Presents practical, teacher-tested tools and techniques based on National Council of Teachers of Mathematics (NCTM) standards for teaching mathematics. Covers Cognitively Guided Instruction (CGI) technique; story problems across the curriculum; advantages of using calculators in instruction; and manipulatives for plane geometry. Includes a chart…

Presents a study that indicates that second grade students (n=117) do select manipulatives that match the story context in measurement and partition division word problems, that they can solve division word problems, especially when matched manipulatives are used, and that division without remainders are more accessible to solution. (39…

The use of restricted item response models to test hypotheses regarding item difficulty ordering and slope uniformity was demonstrated in a study in which 597 algebra students were asked to solve word problems reflecting various types of cognitive processing. Benefits and limitations of the procedures are discussed. (SLD)

Children's (n=70) solution strategies to a variety of multiplication and division word problems were analyzed to determine performance levels and strategies used. Solution strategies were classified at three levels: direct modeling with counting; no direct modeling with counting, additive, or subtractive strategies; and use of known derived facts.…

High school mathematics project in which students interviewed guest speakers about the mathematics used in their jobs. Students wrote five real world problems based on the mathematics used by the person interviewed. The class worked through the problems and found that estimation was often a helpful strategy. (PDD)

Six experiments with 42 kindergartners, 190 first graders, and 15 second graders in Germany investigated why arithmetic word problems with an unknown reference set are more difficult for children than are problems with an unknown compare set. Lack of access to flexible language use makes these problems so difficult. (SLD)

Describes a study of ninth-grade students that evaluated the ability of the Word Problem Solving Tutor, a cognitive tutoring system, to improve the abstract-reasoning component of word-problem solving. Compares combinations of traditional instruction, computer-assisted instruction, and the tutoring program and discusses implications for math…

This article describes a way to provide systematic connections between mathematics and science for students with disabilities through hands-on lessons, word problems, and opportunities for problem-solving. Sample units are presented that integrate science and mathematics at the K-8 level and explore interrelationships among multiplication and…

A within-subjects design was used to compare two instructional methods--explicit timing and interspersing--with 187 second-grade students. Students completed two mathematics word problem assignments under differing conditions. In the explicit timing condition, students were told they would be timed while working long mathematics word problems. In…

This article presents essential principles for mathematics instruction for students with disabilities and those who are at risk for school failure. These students have great difficulty in applying algorithmic knowledge to solve problems and even greater difficulty with abstract problem solving associated with higher level mathematics. A procedural…

This collection of 11 applied algebra curriculum modules can be used independently as supplemental modules for an existing algebra curriculum. They represent diverse curriculum styles that should stimulate the teacher's creativity to adapt them to other algebra concepts. The selected topics have been determined to be those most needed by students…

The information in this supplementary notebook is intended to provide teachers with additional materials, ideas and suggestions, and activities to help in implementing the first 21 units of the Applied Mathematics modules that help develop and refine job-related mathematics skills. An introduction lists the 36 units of the complete Applied…

This publication is a compilation of abstracts and critical comments for 12 published investigations in mathematics education. Information for each study includes: purpose; rationale; research design and procedures; findings; and interpretations. For each study abstractor's comments also provide a brief critique. Topics include: planning problem…

The development and evaluation of several microcomputer-based strategies designed to facilitate learning how to solve mathematics word problems by personalizing examples in accord with individuals' background and interests are described in this paper. The first of two studies conducted with fifth and sixth grade students to evaluate these…

Mathematical word problems are notoriously difficult to solve for students at all grade levels. Performance deficiencies have been attributed to students lacking abstract logico-mathematical knowledge or to insufficiently developed language comprehension skills. At least four general sources of difficulty can be distinguished in mathematical word…