Recognizing schemes, which are different from strategies, can help teachers understand their students' thinking about fractions. Using Steffe's advanced fraction schemes, the authors describe a progression of development that upper elementary and middle school students might follow in understanding fractions. Each scheme can be viewed as a…

Geometric pattern tasks can be a useful tool for developing students' capacities to reason algebraically and in helping establish classroom norms and practices at the beginning of the school year. In this article, the authors consider the mathematical and social purposes that pattern tasks can serve by examining one middle school's…

This article describes one way to introduce fraction, decimal, and percent equivalents by linking student-created Op Art with examples of twentieth-century abstract painting. (Contains 7 figures.)

This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…

This article describes a lesson unit in which students constructed tables and graphs to represent the growth of different trees. Students then compared the graphs to develop an understanding of slope.

Discusses how students construct their own understanding of mathematics as they discover and then learn it in class. Presents Krystal's method to subtract mixed numbers that her peers adopt and name for her. (ASK)

Describes one innovative method that can help middle-grade students become more flexible in their ability to represent fractions, decimals, and percents, and creates a game of concentration using those mathematical subjects. (ASK)

The math trail embodies important goals such as drawing on student skills, exposing them to mathematics in the world around them, and enabling them to connect what they learn in the classroom with the real world. Presents an activity in which students discover the mathematical side of Boston on a day-long field trip. (ASK)

Explores the study of ordered pairs to allow students to demonstrate their own creativity, apply previously learned computer skills, evaluate their own work, and draw connections to other mathematical strands. Using a spreadsheet, students construct a drawing composed of connected ordered pairs, the inverse, and the negative of the drawing. (ASK)

Describes a way to assign points to the problem-solving process. Provides a rubric-scoring example. (ASK)

Presents a project that asks students to relate mathematical operations to real-world situations, communicate mathematical concepts in writing, share their ideas with their peers, and exercise their creativity. (ASK)

Uses the chicken problem for sixth grade students to scratch the surface of systems of equations using intuitive approaches. Provides students responses to the problem and suggests similar problems for extensions. (ASK)

How students interpret problems influences how they solve them. Lists lessons learned at the end such as how fair assessment of mathematics set in contexts requires having students explain their reasoning or assumptions, and is done most effectively and accurately over time. (ASK)

Explores misconceptions that students hold about sampling techniques on surveys. Highlights students' thinking and instructional implications from two studies that examined upper-elementary students' written and oral explanations as they responded to survey situations. (ASK)

This article describes a joint effort between a mathematics educator and a middle school art teacher who wanted their students to experience first hand how construction works in the real world. It starts with students designing and building scale models for a large inflatable item in which they display their art and extends to building the…