States that one common goal of improving mathematics education is applicable for all. Bridges of understanding must be built by having students solve mathematical problems that go beyond performing simple arithmetic and simplifying algebraic equations. Students must take an active role in the learning process, and assessment should be used to…

Presents responses to the problem appearing in the March, 2000 issue on data and graph interpretation. (ASK)

Presents responses to a problem appearing in the December, 1998 issue on the concept of determining all possibilities for colored and numbered wristbands for students. (ASK)

A mathematical problem is presented. Teachers are advised to spend time discussing the problem with their students, but they should avoid giving them too much guidance.

The situations created by individual style of problem solving in mathematics by children are discussed. Children can solve their mathematical problem by correcting their misconceptions on their own with the use of open discussions with others.

Specific examples are used to discuss assessment, an integral part of mathematics instruction, with problem posing and assessment of problem posing. General assessment criteria are suggested to evaluate student-generated problems in terms of their quantity, originality, and complexity.

This article explores the origins and potential benefits of the empty number line for the development of mental computation. It also provides a learner's perspective of its use through the reflections of nine-year-old Emily. (Contains 3 figures.)

This article explores how counting collections of objects helps elementary-age children develop number sense and number relations. The authors provide evidence that counting collections offers multiple entry points for children at different places on the counting trajectory. It is suggested that the teacher's role is one of noticing, questioning,…

This article describes how the promotion of purposeful mathematical discussions can enhance young mathematicians' construction of knowledge and their explanation of strategy use.

This article illustrates effective instructional strategies for English Language learners. (Contains 5 figures.)

When permitted, children frequently devise approaches to solving problems that are distinct from those typically used by adults. Presents examples of children's thinking from Project IMPACT which illustrate the crucial interplay between a teacher's instructional decisions and children's thinking while confronting mathematical misconceptions.…

Presents examples of direct modeling and invented strategies of students for problem solving. Teachers are encouraged to capitalize on children's abilities to use these invented strategies and in time guide the student toward a standard, more efficient strategy. (AIM)

Presents a problem of triangular tiles that involves counting and probability. Includes instructor guiding questions. (KHR)

Presents activities that focus on number sense. (KHR)

Endorses the projects approach to learning as helping students acquire contextual, personal knowledge rather than learning only isolated bits of content information. Describes the five-step process for doing projects which includes productive thinking or generating ideas, the planning or organizing of ideas, decision making, communication or…