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 goal of this study was to investigate understanding of inservice elementary school teachers in Taiwan about number sense, teaching strategies of number sense and the development of number sense of students; and the profile of integrating number sense into mathematical instruction , and teaching practice. Data was gathered through interviews of…

Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…

Background: Several studies have examined young primary school children's use of strategies when solving simple addition and subtraction problems. Most of these studies have investigated students' strategy use as if they were isolated processes. To date, we have little knowledge about how math strategies in young students are related to other…

As education continues to progress schools are constantly seeking innovative ways to cultivate and enhance achievement for all students. As a result many public schools are pushing toward the inclusion model. This model includes co-taught instruction to meet the many needs of special education students. This research study was implemented to…

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.…

It is well known that simple examples are really encouraging in the understanding of rearrangements of infinite series. In this paper a similar role is played by simple examples in the case of infinite products. Iterated products of double products seem to have a similar spirit of rearrangements of products, although they are not the same.…

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…

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…

The current study investigated the effects of different external representational formats on learning combinatorics and probability theory in an inquiry based learning environment. Five conditions were compared in a pre-test post-test design: three conditions each using a single external representational format (Diagram, Arithmetic, or Text), and…