The authors examined the effectiveness of strategy instruction taught by general educators in mixed-ability classrooms. Specifically, the authors compared the mathematical word problem-solving performance and computational skills of students who received schema-based instruction (SBI) with students who received general strategy instruction (GSI).…

Arguing that college mathematics education must be made more effective, especially for technology, engineering, mathematical sciences, and physical sciences students, this paper presents nine general principles to enhance math instruction for all students. Introductory material argues that changes in perception, attitudes, and role models are…

This paper suggests a route to deep, long-term algebra reform that begins not with more new approaches but with elementary school teachers and the reform efforts that currently exist. This route involves generalization and expression of that generality using increasingly formal languages, beginning with arithmetic, modeling situations, geometry,…

Represents a college professor's view of children doing math after seven consecutive years of working with approximately 150 children solving word problems. (ASK)

Discusses issues regarding problem solving environments via problem posing. Recognizes the importance of the teacher's questions; language characteristics of problems; problem structure and feature; solution structure; teacher's questions used before, during, or after solving a problem; and introducing problem-posing questions in mathematics…

This book addresses different types of thinking, including critical, creative, and analytical, and presents a variety of problem-solving strategies, along with specific ways they can be taught to students. The main emphases of the book are thinking and mathematics, problem solving, and the application of computational skills. The problem-solving…

Discusses how students construct their own understanding of mathematics as they discover and then learn it in class. Presents Krystal's method to subtract mixed numbers that her peers adopt and name for her. (ASK)

The Math Lab is a creative approach to teaching math concepts. Students are introduced to skills through several conceptual levels. Concrete level activities are followed by semiconcrete, semiabstract, and abstract levels of instruction. Examples of teaching methods for each level are offered. (DF)

The poor achievement of secondary students with learning disabilities in mathematics is often affected by prior low achievement, low expectations for success, and inadequate instruction. Good instruction involves careful selection of examples; explicit instructional design; a parsimonious use of time and resources; and techniques such as direct…

Describes first grade students' mathematical investigation of the number of spots on a cheetah. The exploration of counting and estimation strategies that grew from the investigation gives evidence that mathematicians come in all ages. (ASK)

Students in adult basic education/general educational development classes need skills in analyzing and solving programs, extending beyond those learned through word problems in the mathematics curriculum. The following strategies can help students broaden their problem-solving skills: (1) act it out, (2) construct a table, (3) draw a picture, (4)…

Describes and illustrates five areas of instructional design in mathematics well suited to students with learning disabilities. Suggested learning strategies for teachers to incorporate include using big ideas and conspicuous strategies; teaching efficient use of time; giving clear, explicit instruction on strategies; and taking time for…

Strategies for rapid mental computation are explained, including multiplying by 11 (or 21, 31, etc.); adding columns of numbers; and multiplying 2-digit numbers. Rapid mental computation is suggested as a motivator for investigating the underlying mathematical principles. (DB)

This article offers suggestions for incorporating cognitive principles into mathematics instruction for students with disabilities, such as identifying underlying concepts and relationships and teaching them explicitly, and presenting instruction from a problem-solving perspective. A checklist is provided for determining whether or not…

Describes a student project that enables students to experience problem-solving strategies and construct their own understandings of the problem-solving strategies by researching the problem-solving process itself, uncovering and defining strategies that they can subsequently use to solve problems, and exploring the impact that attitude has on…