The field of mathematics is complex, areas such as arithmetic, and geometry each consist of several sub-domains and encompass many cognitive processes. Achievement tests for elementary pupils assess a wide range of arithmetic skills such as number sense, procedural knowledge, and using problem solving strategies. Although mathematical tests often…

Three studies were conducted with middle school students to evaluate a web-based intelligent tutoring system (ITS) for arithmetic and fractions. The studies involved pre and post test comparisons, as well as group comparisons to assess the impact of the ITS on students' math problem solving. Results indicated that students improved from pre to…

Children's symbolic number sense was examined at the beginning of first grade with a short screen of competencies related to counting, number knowledge, and arithmetic operations. Conventional mathematics achievement was then assessed at the end of both first and third grades. Controlling for age and cognitive abilities (i.e., language, spatial,…

Previous research has demonstrated close relationships between working memory and children's scholastic attainment. The aim of the present study was to explore a method of improving working memory, using memory strategy training. Two hundred and fifty-four children aged five to eight years were tested on measures of the phonological loop,…

The current study was designed to examine the possible existence of two limited-capacity pools of central executive resources: one each for verbal and visuospatial processing. Ninety-one college students (M age = 19.0, SD = 2.2) were administered a verbal working memory task that involved updating numbers in 2-, 3-, and 4-load conditions. The task…

It has been suggested that individuals with dyslexia show poorer performance on those aspects of arithmetic that involve the manipulation of verbal representations, such as the use of fact retrieval strategies. The present study examined this in 13 children with dyslexia who showed normal general mathematics achievement and 16 matched controls.…

Understanding the equivalence in relation to fractions is centrally important. Students need many experiences of flexibly combining simple fractions in ways that reinforce equivalences among them. This article presents several ideas that are contributed by a range of people. They are designed to help students to develop understandings of…

As extended by Ginsberg, Midi's theorem says that if the repeated section of a decimal expansion of a prime is split into appropriate blocks and these are added, the result is a string of nines. We show that if the expansion of 1/p[superscript n+1] is treated the same way, instead of being a string of nines, the sum is related to the period of…

This article explores prospective teachers' understandings of one million to gain insights into the development of adult understanding of large numbers. Themes in the prospective teachers' work included number associated with a quantity of objects, number as an abstraction, and additive and multiplicative approaches. The authors suggest that the…

The aim of this study was to test a training program intended to fine-tune the mental representations of double-digit numbers, thus increasing the discriminability of such numbers. The authors' assumption was that increased fluency in math could be achieved by improving the analogic representations of numbers. The study was completed in the…

Fifty percent of college-bound students graduate from high school underprepared for mathematics at the post-secondary level. As a result, thirty-five percent of college students take developmental mathematics courses. What is even more shocking is the high failure rate (ranging from 35 to 42 percent) of students enrolled in developmental…

Contemporary teachers need instructional practices that are (a) powerful enough to meet the needs of a rapidly diversifying student population, (b) feasible to implement on a classwide basis, and (c) socially acceptable to them and their pupils. Classwide peer tutoring (CWPT) is one such instructional practice. In addition to describing CWPT, its…

This study examined how four domain-specific skills (arithmetic procedural skills, number fact retrieval, place value concept, and number sense) and two domain-general processing skills (working memory and processing speed) may account for Chinese children's mathematics learning difficulties. Children with mathematics difficulties (MD) of two age…

Difficulties in phonological processing and reading that characterize developmental dyslexia have been suggested also to affect those with attention-deficit/hyperactivity disorder (ADHD). However, it is not known to what extent various intervening factors, such as low intelligence quotient or age, explain the observed difficulties. In this study,…

The purpose of this study was to explore word problems as a subject matter in mathematics textbook curricula. The motivation for the study derived from the following evidence: (a) American students find some word problems are more difficult than others (Garcia, Jimenez, & Hess, 2006; Riley & Green, 1988; Stern, 2001), and (b) one of the…