Learning Geometric Concepts through Ceramic Tile Design
Clare V. Bell
Article presents a sequence of lessons to engage middle school students in the use of two-dimensional geometry through the creation of individually designed tiles.
Using Literature to Engage Students in Proportional Reasoning
Sherri L. Martinie and Jennifer M. Bay-Williams
Article presents three literature-based mathematics tasks. In addition, it describes proportional thinking as it appears across mathematical strands. Recommended connections to literature are included.
Building on Students' Intuitive Strategies to Make Sense of Cross Multiplication
Melissa D. Boston, Margaret S. Smith, and Amy F. Hillen
Article describes the intuitive proportional reasoning strategies that students used to solve a set of missing value problems and how these strategies might be used to build meaning and understanding for the cross-multiplication algorithm.
Assessing Proportional Thinking
George W. Bright, Jeane M. Joyner, and Charles Wallis
Article explores the performance and thinking of eighth- and ninth-grade students in their solution to proportional reasoning problems in multiple-choice and open-ended formats. The two formats provide different pictures of students' proportional reasoning strategies. The assessment analyzed in provided with sample student responses.
Using Friday Puzzlers to Discover Arithmetic Sequences
Article shows how the solutions to five simple problems can be used to develop the concept and formula for the sum of an arithmetic sequence. Five problems and sample student responses are included.
Turning Traditional Textbook Problems into Open-Ended Problems
Mary S. Kabiri and Nancy L. Smith
Article demonstrates how to take traditional textbook problems and rewrite them to be more open-ended to better meet the needs of diverse learners in a classroom.