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
Hyewon Chang and Barbara J. Reys
Using Clairaut's historic-dynamic approach and dynamic geometry tools in middle school can develop students' conceptual understanding before they encounter formal proof in geometry.
Justin T. Burris
Compare how third graders think mathematically when using virtual versus concrete base-ten blocks to learn place-value concepts.
This department showcases students' in-depth thinking and work on previously published problems. The August 2012 problem scenario leverages back-to-school shopping advertisements for this real-life scenario about making purchases using discount coupons. To access the full-size activity sheet, go to http://www.nctm.org/tcm, Back Issues.
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.
Rochelle Goldberg Kaplan and Sandra Alon
Professional development equips practitioners with skills to enhance student learning.
Katherine A. G. Phelps
Fourth- and fifth-grade learners can use differentiated number sets within CGI problem structures to add and subtract fractions with unlike denominators.
Pamela Edwards Johnson, Melissa Campet, Kelsey Gaber, and Emma Zuidema
Three preservice teachers used virtual manipulatives during clinical interviews with students of elementary school age. The technology exposed students' problem-solving strategies and mathematical understanding, promoting just-in-time teaching about the target content. The process of completing and reflecting on the interviews contributed to growth of the preservice teachers' technological pedagogical content knowledge.