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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Students' Understanding of Counterexamples
Rebecca Vinsonhaler and Alison G. Lynch
Capturing Mathematical Curiosity with Notice and Wonder
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.
Designing for Voice and Agency
Laurie Speranzo and Erik Tillema
Specific teacher moves and lesson planning can facilitate student empowerment in the middle school classroom.
Investigating a Super-Bear
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.
Letters to the editor
License to Do Math with a Full Tank
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.
May 2019 Calendar and Solutions
Problems
Stephen Phelps
Edited by Anna F. DeJarnette
A monthly set of problems targets a variety of ability levels.
Prove It to Me!
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.
Soccer for Real
Imani M. Goffney
Edited by Naima F. Goffney
My name is Naima Goffney, and I am an eleven-year-old seventh grader at Julius West Middle School. I am taking algebra 1 this year. I wanted to write the Math for Real because in math class I do not always think that what we are learning is related to the real world. At home, my mom shows me all the different ways I am mathematically smart, which makes me want to try harder in school during the “rougher” days. We can use math to know more about how to improve our skills and find the math we learn in school more interesting and more related to our real world as middle schoolers.
