Many joint decisions in everyday life (e.g., Which bar is less crowded?) depend on approximate enumeration, but very little is known about the psychological characteristics of counting together. Here we systematically investigated collective approximate enumeration. Pairs of participants made individual and collective enumeration judgments in a…

The purpose of the present study was to determine if numeral knowledge--the ability to identify Arabic numerals and connect Arabic numerals to their respective quantities--mediates the relation between informal and formal mathematical knowledge. A total of 206 3- to 5-year-old preschool children were assessed on 6 informal mathematics tasks and 2…

The priming of concepts has been shown to influence peoples' subsequent actions, often unconsciously. We propose 3 mechanisms (psychological, cultural, and biological) as a unified explanation of such effects. (a) Primed concepts influence holistic representations of situations by parallel constraint satisfaction. (b) The constraints among…

This article describes a comprehensive and novel approach to assessment in early numeracy. Topics include the significance of early numeracy, developing a nomenclature for early numeracy, and describing the context for the development of this approach to assessment. The largely unrealised importance of numerals and numeral sequences in early…

The main purpose of this study is to improve estimation efficiency in obtaining full-information maximum likelihood (FIML) estimates of contextual effects in the framework of a nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM; Cai, 2008, 2010a, 2010b). Results indicate that the MH-RM…

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…