A classic manipulative, used since the 1960s, continues to offer opportunities for intriguing problem solving involving proportions.
Joe Champion and Ann Wheeler
Kyle T. Schultz and Stephen F. Bismarck
A geometric approach using exact square manipulatives can promote an understanding of the algorithm to dismantle radical expressions.
Jessica F. Shumway
Three days of using building blocks significantly enriched second graders' thinking about multiple dimensions.
The relationship between a midpoint and an average showcases the interplay between procedural knowledge and conceptual knowledge in learning mathematics for teaching.
Sarah J. Selmer and Kimberly Floyd
A proactive preschool teacher differentiates instruction by using the Universal Design for Learning framework to decrease barriers that limit students' access to classroom learning.
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.
Trena L. Wilkerson, Tommy Bryan, and Jane Curry
Using candy bars as models gives students a taste for learning to represent fractions whose denominators are factors of twelve.
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.
Katie L. Anderson
Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K–grade 6 classrooms. This article describes a set of lessons where sixth graders use virtual pattern blocks to develop proportional reasoning. Students' work with the virtual manipulatives reveals a variety of creative solutions and promotes active engagement. The author suggests that technology is most effective when coupled with worthwhile mathematical tasks and rich classroom discussions.
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.