This study examined whether the quality of first graders' (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children's pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be…

The aim of the National Numeracy Strategy is to raise standards in numeracy. Strong evidence for its success has, however, been lacking: most of the available data come from performance on National Test assessments administered in schools or from Ofsted reports, and is vulnerable to suggestions of bias. An opportunistic analysis of data from a…

The purpose of this study was to evaluate the effects of the copy, cover, and compare (CCC) procedure on improving the mathematics and spelling performance of a freshman attending a high school special education class. The participant was a 16-year-old high school student enrolled in special education classes for 3 periods of the school day. Math…

This study examined the effects on math performance of the use of the rekenrek, a manipulative developed by Adrian Treffers. The rekenrek looks like an abacus, but differs in that it is based on a five-structure and not a ten-structure system. It is comprised of two rows of 10 beads, each broken into two sets of 5 by color (i.e., in each row the…

This article shares an assessment tool that uses student-written word problems to provide meaningful information regarding the depth of mathematical understanding. Students' word problems representing 6 [division] 1/2 were classified using the scoring categories described in the NAEP. By categorizing the problems, students' levels of understanding…

This article reviews two sets of research studies from outside of mathematics education to consider how they may be relevant to the study of bilingual mathematics learners using two languages. The first set of studies is psycholinguistics experiments comparing monolinguals and bilinguals using two languages during arithmetic computation (language…

In 4 experiments, the authors examined the use of the hands in simple arithmetic tasks. Experiments 1 and 2 demonstrated that pointing increases both accuracy and speed in counting arrays of items, whether those items are identical or distinctive. Experiment 3 demonstrated that individuals tend to nod their heads when not allowed to point and that…

This book includes two main sections: a discussion of problem solving and a section on computation with whole numbers. A primary theme of the text is that problem solving sets the stage for meaning and conceptual development with respect to numbers. The section on problem solving includes numerous problem-solving activities that have a dual…

Passive and active visuospatial working memory (VSWM) were investigated in relation to maths performance. The mental rotation task was employed as a measure of active VSWM whereas passive VSWM was investigated using a modified Corsi Blocks task and a matrix pattern task. The Raven Progressive Matrices Test measured fluid intelligence. A total of…

Why should prospective elementary and high school teachers study group theory in college? This paper examines applications of abstract algebra to the familiar algorithm for converting fractions to repeating decimals, revealing ideas of surprising substance beneath an innocent facade.

The adaptive use of approximate calculation was examined using a verification task with 18 third graders with mathematics learning disabilities, 22 typically achieving third graders, and 21 typically achieving second graders. Participants were asked to make true-false decisions on simple and complex addition problems while the distance between the…

"Focus in Grade 1: Teaching with Curriculum Focal Points" describes and illustrates learning paths for the mathematical concepts and skills of each grade 1 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate…

This textbook's main objective is to provide a connecting link between the study of arithmetic and algebra, and to show how to solve problems. It seeks to show practical applications of the theory discussed. While this book was designed originally for the use of those whose educational training had been limited, it has been so remodeled as to…

This textbook is a young mathematician's guide to mathematics. The following five parts are presented: (1) Arithmetick, vulgar, and decimal, with all the useful rules; and a general method of extracting the roots of all single powers; (2) Algebra, or arithmetick in species; wherein the method of raising and resolving equations is rendered easie;…