The relationship between a midpoint and an average showcases the interplay between procedural knowledge and conceptual knowledge in learning mathematics for teaching.
Jeffrey J. Wanko, Michael Todd Edwards, and Steve Phelps
The Measure-Trace-Algebratize (MTA) approach allows students to uncover algebraic relationships within familiar geometric objects.
Adam Poetzel, Joseph Muskin, Anne Munroe, and Craig Russell
Using simple materials, a Mathematica software application, and their knowledge of function transformations, students design and create real mathematical sculptures.
An origami activity can lead to rich tasks in several branches of mathematics.
Christine K. Pritchard and John H. Lamb
Teaching a visual subject to a visually challenged student inspires strategies that benefit all students in a class.
Mathematical Lens uses photographs as a springboard for mathematical inquiry and appears in every issue of Mathematics Teacher. all submissions should be sent to the department editors. For more background information on Mathematical Lens and guidelines for submitting a photograph and questions, please visit http://www.nctm.org/publications/content.aspx?id=10440#lens.
Tongta Somchaipeng, Tussatrin Kruatong, and Bhinyo Panijpan
Students use balls and disks to prove the general formulas for sums of squares and cubes.
Timothy McKeny and Joanne Caniglia
Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month, the art of sculptor and painter Sol LeWitt is analyzed. Counting, combinatorics, and spatial visualization are among the mathematical themes evinced.
Harold Reiter, Arthur Holshouser, and Patrick Vennebush
This method for counting lattice octagons strengthens students' counting skills and geometrical thinking.
Emiliano Gómez and Risa A. Wolfson
In this activity, students gradually fill bottles of different shapes and graph the water level (height) versus the volume of water inside the bottles. Then they explore the relationship between the shape of a bottle and the resulting graph.