How do children learn the meanings of number words like "one," "two," and "three"? Whereas many words that children learn in early acquisition denote individual things and their properties (e.g., cats, colors, shapes), numerals, like quantifiers, denote the properties of sets. Unlike quantifiers such as "several" and "many," numerals denote…

It is of deep interest to both linguists and psychologists alike to account for how young children acquire an understanding of number words. In their commentaries, Barner and Butterworth both point out that an important question highlighted by the work of Syrett, Musolino, and Gelman, and one that remains highly controversial, is where number…

The ability to count has traditionally been considered an important milestone in children's development of number sense. However, using counting (e.g., counting on, counting all) strategies to solve addition problems is not the best way for children to achieve their full mathematical potential and to prepare them to develop more complex and…

We measure the impact of observed teacher characteristics on student math and reading proficiency using a rich dataset from Florida. We expand upon prior work by accounting directly for nonrandom attrition of teachers from the classroom in a sample selection framework. We find evidence that sample selection is present in the estimation of the…

This research analyzes how external representations created by a student, Robert, helped him in building mathematical understanding over a sixteen-year period. Robert (also known as Bobby), was an original participant of the Rutgers longitudinal study where students were encouraged to work on problem-solving tasks with minimum intervention (Maher,…

Inverse probability weighting (IPW) estimates are widely used in applications where data are missing due to nonresponse or censoring or in observational studies of causal effects where the counterfactuals cannot be observed. This extensive literature has shown the estimators to be consistent and asymptotically normal under very general conditions,…

A consequence of the curvature of the Earth is that distant ships apparently disappear over the horizon. This article shows how you can use a simple photograph to help students obtain a reasonable estimate of the size of the Earth using little more than the mathematics of Pythagoras. (Contains 5 figures.)

Growing interest in fully Bayesian item response models begs the question: To what extent can model parameter posterior draws enhance existing practices? One practice that has traditionally relied on model parameter point estimates but may be improved by using posterior draws is the development of a common metric for two independently calibrated…

In the last 2 decades attention to causal (and formative) indicators has grown. Accompanying this growth has been the belief that one can classify indicators into 2 categories: effect (reflective) indicators and causal (formative) indicators. We argue that the dichotomous view is too simple. Instead, there are effect indicators and 3 types of…

Categorical structural equation modeling (SEM) methods that fit the model to estimated polychoric correlations have become popular in the social sciences. When population thresholds are high in absolute value, contingency tables in small samples are likely to contain zero frequency cells. Such cells make the estimation of the polychoric…

In response to the low standards in short form development, Smith, McCarthy, and Anderson (2000) introduced a set of guidelines for the construction and evaluation of short forms of psychological tests. One of their recommendations requires researches to show that the variance overlap between the short form and its long form is adequate. This…

Certain risk factors associated with overweight and obesity may lead to reduced productivity in the workforce (i.e., increased absenteeism and presenteeism). Participants in a large, Internet-based worksite weight loss intervention, who were present at follow-up (N = 1,030), completed a self-reported productivity measure (World Health…

Blind students are bound to make up a very small part of the population most university lecturers will encounter during their careers. Research to date shows that good communication between staff and student improves the chances of a successful outcome for both parties. The research does show, however, that the exercise seems to be one of…

The purpose of this study was to use calculator-assisted instruction to help two fifth-grade low-achievers learn number sense. The research process includes three stages: (1) pre-test interview to detect what kinds of number sense the students did not have; (2) calculator-assisted instruction to help them develop number sense; and (3) post-test…

Academic medical centers nationwide face numerous fiscal challenges resulting from implementation of restructured healthcare delivery models, contracting state support for higher education, and increased competition for federal and other sources of biomedical research funding. In pursuing greater accountability and transparency in its fiscal…