The preschool years are a time of great advances in children's numerical thinking, most notably as they master verbal counting. The present research assessed the relation between analog magnitude representations and cardinal number knowledge in preschool-aged children to ask two questions: (1) Is there a relationship between acuity in the analog…

The present study tested the "interference hypothesis"-that learning and using more advanced representations and strategies requires the inhibition of prior, less advanced ones. Specifically, it examined the relation between inhibitory control and number line estimation performance. Experiment 1 compared the accuracy of adults' (N = 53)…

Prior work on the "CBAL"™ mathematics competency model resulted in an initial competency model for middle school grades with several learning progressions (LPs) that elaborate central ideas in the competency model and provide a basis for connecting summative and formative assessment. In the current project, we created a competency model…

The accrediting body for media education, the Accrediting Council on Education in Journalism and Mass Communications (ACEJMC), has established twelve professional values and competencies that all students must demonstrate before graduating from accredited journalism and mass communication programs. A close reading suggests that these twelve…

Mathematical knowledge at school entry predicts school achievement, and children from low-income families are at risk for low math achievement. The study purpose was to observe low-income parents' numeracy guidance in two contexts, a board game and a number concept assessment, and to compare preschoolers' independent and guided math…

The purpose of this paper is to provide a narrative of work in progress to validate a math app designed for number sense. To date I have conducted classroom research and pilot studies across ten early childhood classrooms in two schools and will begin an empirical study at the beginning of the 2014-2015 school year. Through my work I believe the…

Children's early mathematics skills develop in a cumulative fashion; foundational skills form a basis for the acquisition of later skills. However, non-mathematical factors such as working memory and language skills have also been linked to mathematical development at a broad level. Unfortunately, little research has been conducted to evaluate the…

How do children use physical and virtual tools to develop new numerical knowledge? While concrete instructional materials may support the delivery of novel information to learners, they may also over-simplify the task, unintentionally reducing learners' performance in recall and transfer tasks. This reduction in testing performance may be…

Two 12-question estimation instruments were designed to compare the differences of estimating strategies used by the 8th-graders when solving contextual and numerical problems. Both instruments are parallel, meaning that the numbers used in both instruments are the same; however, they were presented differently. One hundred and ninety-eight…

Research on toddlers' mathematical knowledge is sparse. Studies on children's mathematical competencies before school age have mostly focused on older children. Few of the previous studies have included large groups of toddlers, few have been conducted in natural settings, and few have been directed at a broad field of mathematical knowledge. The…

Children's estimation patterns on a number line estimation task may provide information about the mental representation of the magnitude of numbers. Siegler and his colleagues concluded that children's mental representations shift from a logarithmic-ruler representation to a linear-ruler representation. However, there are important methodological…

The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research…

Children (n = 130; M[subscript age] = 8.51-15.68 years) and college-aged adults (n = 72; M[subscript age] = 20.50 years) completed numerosity discrimination and lexical decision tasks. Children produced longer response times (RTs) than adults. R. Ratcliff's (1978) diffusion model, which divides processing into components (e.g., quality of…

Experience engenders learning, but not all learning involves representational change. In this paper, we provide a dramatic case study of the distinction between learning and representational change. Specifically, we examined long- and short-term changes in representations of numeric magnitudes by asking individuals with Williams syndrome (WS) and…

Dyscalculia has been described as a specific learning difficulty affecting the ability to acquire arithmetical skills. In recent years, it has become a topic for discussion in the popular media, yet there has been little research undertaken by educational psychologists. This paper provides a summary of neuroscientific research into the development…