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## Influence and Legacy of NCTM Journals

A personal reflection by Ed Dickey on the influence and legacy of NCTM's journals.

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## Quick Blocks: Developing Spatial Sense

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.

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## Well Played

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.

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## Authenticity of Mathematical Modeling

The choice and context of authentic problems—such as designing a staircase or a soda can—illustrate the modeling process in several stages.

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## The Back Page: My Favorite Lesson: All Knotted Up

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.

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## Activities for Students: The Hands Project

The author presents an activity in which the lines in students' hands are analyzed, with curves and lines fit to each one.

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## Errors in Mathematics Aren't Always Bad

We tell students that mathematical errors should be avoided, but understanding errors is an important tool in developing numerical methods.