A two-part calculus activity uses true-false questions and a descriptive outline designed to promote active learning.

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## 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).

### 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).

### Janet Sharp and Rachael M. Welder

Students notoriously struggle with division of fractions in 5 key areas. Hear what those 5 areas are and how recommendations address the limitations.

### Jennifer Knudsen, Teresa Lara-Meloy, Harriette Stallworth Stevens, and Daisy Wise Rutstein

“Telling” can be an effective tool in helping students engage in intellectually demanding argumentation and productive behavior.

### D. Bruce Jackson

Given two slices of bread—a problem and the answer—students fill in the fixings: their own mathematics reasoning.

### Agida G. Manizade and Marguerite M. Mason

When calculating the area of a trapezoid, students use a range of problem-solving strategies and measurement concepts.

### Karin E. Lange, Julie L. Booth, and Kristie J. Newton

Presenting examples of both correctly and incorrectly worked solutions is a practical classroom strategy that helps students counter misconceptions about algebra.

### Erik Jacobson

Table representations of functions allow students to compare rows as well as values in the same row.

### Ann E. West

The use of mnemonic devices, or “tricks,” in the mathematics classroom has been criticized by some authors. However, when used in the proper context, such “tricks” can be extraordinarily helpful in motivating students and helping them remember procedures while understanding concepts and mastering appropriate mathematical vocabulary.