Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

When presented with a problem in mathematics class, students often function as problem performers rather than problem solvers (Rigelman 2007). That is, rather than understanding the problem, students focus on using an operation to complete it. Students' tendencies to act as problem performers can prevent them from suggesting problem-solving…

"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…

Specific teaching strategies to help hearing-impaired secondary students comprehend abstract concepts include (1) pinpointing facts and fallacies, (2) organizing information visually, (3) categorizing ideas, and (4) reinforcing new vocabulary and concepts. Figures provide examples of strategy applications. (DB)

The 16 units of this book are designed as textbook supplements to encourage students to think mathematically and as mathematicians. Each unit begins with an orientation session which raises general concerns that always occur within mathematical exploration. This is followed by a short, original text in which a mathematician creates a particular…

This article offers specific strategies to diagnose and remediate difficulties students may have in learning multiplication facts. Analyzes strategies students use to go from a known fact to an unknown fact. The point is made that, for many students, the order of interpretation of a number fact may affect accuracy. (DB)

This article describes a problem-solving strategy unit to be used as a supplement to the regular mathematics curriculum at the primary level. Specific teaching steps and examples are given for three developmental stages of thinking: (1) concrete, (2) representational, and (3) abstract. (DB)

Effective intervention strategies for learning disabled students should recognize such cognitive deficiencies as weaknesses in attention, memory deficits, and problems in generalizing and abstracting information. Approaches which emphasize enhanced learning processes include: self-monitoring; repetition and deliberate instruction in control…

Discusses prerequisites that help students develop multiple strategies for solving problems as recommended in the National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards." Presents two examples of activities involving addition, subtraction, and permutations that promote multiple strategies. Suggests ways to…

The importance of instructing gifted students in correlational reasoning is emphasized, with attention to what the skill involves and why it is difficult to learn; effective teaching strategies; and successful programs in whole-class, cooperative-learning, and computer formats. Implications in programming for gifted students are discussed. (SW)

Proposed is a way for teachers to distinguish between rich, challenging material that encourages mathematical thinking and material that is unsuitable. Included are multistep problems that encourage a broader understanding of mathematics. (KR)

Describes three activities that the teacher can employ to help students develop thinking skills through mathematics instruction: (1) memorization using the technique of chunking; (2) higher order thinking with magic squares; and (3) predicting games. Identifies eight facets of the teacher's role in promoting thinking skills. (MDH)

Defines a generalization as "a descriptive statement of broad application indicating a relationship between two or more concepts." Argues that successful teaching about generalizations can only occur when students understand the relationship between concepts and facts. Discusses four issues and four approaches related to teaching…

Reviews a monograph which addresses children's higher-order thinking skills. Suggests the following for teaching problem solving: identify and develop content-independent and content-dependent problem-solving skills, connect developed skills through workshop-style activities to subject discipline, and help students identify and reconstruct their…

The use of strategies is an important part of mathematical thinking. Presented are several games that help develop the reasoning strategies of hypothesis making and testing, proving and disproving, looking for patterns, and simplifying a difficult task. (MDH)