Interest in using Bayesian methods for estimating item response theory models has grown at a remarkable rate in recent years. This attentiveness to Bayesian estimation has also inspired a growth in available software such as WinBUGS, R packages, BMIRT, MPLUS, and SAS PROC MCMC. This article intends to provide an accessible overview of Bayesian…

Recently, MDS has been utilized to identify and evaluate cognitive ability latent profiles in a population. However, dimension coordinates do not carry any statistical properties. To cope with statistical incompetence of MDS, we investigated the common aspects of various studies utilizing bootstrapping, and provided an R function for its…

Combinatorial enumeration has a variety of important applications, but there is much evidence indicating that students struggle with solving counting problems. The roots of such difficulty, as well as ways to mitigate such difficulty, have not yet been thoroughly studied. In this paper, one particular aspect of students' counting activity is…

How do children map number words to the numerical magnitudes they represent? Recent work in adults has shown that two distinct mechanisms--structure mapping and associative mapping--connect number words to nonlinguistic numerical representations (Sullivan, J., 2012). This study investigated the development of number word mappings, and the roles of…

Consciousness remains a mystery--"a phenomenon that people do not know how to think about--yet" (Dennett, D. C., 1991, p. 21). Here, I consider how the connectionist perspective on information processing may help us progress toward the goal of understanding the computational principles through which conscious and unconscious processing…

Nonoverlap is widely used as a statistical summary of data; however, these analyses rarely correct unwanted positive baseline trend. This article presents and validates the graph rotation for overlap and trend (GROT) technique, a hand calculation method for controlling positive baseline trend within an analysis of data nonoverlap. GROT is…

I conduct a study of learning in HMAX-like models, which are hierarchical models of visual processing in biological vision systems. Such models compute a new representation for an image based on the similarity of image sub-parts to a number of specific patterns, called prototypes. Despite being a central piece of the overall model, the issue of…

Since the seminal introduction of the propensity score (PS) by Rosenbaum and Rubin, PS-based methods have been widely used for drawing causal inferences in the behavioral and social sciences. However, the PS approach depends on the ignorability assumption: there are no unobserved confounders once observed covariates are taken into account. For…

Recent government moves in many countries have seen coding included in school curricula, or promoted as part of computing, mathematics or science programmes. While these moves have generally been associated with a need to engage more young people in technology study, research has hinted at possible benefits from learning to program including…

This paper argues neoliberal programs of government in education are equipping parents for calculativeness. Regimes of testing and the publication of these results and other organizational data are contributing to a public economy of numbers that increasingly oblige citizens to calculate. Using the notions of calculative and market devices, this…

Surprisingly few empirical studies address how computational thinking works "in the wild" or how games and simulations can support developing computational thinking skills. In this article, the authors report results from a study of computational thinking (CT) as evinced through player discussions around the collaborative board game…

In this paper, we present a third-grade ecology learning environment that integrates two forms of modeling--embodied modeling and agent-based modeling (ABMs)--through the generation of mathematical representations that are common to both forms of modeling. The term "agent" in the context of ABMs indicates individual computational objects…

A laboratory project for the upper-division physical chemistry laboratory is described, and it combines IR and Raman spectroscopies with Gaussian electronic structure calculations to determine the structure of the oxalate anion in solid alkali oxalates and in aqueous solution. The oxalate anion has two limiting structures whose vibrational spectra…

A good formula is like a good story, rich in description, powerful in communication, and eye-opening to readers. The formula presented in this article for determining the coefficients of the binomial expansion of (x + y)n is one such "good read." The beauty of this formula is in its simplicity--both describing a quantitative situation…

A first-grade teacher has students use their hands and fingers to engage in and develop understanding of counting, to combine groups to facilitate counting by fives and tens, and to describe their findings using words and equations.