Jennifer M. Bay-Williams
Deanna Pecaski McLennan
For the Love of Mathematics
Susan Ahrendt, Debra Monson, and Kathleen Cramer
Examine fourth graders’ thinking about the unit, partitioning, order, and equivalence on the number line and consider ways to orchestrate mathematical discussions through the Five Practices.
Brandon G. McMillan and Theodore Sagun
This instructional activity gives teachers access to student thinking that can be leveraged to extend and connect their ideas.
Matt Enlow and S. Asli Özgün-Koca
This month's Growing Problem Solvers focuses on Data Analysis across all grades beginning with visual representations of categorical data and moving to measures of central tendency using a “working backwards” approach.
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.
Patrick M. Kimani, Dana Olanoff, and Joanna O. Masingila
The Mathematics Teaching Practices open the door to helping students engage with meaningful mathematics.
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.
Anne Roche and Doug M. Clarke
Students display a wide variety of creative mathematical thinking and misconceptions when they complete a classroom task that focuses on proportional reasoning.
Amy F. Hillen and Tad Watanabe
Conjecturing is central to the work of reasoning and proving. This task gives fourth and fifth graders a chance to make conjectures and prove (or disprove) them.