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December 2007, Volume 101, Issue 5


Secret Snowflake: Analysis of a Holiday Gift Exchange
Roger Turton
Several discrete mathematics methods used to simulate and solve a rich problem occurring at a holiday gift exchange. What is the probability that two people will select each other's names in a random drawing, and how does this result vary with the total number of participants? Includes code for a computer simulation of the problem, sample work and results.

On Blocks, Stairs, and Beyond: Learning about the Significance of Representations
Laurie Rubel, Betina Zolkower
Article uses the "Blocks Problem" and "Staircase Problem" to demonstrate new ways to focus on representation and the understanding of functions in the classroom. The article discusses the implementation of these two problems in a teacher education course. Sample problems and student work are provided.

New Thinking about College Mathematics: Implications for High School Teaching
Robin Marcus, Tim Fukawa-Connelly, Michael Conklin, James Fey
Recommendations made by participants in a large project of the Mathematical Association of America (MAA), in which representatives of "partner disciplines" shared what they would like students to learn in the first two years of college mathematics. The article further suggests implications for high school mathematics and recommendations for curriculum changes, showing alignment with NCTM's Principles and Standards. The article includes specific priorities recommended for course content, and techniques to implement the new ideas in teaching.

Bridging the Language Barrier in Mathematics
Matthew Winsor
How action research was used to address the challenges of teaching mathematics to ELL students. Several research-based activities used in the classroom are described along with how students reacted to the activities. Resources are given to help a teacher or administrator develop their own ideas to reach ELL students in the mathematics classroom.

The Spirit of Discovery: The Digital Roots of Integers
Eric Milou, Jay Schiffman
Article compels students to analyze patterns and formulate conjectures in the spirit of discovering mathematics. Ideas such as the multiplicative digital root and multiplicative persistence as well as connections to probability and statistics and number sense are included. Sample solutions and data collected from posing the problem in a college level class are provided.