Few high school students associate mathematics with playfulness. In this paper, we offer a series of lessons focused on the underlying algebraic structures of the Rubik's Cube. The Rubik's Cube offers students an interesting space to enjoy the playful side of mathematics, while appreciating mathematics otherwise lost in routine experiences.

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### Aaron Trocki

The advent of dynamic geometry software has changed the way students draw, construct, and measure by using virtual tools instead of or along with physical tools. Use of technology in general and of dynamic geometry in particular has gained traction in mathematics education, as evidenced in the Common Core State Standards for Mathematics (CCSSI 2010).

### 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.

### Kasi C. Allen

Students today come to first-year algebra with considerable prior experience and a wide range of skills. Teachers need to modify their instructional strategies accordingly.

### 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.

### Gloriana González and Anna F. DeJarnette

An open-ended problem about a circle illustrates how problem-based instruction can enable students to develop reasoning and sense-making skills.

### Matt B. Roscoe

Having prospective teachers find the inscribed angle theorem for themselves can foster mathematical reasoning.

### Michael J. Bossé and Kwaku Adu-Gyamfi

A geometry course for teachers—easily adaptable to a high school geometry class—integrates technology, reasoning, communication, collaboration, reading, writing, and multiple representations.

### Robert Reys and Barbara Reys

This op-ed piece gives a historical perspective on curriculum change.

### Sheldon P. Gordon

In the climactic scene in The Wizard of Oz, Toto draws back the curtain to expose the Wizard of Oz, and Frank Morgan admits, “I am really a very good man but just a poor wizard.” This statement is reminiscent of Arthur C. Clarke's famous third law: “Any sufficiently advanced technology is indistinguishable from magic” (Clarke 1962, p. 36). For almost all students, what happens when they push buttons on their calculators is essentially magic, and the techniques used are seemingly pure wizardry.