We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.
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Student Engagement with the “Into Math Graph" Tool
Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton
Students' Understanding of Counterexamples
Rebecca Vinsonhaler and Alison G. Lynch
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.
Attending to Evidence of Students' Thinking during Instruction
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.
Because We Love
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.
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.
Connecting Quadratics, Line Segments, Continued Fractions, and Matrices
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.
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.
Ferris Wheel Graphs
Wayne Nirode
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).
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.
