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…

When competence tests are administered, subjects frequently omit items. These missing responses pose a threat to correctly estimating the proficiency level. Newer model-based approaches aim to take nonignorable missing data processes into account by incorporating a latent missing propensity into the measurement model. Two assumptions are typically…

In large-scale educational surveys, a latent regression model is used to compensate for the shortage of cognitive information. Conventionally, the covariates in the latent regression model are principal components extracted from background data. This operational method has several important disadvantages, such as the handling of missing data and…

Raman spectroscopy is a powerful experimental technique, yet it is often missing from the undergraduate physical chemistry laboratory curriculum. Tetrachloromethane (CCl[subscript 4]) is the ideal molecule for an introductory vibrational spectroscopy experiment and the symmetric stretch vibration contains fine structure due to isotopic variations…

For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

In this article, we test an alternative approach to creating a counterfactual basis for estimating individual and average treatment effects. Instead of using control/comparison groups or before-measures, the so-called Counterfactual as Self-Estimated by Program Participants (CSEPP) relies on program participants' self-estimations of their own…

Of the copious research on the labor market returns to college, very little has adequately modeled the pathways of non-completers or compared their outcomes with those of award holders. In this paper, we present a novel method for linking non-completers with completers according to their program of study. This method allows us to calculate the…