A cartoon exploring a problem about order of operations is coupled with a full-page activity sheet.

# Browse

## Odd Shape Out

### big solutions to little problems

### Jo Ann Cady and Pamela Wells

Solutions to a previous Solve It problem are discussed, and the procedures used with problem solving are explored.

### Matt B. Roscoe and Joe Zephyrs

Pull on the threads of congruence and similarity in a series of lessons that explores transformational geometry.

### Sarah B. Bush, Judith Albanese, and Karen S. Karp

Students engage in an activity of predicting, collecting, organizing, analyzing, and interpreting data by exploring the frequency of names that occur over three generations.

## Mathematical Explorations: A New Twist on Collaborative Learning

### classroom-ready activities

### Stephanie M. Butman

Research on students' learning has made it clear that learning happens through an interaction with others and through communication. In the classroom, the more students talk and discuss their ideas, the more they learn. However, within a one-hour period, it is hard to give everyone an equal opportunity to talk and share their ideas. Organizing students in groups distributes classroom talk more widely and equitably (Cohen and Lotan 1997).

### Joel Amidon and Matt Roscoe

A monthly set of problems is aimed at a variety of ability levels.

## Informing Practice: A Hybrid Perspective on Functions

### research matters for teachers

### Eric Weber

Formal notions of function, which appear in middle school, are discussed in light of how teachers might complement the input-output notion with a covariation perspective.

### Joel Amidon and Matt Roscoe

A monthly set of problems is aimed at a variety of ability levels.

### Shiv Karunakaran, Ben Freeburn, Nursen Konuk, and Fran Arbaugh

Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.

### Signe E. Kastberg, Beatriz S. D'Ambrosio, Kathleen Lynch-Davis, Alexia Mintos, and Kathryn Krawczyk

A Cherry Syrup problem can build links between ratio and graphing.