This geometry lesson uses the work of abstract artist Wassily Kandinsky as a springboard and is intended to promote the conceptual understanding of mathematics through problem solving, group cooperation, mathematical negotiations, and dialogue.

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### Terri L. Kurz

People who lay tile for a living use mathematics every day to decide how much tile, grout, and other supplies are required to complete each job. Measurement and geometry are an integral part of designing tile patterns. Collections of short activities focus on a monthly theme that includes four activities each for grade bands K–2, 3–4, and 5–6 and aims for an inquiry or problem-solving orientation.

### Barbara M. Kinach

The meaningful use of symbols links context and generality.

### David A. Yopp

Asked to “fix” a false conjecture, students combine their reasoning and observations about absolute value inequalities, signed numbers, and distance to write true mathematical statements.

### James A. Preston

A good problem can capture students' curiosity and can serve many functions in the elementary school classroom: to introduce specific concepts the teacher can build on once students recognize the need for additional mathematics or to help students see where to apply already-learned concepts. We encourage teachers to use the monthly problem in their own classrooms and report solutions, strategies, reflections, and misconceptions to the journal audience.

### Aryn A. Siegel and Enrique Ortiz

A simple problem-solving exercise encourages teachers to “start small” to reveal how third graders understand multiple math concepts simultaneously.

Butterflies are beautiful insects for students to study. Unfortunately, some kinds of butterflies are on the endangered species list because their natural habitats are disappearing. Members of our school community are concerned about this dilemma, so we decided to plant a butterfly garden.

### Temple A. Walkowiak

A talkative second grader helps her teacher describe, extend, and generalize about growing patterns.

### Alex Friedlander and Abraham Arcavi

Integrating procedures and thinking processes makes learning more meaningful.

### Daniel R. Ilaria

Students generally first encounter piecewise–defined functions in the form of a step function (perhaps the postage stamp function) in an algebra class. Piecewise–defined functions do not play a central role in mathematics before calculus although they can serve as challenging examples in the precalculus curriculum. Before the advent of the TI–Nspire, entering piecewise–defined functions on the calculator was time consuming and not particularly user friendly. That has changed.