In this innovative book, two experienced educators present a fresh and engaging approach to mathematics learning in the middle grades with the transition from arithmetic to algebra. The authors provide a collection of balanced, multi-dimensional assessment tasks designed to evaluate students' ability to work with mathematical objects and perform…

The data used for the qualitative analysis reported here were generated as part of a larger study to understand and characterize teacher practice related to engaging students in algorithmic thinking associated with the fraction operations of addition, subtraction, multiplication and division. This paper presents ways in which teachers used…

Single Display Groupware (SDG) allows multiple people in the same physical space to interact simultaneously over a single communal display through individual input devices that work on the same machine. The aim of this paper is to show how SDG can be used to improve the way resources are used in schools, allowing students to work simultaneously on…

The involvement of working memory (WM) was examined in two types of mental calculation tasks: exact and approximate. Specifically, children attending Grades 3 and 4 of primary school were involved in three experiments that examined the role of verbal and visuospatial WM in solving addition problems presented in vertical or horizontal format. For…

For community college faculty and administrators who wish to find a higher degree of successful outcomes in a developmental arithmetic course, this study examined whether a conceptual developmental arithmetic instructional approach affects the overall performance of community college students and if it differentially affects the performance of low…

This study investigates the extent to which pre-service elementary teachers (PETs) use their realworld knowledge to solve problems for which the result of the arithmetic operation is problematic, if one takes into consideration the reality of the context. A paper-and-pencil test was administered to 566 PETs enrolled in mathematics content courses.…

This article describes a pilot study in which pre-service elementary teachers (PSTs) used rectangular area models on base-10 grid paper to begin making sense of multiplication of decimal fractions. Although connections were made to multi-digit whole number multiplication and to the distributive property, the PSTs were challenged by interpreting…

Many children in bilingual regions follow lessons in a language at school (school-language) that they hardly ever speak at home or in other informal settings. What are the neural effects of this phenomenon? This functional magnetic resonance imaging (fMRI) study investigates the effects of using school-language on brain activity during a high…

What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…

The aim of this study was to investigate the specific numerical and calculation abilities of 28 children with ADHD without comorbid mathematical learning disabilities (LD), ranging from the 1st to the 5th grade of primary school, and to examine the stability or the development of the arithmetic profile. Our results showed that a high percentage of…

This study examined whether children's mathematics anxiety serves as an underlying pathway between parental involvement and children's mathematics achievement. Participants included 78 low-income, ethnic minority parents and their children residing in a large urban center in the northeastern United States. Parents completed a short survey tapping…

Math preparedness is a barrier to completion for many community college vocational students. With President Obama's (2010) challenge to produce more graduates in order to ensure our nation succeeds in the 21st century, community colleges across the country have an increased focus on graduation or completion. This study was conducted to provide…

We present an empirical study that investigated seventh-, ninth-, and eleventh-grade students' understanding of the infinity of numbers in an interval. The participants (n = 549) were asked how many (i.e., a finite or infinite number of numbers) and what type of numbers (i.e., decimals, fractions, or any type) lie between two rational numbers. The…

Lateralization of the brain is strongly influenced by prenatal androgens, with differential exposure thought to account for cognitive sex differences. This study investigated sex and individual differences and relationships between 2D:4D (the ratio of the 2nd to 4th digit [digit ratio] as a proxy indicator of prenatal testosterone exposure),…

The view of infinity as a metaphor, a basic premise of modern cognitive theory of embodied knowledge, suggests in particular that there may be alternative ways in which one could formalize mathematical ideas about infinity. We discuss the key ideas about infinitesimals via a proceptual analysis of the meaning of the ellipsis "..." in the real…