This article proposes a two-factor theory of mathematics disabilities based on the premise that weak cognitive representations lead to poorer retrieval of information from long term memory. Comparison of children with math disabilities alone (MD) and those with both math and reading disabilities (MD/RD) suggests that weak phonological processing…

Tested 3- to 7-year-olds' ability to calculate with whole numbers, fractions, and mixed-numbers, in a task in which an amount was displayed, then hidden. Subjects were to determine the hidden amount resulting when numbers were added or substracted. Found that, although fraction problems were more difficult than whole-number problems, competence on…

In this study, we investigated patients with focal neurodegenerative diseases to examine a formal linguistic distinction between classes of generalized quantifiers, like "some X" and "less than half of X." Our model of quantifier comprehension proposes that number knowledge is required to understand both first-order and higher-order quantifiers.…

In this study, we examine whether preventive enrichment of pre-math skills has an influence on number knowledge in preschool children from low income families. Our data analyses use two methods to examine the influence of two independent programs implemented during junior kindergarten and kindergarten. The first implies the traditional approach…

This study compared the "Digit Naming Speed Test" (DNS) performance of 20 children with Attention-Deficit/Hyperactivity Disorder (ADHD) to 20 carefully matched peers without ADHD. Matching variables included age, grade, gender, and word reading ability. Sample construction included procedures that allowed for the identification and removal from…

This paper reports the results of an exploratory study of the perceptions of and approaches to mathematical proof of undergraduates enrolled in lecture-based and problem-based "transition to proof" courses. While the students in the lecture-based course demonstrated conceptions of proof that reflect those reported in the research literature as…

This article discusses three solutions to the "Tower of Hanoi" problem offered by students in a mathematics content course for prospective elementary school teachers. The course uses standards-based pedagogy and teaching via problem solving. Within this work, we consider the growth supported by collaboration at both the students' level…

This study contributes to the debate about the Flynn effect by proposing a long-term comparison (1921-2001) of the numerical knowledge of two cohorts of three- to five-and-a-half year-old children. In 1921, Beckmann (1923) assessed the numerical development of children using four tasks (Production, Distinction, Recognition, and Naming). In 2001,…

Computer operations involving complex numbers, essential in such applications as Fourier transforms or image processing, are normally performed in a "divide-and-conquer" approach dealing separately with real and imaginary parts. A number of proposals have treated complex numbers as a single unit but all have foundered on the problem of the…

In math classes, teachers often focus instruction on the formulas and processes needed to solve different types of problems, but neglect to teach the concepts on which these tools are based. In this article, the author argues that before they can do this, teachers themselves need to understand "understanding math." Teaching mathematics with…

Estimation is an important skill for everyday living. Good estimators usually have a sound knowledge of basic facts, understand place value and use a variety of strategies to make their estimates. This paper describes an activity which is designed to provide students with opportunities to practice their rounding strategies with addition and…

The purpose of this study was to examine effectiveness of simultaneous prompting in teaching pointing to numerals to individuals with autism. Three individuals with autism were taught pointing to numerals, which were orally named by the teacher using simultaneous prompting. A multiple probe design was used across three behaviors and replicated…

The "Curriculum and Evaluation Standards for School Mathematics" (1989) provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. The document not only addresses what mathematics students should…

This volume is a teacher's edition in a series of books that contain open-ended exploration activities and experiments. These activities allow and encourage students to set their own goals, use their own creativity and ideas, investigate the wonders of nature, learn about the workings of real businesses, and draw conclusions from their…

This book leads students through a journey of hands-on investigations of skill-based estimation. The 30 lessons in the book are grouped into four units: Holding Hands, The Real Scoop, Container Calculations, and Estimeasurements. In each unit children work with unique, real materials intended to build an awareness of number, quantity, and…