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.
Rebecca Vinsonhaler and Alison G. Lynch
Sherin Gamoran Miriam and James Lynn
This article explores three processes involved in attending to evidence of students' thinking, one of the Mathematics Teaching Practices in Principles to Actions: Ensuring Mathematical Success for All. These processes, explored during an activity on proportional relationships, are discussed in this article, another installment in the series.
Sarah K. Bleiler-Baxter, Sister Cecilia Anne Wanner O.P., and Jeremy F. Strayer
Explore what it means to balance love for mathematics with love for students.
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.
Lee Melvin M. Peralta
One of the many benefits of teaching mathematics is having the opportunity to encounter unexpected mathematical connections while planning lessons or exploring ideas with students and colleagues. Consider the two problems in figure 1.
Laurie Speranzo and Erik Tillema
Specific teacher moves and lesson planning can facilitate student empowerment in the middle school classroom.
To introduce sinusoidal functions, I use an animation of a Ferris wheel rotating for 60 seconds, with one seat labeled You (see fig. 1). Students draw a graph of their height above ground as a function of time with appropriate units and scales on both axes. Next a volunteer shares his or her graph. I then ask someone to share a different graph. I choose one student with a curved graph (see fig. 2a) and another with a piece-wise linear (sawtooth) graph (see fig. 2b).
Clayton M. Edwards, Rebecca R. Robichaux-Davis, and Brian E. Townsend
Three inquiry-based tasks highlight the planning, classroom discourse, positive results, and growth in one class's journey.
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.