Children's failure to reason often leads to their mathematical performance being shaped by spurious associations from problem input and overgeneralization of inapplicable procedures rather than by whether answers and procedures make sense. In particular, imbalanced distributions of problems, particularly in textbooks, lead children to create…

As science becomes increasingly computationally intensive, the need for computational thinking (CT) and computer science (CS) practices in K-12 science education is becoming paramount. Incorporation of CT/CS practices in K-12 education can be seen in national standards and a variety of allied initiatives. One way to build capacity around an…

Spearman's correction for attenuation (measurement error) corrects a correlation coefficient for measurement errors in either-or-both of two variables, and follows from the assumptions of classical test theory. Spearman's equation removes all measurement error from a correlation coefficient which translates into "increasing the reliability of…

A simulation study that used 3,000 computer-generated event streams with known behavior rates, interval durations, and session durations was conducted to test whether the main and interaction effects of true rate and interval duration affect the error level of uncorrected and Poisson-transformed (i.e., "corrected") count as estimated by…

Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-conditional independence of features. This feature independence assumption simplifies the inference…

Development and refinement of self-report measures generally involves selecting a subset of indicators from a larger set. Despite the importance of this task, methods applied to accomplish this are often idiosyncratic and ad hoc, or based on incomplete statistical criteria. We describe a structural equation modeling (SEM)-based technique, based on…

Evaluating the quality of students' programs is necessary for better teaching and learning. Although many innovative learning environments for computer science have been introduced, the scarcity of program evaluation frames and tools is a demanding issue in the teaching practice. This study examined the quality of students' Scratch programs by…

Finger counting is widely considered an important step in children's early mathematical development. Presumably, children's ability to move their fingers during early counting experiences to aid number representation depends in part on their early fine motor skills (FMS). Specifically, FMS should link to children's procedural counting skills…

Policymakers have grown increasingly interested in how experimental results may generalize to a larger population. However, recently developed propensity score-based methods are limited by small sample sizes, where the experimental study is generalized to a population that is at least 20 times larger. This is particularly problematic for methods…

Manipulatives have been found to be effective in increasing mathematics achievement when they are put to good use (Canny, 1984; Clements & Battista, 1990; Clements, 1999; Sowell, 1989; Suydam, 1984), but their use in mathematics instruction is not clear and it is often debated to be effective (Ball, 1992; McNeil & Jarvin, 2007). The…

We are concerned with the unbiased estimation of a treatment effect in the context of non-experimental studies with grouped or multilevel data. When analyzing such data with this goal, practitioners typically include as many predictors (controls) as possible, in an attempt to satisfy ignorability of the treatment assignment. In the multilevel…

In basic regression discontinuity (RD) designs, causal inference is limited to the local area near a single cutoff. To strengthen the generality of the RD treatment estimate, a design with multiple cutoffs along the assignment variable continuum can be applied. The availability of multiple cutoffs allows estimation of a pooled average treatment…

In basic regression discontinuity (RD) designs, causal inference is limited to the local area near a single cutoff. To strengthen the generality of the RD treatment estimate, a design with multiple cutoffs along the assignment variable continuum can be applied. The availability of multiple cutoffs allows estimation of a pooled average treatment…

Howe (2014, Three pillars of first grade mathematics, and beyond. In: Li Y. & Lappan G. (eds), Mathematics curriculum in school education, Springer, Dordrecht, pp 183-207) identified three pillars of first grade mathematics and beyond that described central mathematical and sense-making aspects of major Common Core State Standards Math…

The purpose of this note is to study the equivalence of observed and expected (Fisher) information functions with polytomous item response theory (IRT) models. It is established that observed and expected information functions are equivalent for the class of divide-by-total models (including partial credit, generalized partial credit, rating…