This analysis of a problem that is frequently posed at professional development workshops, in print, and on the Web--the coffee-milk mixture riddle--illustrates the timeless advice of George Pólya's masterpiece on problem solving in mathematics, "How to Solve It." In his book, Pólya recommends that problems previously solved and put…

This study investigated the sets of mental computation strategies used by prospective elementary teachers to compute sums and differences of whole numbers. In the context of an intervention designed to improve the number sense of prospective elementary teachers, participants were interviewed pre/post, and their mental computation strategies were…

Computational modeling and eye-tracking were used to investigate how phonological and semantic information interact to influence the time course of spoken word recognition. We extended our recent models (Chen & Mirman, 2012; Mirman, Britt, & Chen, 2013) to account for new evidence that competition among phonological neighbors influences…

In this study, we examined the impact of covariate measurement error (ME) on the estimation of quantile regression and student growth percentiles (SGPs), and find that SGPs tend to be overestimated among students with higher prior achievement and underestimated among those with lower prior achievement, a problem we describe as ME endogeneity in…

Student growth percentiles (SGPs) express students' current observed scores as percentile ranks in the distribution of scores among students with the same prior-year scores. A common concern about SGPs at the student level, and mean or median SGPs (MGPs) at the aggregate level, is potential bias due to test measurement error (ME). Shang,…

This emerging technology report describes virtual environment interactions an approach for blending movement and computer programming as an embodied way to support girls in building computational thinking skills. The authors seek to understand how body syntonicity might enable young learners to bootstrap their intuitive knowledge in order to…

Research on equating with small samples has shown that methods with stronger assumptions and fewer statistical estimates can lead to decreased error in the estimated equating function. This article introduces a new approach to linear observed-score equating, one which provides flexible control over how form difficulty is assumed versus estimated…

The assessment of differential item functioning (DIF) is routinely conducted to ensure test fairness and validity. Although many DIF assessment methods have been developed in the context of classical test theory and item response theory, they are not applicable for cognitive diagnosis models (CDMs), as the underlying latent attributes of CDMs are…

We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…

Teachers often promote care in doing calculations, but for most students a single mistake rarely has major consequences. This article presents several real-life events in which relatively minor mathematical errors led to situations that ranged from public embarrassment to the loss of millions of dollars' worth of equipment. The stories here…

Intelligent behavior of adaptive educational systems is based on student models. Most research in student modeling focuses on student learning (acquisition of skills). We focus on prior knowledge, which gets much less attention in modeling and yet can be highly varied and have important consequences for the use of educational systems. We describe…

The field of education is increasingly committed to adopting evidence-based practices. Although randomized experimental designs provide strong evidence of the causal effects of interventions, they are not always feasible. For example, depending upon the research question, it may be difficult for researchers to find the number of children necessary…

The widely used percentage of nonoverlapping data (PND) treatment effect calculation was compared to more recently developed methods which, it has been argued, better account for outlying variables and trend in single-case design (SCD) intervention studies. Percentage of all nonoverlapping data (PAND) and nonoverlap of all pairs (NAP) were…

School districts across the United States increasingly use value-added models (VAMs) to evaluate teachers. In practice, VAMs typically rely on lagged test scores from the previous academic year, which necessarily conflate summer with school-year learning and potentially bias estimates of teacher effectiveness. We investigate the practical…

The aim of the study was to measure the level of anxiety towards mathematics among workers in the production area of a factory in the sugar industry. In order to carry out this study, the Muñoz y Mato-Vázquez scale was used (2007) and adapted to the working area. 283 workers from the three different shifts (morning, afternoon and night) were…