A personal reflection by Ed Dickey on the influence and legacy of NCTM's journals.
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.
Eric Weber, Amy Ellis, Torrey Kulow, and Zekiye Ozgur
Modeling the motion of a speeding car or the growth of a Jactus plant, teachers can use six practical tips to help students develop quantitative reasoning.
Dung Tran and Barbara J. Dougherty
The choice and context of authentic problems—such as designing a staircase or a soda can—illustrate the modeling process in several stages.
Table representations of functions allow students to compare rows as well as values in the same row.
Alison L. Mall and Mike Risinger
Our favorite lesson, an interactive experiment that models exponential decay, launches with a loud dice roll. This exploration engages students in lively data collection that motivates interest in key components of the Common Core State Standards for Mathematics: functions, modeling, and statistics and probability (CCSSI 2010).
S. Asli Özgün-Koca, Michael Todd Edwards, and Michael Meagher
The Spaghetti Sine Curves activity, which uses GeoGebra applets to enhance student learning, illustrates how technology supports effective use of physical materials.
Jamie-Marie L. Wilder and Molly H. Fisher
Our favorite lesson is a hands-on activity that helps students visually “tie” (pun intended) the concepts of rate of change and y-intercept together in a meaningful context using strings and ropes. Students tie knots in ropes of various thicknesses and then measure the length of the rope as the number of knots increases. We provide clothesline, twine, bungee cord, and other ropes found at local crafts, sporting goods, and home stores. We avoid very thin string, such as thread or knitting yarn, because the knots are small and the string length does not change enough to explore a rate of change. A variety of thicknesses is important because this allows for variability in the rates of change.
Dan Kalman and Daniel J. Teague
Using ideas of Galileo and Gauss but avoiding calculus, students create a model that predicts whether a fly ball will clear the famous left-field wall at Fenway Park.