Discusses using Alan Bell's "Principles for the Design of Teaching" with student teachers. Discusses choosing genuine and substantial mathematical activities, exposing and resolving cognitive conflict, using flexible tasks in which the degree of challenge can be adjusted or a single starting point can develop into multiple tasks, using feedback,…

Mathematics truly is magical, especially for students with strong number sense and algebra skills. This paper describes a variety of mathematical surprises that will capture students' interest and motivate exploration of mathematical ideas. While the tricks themselves are fascinating, push students to think about the reasons why these stunning…

This comment attempts to identify different "semiotic perspectives" proposed by the authors of this special issue according to the problems they discuss. These problems can be distinguished as problems concerning the representation of mathematical knowledge, the definition and objectivity of meaning, epistemological questions of learning and…

Defines virtual manipulatives and stresses their advantages for classroom use. Presents examples on the Internet and discusses current and potential use of virtual manipulatives. (KHR)

Investigates the effects of computers and Internet technology on teaching and learning. Presents electronic examples that integrate well with high-quality mathematics instructional programs. (KHR)

This paper discusses a pedagogical technique called the discovery approach in teaching remedial and college algebra. Examples of how to introduce and enhance some algebra topics using this approach in mathematics classrooms are illustrated. It is argued that student performance would improve if more topics were presented in a discovery fashion.…

Evaluates the use of modern CAD methods to solve geometric problems. Solves descriptive geometry problems using the layout and position of the successive auxiliary views from the projection of three-dimensional figures onto a two-dimensional plane of paper. (CCM)

Diversity can be introduced in algebra without needing extra time. Explores three opportunities to encounter and engage diversity: (1) history; (2) multiple representations; and (3) object concept of function. (ASK)

Summarizes the basic position and recommendations of a recently released joint position statement of the National Association for the Education of Young Children and the National Council of Teachers of Mathematics regarding effective, engaging early childhood mathematics education. Recommended educational practices include integrating mathematics…

In early 2004, Cabrilog released version "II plus" of their interactive geometry package. According to the author, "Cabri Geometry II plus" is clearly a much more useful package than the earlier version. However, unlike other sophisticated applications packages, the designers have avoided creating so many options that secondary students lose their…

As a learning theory, constructivism describes knowledge as being in flux--where an individual internally constructs knowledge through social and cultural mediation. Constructivist learning theorists contend that social activity and discourse must play important roles in order for understanding to occur. This paper describes how the social…

Analyzes mathematics software programs to find engaging and easy-to-use software for integration into the elementary school mathematics curriculum. Discusses criteria for judging good software and useful classroom implementation. (KHR)

Reviews communication as a fundamental component in implementing a balanced and effective mathematics program. Presents a classroom episode in which students solve problems, use rubrics to rate the written response of a peer, and discuss solutions and decisions for rating their peers' papers. (KHR)

Discusses the use of children's literature to integrate language arts and mathematical problem solving in the middle school classroom. Considers selecting a book and writing the language arts and problem solving lessons; describes the process of creating and solving a mathematical problem based on a story. (JPB)

Asserts that graphing calculators give students and teachers the ability to investigate, explore, compare, and discover concepts in a much more comprehensive way than simple calculators or no calculators at all. Offers specific examples that illustrate the advantage of graphing calculators in the Montessori middle school classroom. Lists three…