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.
Carolyn James, Ana Casas, and Douglas Grant
Encouraging students to justify earlier as they attempt to solve an open-ended task can lead to greater understanding and engagement.
big solutions to little problems
Jo Ann Cady and Pamela J. Wells
Solutions to a previous Solve It problem are discussed, and the procedures used with problem solving are explored.
Patrick M. Kimani, Dana Olanoff, and Joanna O. Masingila
The Mathematics Teaching Practices open the door to helping students engage with meaningful mathematics.
Stephanie M. Butman
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).
Ryota Matsuura and Yu Yan Xu
This activity involves finding the distance between two points in a coordinate plane and emphasizes reasoning from repeated calculations, which is one of the mathematical practices specified by the Common Core State Standards for Mathematics.
“when will I ever use this?”
Fred Dillon and Kevin Dykema
This problem ties into the real-life measurement found in the Richter scale.
D. Bruce Jackson
Given two slices of bread—a problem and the answer—students fill in the fixings: their own mathematics reasoning.
Jane M. Wilburne and Ashley Kulbacki
A sixth-grade teacher's word task uncovers higher-level thinking and engages her students in the Standards for Mathematical Practice.
Shiv Karunakaran, Ben Freeburn, Nursen Konuk, and Fran Arbaugh
Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.