This article focuses on students use and understanding of counterexamples and is part of a research project on the role of examples in proving. We share student interviews and offer suggestions for how teachers can support student reasoning and thinking and promote productive struggle by incorporating counterexamples into the classroom.
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Aaron M. Rumack and DeAnn Huinker
Capturing students' own observations before solving a problem propelled a culture of sense making by meeting needs typical of middle school learners.
Laurie Speranzo and Erik Tillema
Specific teacher moves and lesson planning can facilitate student empowerment in the middle school classroom.
Ron Lancaster
Since its inception, the Mathematical Lens column has provided teachers with resources to use with their students to make connections between mathematics and the world around us through the use of photographs. The editors and the dozens of teachers who submitted material for columns have taken all of us on a journey around the world to discover where mathematics lives. These columns have offered teachers a license to do mathematics everywhere and to travel far with their students with a full tank of resources.
Stephen Phelps
Edited by Anna F. DeJarnette
A monthly set of problems targets a variety of ability levels.
Jo Boaler
Engage your learners through tasks proven to significantly promote reasoning and problem solving, which touch on many of the Mathematics Teaching Practices in Principles to Actions: Ensuring Mathematical Success for All. These tasks are discussed in this article, another installment in the series.
P. Reneé Hill-Cunningham
Hundreds of species of animals around the world are losing their habitats and food supplies, are facing extinction, or have been hunted or otherwise negatively influenced by humans. Students learn about some of these animals and explore multiple solution strategies as they solve this month's problems. Math by the Month features collections of short activities focused on a monthly theme. These articles aim for an inquiry or problem-solving orientation that includes four activities each for grade bands K–2, 3–4, and 5–6.
Peter Wiles, Travis Lemon, and Alessandra King
Students move from slides, flips, and turns into reasoning about the characteristics of rigid transformations.
