Research on students' learning has made it clear that learning happens through an interaction with others and through communication. In the classroom, the more students talk and discuss their ideas, the more they learn. However, within a one-hour period, it is hard to give everyone an equal opportunity to talk and share their ideas. Organizing students in groups distributes classroom talk more widely and equitably (Cohen and Lotan 1997).
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Mathematical Explorations: A New Twist on Collaborative Learning
classroom-ready activities
Stephanie M. Butman
Harold B. Reiter, John Thornton, and G. Patrick Vennebush
Through KenKen puzzles, students can explore parity, counting, subsets, and various problem-solving strategies.
Peter Wiles
Students fold paper to make and test conjectures while reasoning about and discussing geometric ideas.
Bobson Wong and Larisa Bukalov
Parallel geometry tasks with four levels of complexity involve students in writing and understanding proof.
Michael K. Weiss and Deborah Moore-Russo
The moves that mathematicians use to generate new questions can also be used by teachers and students to tie content together and spur exploration.
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.
Informing Practice: Examples as Tools for Constructing Justifications
research matters for teachers
Kristen N. Bieda and Jerilynn Lepak
Research explores how to help students build from, instead of building with, examples when justifying mathematical ideas.
Terri L. Kurz
After analyzing advertising claims regarding water shooters, students present their findings.
Dustin L. Jones and Max Coleman
Many everyday objects–paper cups, muffins, and flowerpots–are examples of conical frustums. Shouldn't the volume of such figures have a central place in the geometry curriculum?
R. Alan Russell
In trying to find the ideal dimensions of rectangular paper for folding origami, students explore various paper sizes, encountering basic number theory, geometry, and algebra along the way.
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