As literate adults, we appreciate numerical values as abstract entities that can be represented by a numeral, a word, a number of lines on a scorecard, or a sequence of chimes from a clock. This abstract, notation-independent appreciation of numbers develops gradually over the first several years of life. Here, using functional magnetic resonance…

Behavioral studies show that infants are capable of discriminating the number of objects or events in their environment, while also suggesting that number discrimination in infancy may be ratio-dependent. However, due to limitations of the dependent measures used with infant behavioral studies, the evidence for ratio dependence falls short of the…

Transcoding Arabic numbers from and into verbal number words is one of the most basic number processing tasks commonly used to index the verbal representation of numbers. The inversion property, which is an important feature of some number word systems (e.g., German "einundzwanzig" [one and twenty]), might represent a major difficulty in…

Sets of numbers where not only their sums are equal but the sums of other powers are also equal have been called multigrades. This article presents several mathematical equations that portray how multigrades are generated. By further extension of the process outlined in this article, students can generate higher-order multigrades. (Contains 1…

Early math skills are the strongest predictors of later math achievement in school. This two-wave study addressed three research questions about the role of families in fostering these skills in preschool-aged children. First, how do families talk about math at home? Second, how do these conversations vary across families with different…

Many middle-school students struggle with decimals and fractions, even if they do not have a mathematical learning disability (MLD). In the present longitudinal study, we examined whether children with MLD have weaker rational number knowledge than children whose difficulty with rational numbers occurs in the absence of MLD. We found that children…

The purpose of this three-paper manuscript dissertation is to add value to the limited knowledge base of research surrounding the quality of teacher-child interactions in pre-k mathematics contexts. The first paper, based on an extensive review of literature, presents a theoretical basis for using five-frames to support children's development of…

There is a strong push from within mathematics education reform to incorporate representations in math classrooms (Behr, Harel, Post, & Lesh, 1993; Kieren, 1993; NCTM, 2000). However, questions regarding what representations should be used (for a given topic) and how representations should be used (such that students gain a deep understanding of…

Creating meaningful math experiences that reach children with diverse abilities, home languages, learning styles, and backgrounds is a daunting challenge for all teachers. Primary teachers often receive little professional support for achieving this complicated task in mathematics (NCTM 2000). This article explores how five different math…

This study mainly aims to develop an effective strategy to overcome the known difficulties in teaching negative numbers. Another aim is to measure the success of this teaching strategy among a group of elementary level pupils in Izmir, Turkey. Learning negative concepts are supported by computer animations. The academic achievement test developed…

This study examines presentations of the distributive property (DP) in two widely used U.S. elementary text series and one main Chinese text series along three dimensions: problem contexts, typical problem types within each problem context, and variability in using the DP. In general, the two U.S. texts were found to resemble each other but to…

This study examines the reliability and validity of a Chinese-translated version of the Gifted Rating Scales-Preschool/Kindergarten Form (GRS-P) and explores the effect of gender and age on each of the subscales. Data were collected from 250 kindergarten children, with age ranging from 4 years, 0 months to 6 years, 11 months. Results indicated…

Action research (AR) is defined by Macintyre to be: "an investigation, where, as a result of rigorous self-appraisal of current practice, the researcher focuses on a problem,or a topic or an issue which needs to be explained, and on the basis of information, plans, implements, then evaluates an action then draws conclusions on the basis of…

Contemporary argument increasingly relies on quantitative information and reasoning, yet our profession neglects to view these means of persuasion as central to rhetorical arts. Such omission ironically serves to privilege quantitative arguments as above "mere rhetoric." Changes are needed to our textbooks, writing assignments, and instructor…

This is the second and final report of the Middle School Mathematics Professional Development Impact Study, which examines the impact of providing a professional development (PD) program in rational number topics to seventh-grade mathematics teachers. An interim report (Garet et al. 2010) described the findings after one year of PD. The current…