Previous research has emphasized the importance of language for learning mathematics. This is especially true when mathematical problems have to be extracted from a meaningful context, as in arithmetic word problems. Bilingual learners with a low command of the instructional language thus may face challenges when dealing with mathematical…

The goal of this first major report from the Western Reserve Reading Project Math component is to explore the etiology of the relationship among tester-administered measures of mathematics ability, reading ability, and general cognitive ability. Data are available on 314 pairs of monozygotic and same-sex dizygotic twins analyzed across 5 waves of…

This article explores the complementary strengths and weaknesses of grounded and abstract representations in the domain of early algebra. Abstract representations, such as algebraic symbols, are concise and easy to manipulate but are distanced from any physical referents. Grounded representations, such as verbal descriptions of situations, are…

Developing meaning for symbolic representations is an important part of the middle school mathematics experience for all students. Teachers must not see simply writing symbolic representations as the end goal, but focus on the internal meaning that students ascribe to these symbols. Too often, students lack a deep understanding of the algebraic…

This article introduces a framework for the remediation of number combination (NC) deficits. Research on the remediation of NC deficits is summarized, and research program studies are used to illustrate the 3 approaches to remediation. The Framework comprises a 2-stage system of remediation. The less intensive stage implementing 1 of 3…

Student underachievement on standardized math achievement tests is a major concern in American public schools. One of the speculated reasons for student underachievement is the inability to solve math word problems. Word problems are the most challenging problems in math because word problem solving requires the use of skills in language,…

English language learners (ELLs) struggle with solving word problems for a number of reasons beyond math procedures or calculation challenges. As a result, ELLs may not only need math support but also reading and linguistic support. The purpose of this study was to assess the effectiveness of a math comprehension strategy called Dynamic Strategic…

This article discusses schema-based instruction (SBI) as an alternative to traditional instruction for enhancing the mathematical problem solving performance of students with learning disabilities (LD). In the authors' most recent research and developmental efforts, they designed SBI to meet the needs of middle school students with LD in inclusive…

The mathematics methodology subjects the author undertook in the early 1980s encouraged him to adopt a very expository style of teaching in which each new concept is introduced by its formal definition. The teacher should then explain a few carefully chosen examples for students to copy into their books, and then provide plenty of graded practice…

Previous work has investigated adults' knowledge of principles for arithmetic with positive numbers (Dixon, Deets, & Bangert, 2001). The current study extends this past work to address adults' knowledge of principles of arithmetic with a negative number, and also investigates links between knowledge of principles and problem representation.…

Critical user interface design features of computer-assisted instruction programs in mathematics for students with learning disabilities and corresponding implementation guidelines were identified in this study. Based on the identified features and guidelines, a multimedia computer-assisted instruction program, "Math Explorer", which delivers…

Mathematical word problems represent a common item format for assessing student competencies. Automatic item generation (AIG) is an effective way of constructing many items with predictable difficulties, based on a set of predefined task parameters. The current study presents a framework for the automatic generation of probability word problems…

Solving word problems plays an important role in primary school mathematics education. However, many students have difficulty solving such tasks. In order to improve students' metacognitive and problem-solving skills, a computer program was developed consisting of word problems and metacognitive hints. The experimental group of Grade 5 (n = 23)…

Algebra uses symbols for generalizing arithmetic. These symbols have different meanings and interpretations in different situations. Students have different perceptions about these symbols, letters and signs. Despite the vast research by on the students' difficulties in understanding letters in Algebra, the overall image that emerges from the…

Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…