When I first started teaching, I was strictly a by-the-book teacher. Students entered my classroom, I presented the material, and then I assigned homework. In the spring of 1967, however, a student brought in a newspaper article in which the author claimed to have trisected an angle using only a compass and a straightedge. My class was excited and wanted to know if his construction was correct. At that moment, my approach to classroom teaching changed. This experience taught me to actively involve students in all aspects of the classroom and has led to some of my favorite lessons. I soon began to create, collect, and present to students mathematics problems for them to explore. Here, I share one such problem that I have used in Algebra 1, Geometry, and Algebra 2 with Trig courses.
Andrew Samide and Christine Kincaid Dewey
This article describes an open-ended problem-solving task that starts with a simple 3 in. × 5 in. note card and leads to a rich discussion of geometry and coordinate graph representations.
Andrew J. Samide and Amanda M. Warfield
Students have an uncanny knack for inventing solutions to problems that intrigue classmates who immediately want to know if they hold true in all cases.