each other's names in a random drawing, and how does this result vary with the total number of participants? (Contains 5 figures.)

The paper's aim is to demonstrate the utility of the well-known Nim game when it is used as a tool in teaching the binary system. A way to increase student comprehension, it also forms a basis for student projects and extracurricular activities on the topic. The paper offers descriptions of two versions of the game and the underlying mathematical…

A theory of the dynamics of dyadic interaction is presented, based on the concepts of "concern" (i.e., intentions, goals, and interests), "appraisal" and "contagiousness." Differences between children who participate in a specific interaction are linked to differences in social competence and social power. An overview is given of the social…

A general linear model (GLM) framework is used to suggest that structure coefficients ought to be interpreted in structural equation modeling confirmatory factor analysis (CFA) studies in which factors are correlated. The computation of structure coefficients in explanatory factor analysis and CFA is explained. Two heuristic data sets are used to…

This paper presents an alternate perspective for utilizing the action/process/object framework when discussing student conceptions of function. This perspective extends previously used frameworks by incorporating student conceptions that deal with functional properties and situational contexts, but differs in the analysis of the nature of the…

The use of a covariate for randomized response (RRT) research has been shown to reduce standard errors of sensitive trait proportion estimates. At the same time, the model has been shown to be subject to serious misspecification when the relationship between the covariate and the sensitive trait is non-monotonic. The RRT covariate model is adapted…

This paper provides a concise summary of 10 years of research into defining appropriate statistical models for estimating school and teacher effect on student learning and other important educational outcomes. It discusses criteria for judging models and presents the formulae for the two-stage, two-level student-school hierarchical linear modeling…

Test data generated according to two different multidimensional item response theory (IRT) models were compared at both the item response level and the test score level to determine whether measurable differences between the models could be detected when the data sets were constrained to be equivalent in terms of item "p"-values. The…

Analysis of covariance (ANCOVA) is a data analysis method that is often used to control extraneous sources of variation in non-equivalent group designs. It is commonly believed that as long as the covariate is highly correlated with the dependent variable there is nothing to lose in using ANCOVA, even in non-randomized studies. This paper examines…

Discusses how to check the accuracy of different enrollment projection methods for different educational systems. (Author)