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## Changing the Rules to Increase Discourse

A second-grade teacher challenges the raise-your-hand-to-speak tradition and enables a classroom community of student-driven conversations that share both mathematical understandings and misunderstandings.

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## Redesigning Caesar's Wheel with a modeling perspective

Use this example of a model-eliciting activity to teach cryptology. Contributors to the iSTEM (Integrating Science, Technology, Engineering, and Mathematics) department share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K–grade 6 classrooms.

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## Diving deeper into data

Each month, this section of the Problem Solvers department showcases students' in-depth thinking and discusses the classroom results of using problems presented in previous issues of Teaching Children Mathematics. During this investigation, students have the opportunity to explore the structure of pictographs and bar graphs and to examine, compare, and analyze data.

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## Investigations: My bar graph tells a story

Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy (Blubaugh and Emmons 1999; Maus 2005; NCTM 2000). Even students who are able to create bar graphs may struggle to correctly interpret them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information from a graph even without the availability of numeric labels. This investigation addresses the Data Analysis and Probability Standard (NCTM 2000) and explores the value of connecting stories with qualitative bar graph instruction, which too often focuses on only counting, tallying, and creating bar graphs.

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## How Long Can You Stand on One Foot?

How Long Can You Stand on One Foot? is a classic problem that has variations in a range of mathematics and physical education curricula. This problem allows students to go through the statistical investigation PCAI process (posing a question, collecting data, analyzing data, and then interpreting data).

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## Surviving an Avalanche of Data

Help first-grade students learn to competently generate, test, revise, and represent data before being formally taught to do so.

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## Statistics at Play

Three core components in developing children's understanding and appreciation of data—establish a context, pose and answer statistical questions, represent and interpret data—lay the foundation for the fourth component: use data to enhance existing context.

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## A-Maize-ing Mathematics

In the set of percentage change activities described in this article, students learn about food scarcity in sub-Saharan Africa, how two specific viruses are spreading through maize in the region, and how scientists are using mathematical modeling to solve the problem. This context was particularly relevant to my students who live in the Mississippi Delta, an area where agriculture is the dominant industry. In this activity, students use spreadsheets to perform calculations on a set of data. The goals of this activity, designed for a prealgebra or algebra class, are to encourage students to examine how percentage change is computed in real-world problems, to look for and analyze patterns, and to create their own functions on the basis of actual data.

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## Mining Data with USA Today's Snapshots

The Snapshots section of USA Today offers quick pictures of intriguing data collected for a specific question. A variety of subject matter is available online at http://www.usatoday.com/news/snapshot.htm, and the graphics change frequently. To use this month's activities, first visit the site to review the current topics and choose what is best for your class. If you do not have class access to the Internet, just download a couple of data snapshots, print them for examples for your class, and let students start mining. If an appropriate fit is not available, adapt or create your own. The focus of the following generic problems and activities allows students to collect their own data, transform problems, and process data in meaningful ways.

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## Pencils and crayons

Each month this section of the Problem Solvers department discusses the classroom results from using problems presented in previous issues of Teaching Children Mathematics. Find detailed submission guidelines for all departments at www.nctm.org/tcmdepartments.