In this article, we discuss funky protractor tasks, which we designed to provide opportunities for students to reason about protractors and angle measure. We address how we have implemented these tasks, as well as how students have engaged with them.
Hamilton L. Hardison and Hwa Young Lee
The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle centers.
Thomas G. Edwards and Kenneth R. Chelst
In a 1999 article in Mathematics Teacher, we demonstrated how graphing systems of linear inequalities could be motivated using real-world linear programming problems (Edwards and Chelst 1999). At that time, the graphs were drawn by hand, and the corner-point principle was applied to find the optimal solution. However, that approach limits the number of decision variables to two, and problems with only two decision variables are often transparent and inauthentic.
Chris Harrow and Lillian Chin
Exploration, innovation, proof: For students, teachers, and others who are curious, keeping your mind open and ready to investigate unusual or unexpected properties will always lead to learning something new. Technology can further this process, allowing various behaviors to be analyzed that were previously memorized or poorly understood. This article shares the adventure of one such discovery of exploration, innovation, and proof that was uncovered when a teacher tried to find a smoother way to model conic sections using dynamic technology. When an unexpected pattern regarding the locus of an ellipse's or hyperbola's foci emerged, he pitched the problem to a ninth grader as a challenge, resulting in a marvelous adventure for both teacher and student. Beginning with the evolution of the ideas that led to the discovery of the focal locus and ending with the significant student-written proof and conclusion, we hope to inspire further classroom use of technology to enhance student learning and discovery.
I always seek activities that might stretch my students yet would be accessible to them; that might require logical thought yet would contain counterintuitive elements; that might provide the opportunity to venture into new mathematical realms yet would have a simple starting point. This article and the activity that inspired it did indeed arise by way of a relatively straightforward problem that I proposed to one of my classes.
Readers comment on published articles or offer their own ideas.
Processes using linear measurement can be adapted to teach complex topics such as polynomial multiplication, rational exponents, and logarithms.
Brandt S. Lapko
Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K–grade 6 classrooms. This article describes how students can use available technology to communicate and share their thinking in popular media formats.
Kurt J. Rosenkrantz
Students say some amazing things. Back Talk highlights the learning of one or two students and their approach to solving a math problem or prompt. Each article includes the prompt used to initiate the discussion, a portion of dialogue, student work samples (when applicable) and teacher insights into the mathematical thinking of the students. In this month's episode, a six-year-old rising first grader uses a computer simulation to understand addition and subtraction on the number line.
Jennifer Orr and Jennifer Suh
Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K—grade 6 classrooms. One way to keep young students engaged and interested in practicing counting is to involve them in using cameras. This article explains how first graders capture 100 images, use Windows MovieMaker or PhotoStory to turn the still images into a video, and then narrate a story using precise math vocabulary to explain their mathematical thinking.