This article describes physical activities and modeling process through which–exponential patterns are understood and felt.
Gabriel Matney, Julia Porcella, and Shannon Gladieux
This article shares the importance of giving K-12 students opportunities to develop spatial sense. We explain how we designed Quick Blocks as an activity to engage our students in both spatial reasoning and number sense. Several examples of students thinking are shared as well as a classroom dialogue.
Angela T. Barlow
In this commentary, I share my changing perspective of our new journal as I advanced through the process of becoming the inaugural Editor-in-Chief. Within this narrative, I offer insights into the affordances of the new features of the journal and its contents.
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.
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).