In this commentary, we explore tensions between engaging students in authentic disciplinary mathematical activity and insights from critical theorists who analyze equity in mathematics education. The tensions arise as engaging students in authentic mathematical activity usually involve having students adopt the language and norms of another…

A common view seems to be emerging in the mathematics education world at the moment that the development and use of "rich tasks" is a good thing; a "right thing" to do. There are many examples of these "rich tasks" and teachers are encouraged to use them whenever they can. Professional learners don't just accept this uncritically, but question…

The author drew the 2008 Easter conference to a close. During the final address, the author chose to focus on the domain of perimeter and area both because it is a topic accessible to teachers of all ages and because learners display considerable confusion between them. The core difficulty seems to lie in the necessity to attend either to the…

The easiest way to learn anything is to make the topic or activity relevant to life. The same is true for math. If teachers clearly demonstrate the relevancy of math to everyday life, students can more easily see the purpose of learning and embracing the subject. But before teachers make math relevant, they will need to overcome one more…

Finds that many activities that have been called "problems" are merely exercises or tricks. Offers a clearer definition of the word "problem". Notes some of the classroom implications of the new insight. (Author/CCM)

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…

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)

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…

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)

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…