When counting, the final word used to tag the final item in a set represents the cardinality, or total number, of the set. Understanding of this concept serves as a foundation for children's basic mathematical skills, such as arithmetic. However, little is known about how variations in the early learning environment affect children's understanding…

Single case designs (SCDs) generally consist of a small number of short time series in two or more phases. The analysis of SCDs statistically fits in the framework of a multilevel model, or hierarchical model. The usual analysis does not take into account the uncertainty in the estimation of the random effects. This not only has an effect on the…

How much information do natural systems store and process? In this work we attempt to answer this question in multiple ways. We first establish a mathematical framework where natural systems are represented by a canonical form of edge-labeled hidden fc models called e-machines. Then, utilizing this framework, a variety of measures are defined and…

The increasing availability of data from multi-site randomized trials provides a potential opportunity to use instrumental variables methods to study the effects of multiple hypothesized mediators of the effect of a treatment. We derive nine assumptions needed to identify the effects of multiple mediators when using site-by-treatment interactions…

The goal of this study was to investigate reliable cognitive change in epilepsy by developing computational procedures to determine reliable change index scores (RCIs) for the Dutch Wechsler Intelligence Scales for Children. First, RCIs were calculated based on stability coefficients from a reference sample. Then, these RCIs were applied to a…

Computational estimation is an important skill necessary for students' mathematical development. Students who can estimate well for computations rely on an understanding of many mathematical topics, including a strong number sense, which facilitates understanding the mathematical operations and contextual evidence within a problem. In turn, good…

This article presents a sequence of learning activities that lead to using the area model of multiplication to understand the distributive property (DP). The connection between area and multiplication is an important one, both for algebraic thinking and for geometry, as indicated in two of the critical areas for the third grade in the Common Core…

The purpose of this paper is to explore middle school in-service mathematics teachers' ability (1) to identify and explain students' actions in pattern generalization and (2) to account for the variation in teachers' explanations of students' actions in terms of task and teachers' factors. Two questionnaires were developed: (1) a questionnaire to…

During the second half of the twentieth century, a process of privatization took place in the Argentine education system. This paper seeks to explain the growth of private enrollments in Argentina over the last years. Drawing on the concept of quasi-monopoly, we run a random-effects estimation on panel data to analyze the determinants of the…

This study reports on the statistical content of five U.S. textbook series written for elementary students in grades 1-5. The researchers examined 17,688 pages and coded 7445 statistical tasks to determine (1) the distribution of statistical topics within textbooks, and (2) the relative emphasis on the phases of the statistical problem solving…

With widespread adoption of Learning Management Systems (LMS) and other learning technology, large amounts of data--commonly known as trace data--are readily accessible to researchers. Trace data has been extensively used to calculate time that students spend on different learning activities--typically referred to as time-on-task. These measures…

Student modeling in intelligent tutoring systems is mostly concerned with modeling correctness of students' answers. As interactive problem solving activities become increasingly common in educational systems, it is useful to focus also on timing information associated with problem solving. We argue that the focus on timing is natural for certain…

This paper takes an innovative approach. We have used the idea of converting international evidence of the size of higher education externalities as a proportion of GDP into Australian-specific dollar equivalents and added these estimates to estimates of lifetime fiscal returns to graduates. This allows us to estimate the expected spillovers over…

This article's focus is on including computing and computational thinking in K-12 instruction within science, technology, engineering, and mathematics (STEM) education, and to provide that instruction in ways that promote access for students traditionally underrepresented in the STEM fields, such as students with disabilities. Providing computing…

Novel management strategies for autism spectrum disorder (ASD) propose providing interventions before diagnosis. We performed a cost-effectiveness analysis comparing the costs and dependency-free life years (DFLYs) generated by pre-diagnosis intensive Early Start Denver Model (ESDM-I); pre-diagnosis parent-delivered ESDM (ESDM-PD); and the Ontario…