The two provided activities are geared for students in middle school to facilitate and deepen their understanding of the arithmetic mean. Through these activities, students analyze visual representations and use a special type of statistical thinking called transnumerative thinking.
Michael Daiga and Shannon Driskell
This simple dice game supports students' development of flexibility with numbers, the properties of the four operations (+, −, ×, ÷), and the order of operations. It requires only dice and a game board for each player.
Joe Champion and Ann Wheeler
A classic manipulative, used since the 1960s, continues to offer opportunities for intriguing problem solving involving proportions.
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.
Robin S. O'Dell
Using a rule as a seesaw helps students steady their understanding of the mean.
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.
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.