Students make strategic choices–and justify them–to solve a system of two linear equations.

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### Elana Reiser

Use popular culture to draw students' attention to mathematical topics.

### Michael Weiss

Core content provides opportunities to focus on the structure of mathematical theory, proof, and anticipation of subsequent topics.

### Marla A. Sole

Using bivariate data, students investigate the ingredients in pasta sauce.

### 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.

### Darla R. Berks and Amber N. Vlasnik

Two teachers discuss the planning and observed results of an introductory problem to help students nail a conceptual approach to solving systems of equations.

### Barbara M. Kinach

The meaningful use of symbols links context and generality.

### Rachel Levy

The mathematical concept of slope can be made real through a set of simple, inexpensive, and safe experiments that can be conducted in the classroom or at home. The experiments help connect the idea of slope with physical phenomena related to surface tension. In the experiments, changes in surface tension across the surface of the water, which correspond to greater slopes on the graph, lead to increased motion of the fluid. The mathematical content, targeted to middle school and high school students, can be used in a classroom or workshop setting and can be tailored to a single session of thirty to ninety minutes.

### Patricia Wallace-Gomez

Three graphing activities lead students to discover the shapes and properties of the graphs for linear, quadratic, and absolute value functions and inequalities.

### Ethan M. Merlin

Exercises about glue and trees and addresses can inoculate students against their notorious tendency to reduce incorrectly when simplifying expressions.