Free Articles from NCTM Middle School Math Journal

Take a free look at the articles from the NCTM middle school journal – Mathematics: Teaching in the Middle School. Explore and share with others. Check out the Reflection Guides. They provide professional development support linked to specific articles for individual, small groups or school use.Digesting

Student-Authored Story Problems
August 2010, Volume 16, Issue  1

Problems with nth-Term Problems:
Reflect and Discuss
September 2010, Volume  16, Issue  2

Map the Race to the White House
October 2010, Volume  16, Issue  3

Exploring Our Complex Math Identities
November 2010, Volume  16, Issue  4

Multiplication Fact Fluency Using Doubles
December 2010, Volume  16, Issue  5

Fold in Origami and Unfold Math
February 2011, Volume  16, Issue  6

All These Rays! What’s the Point?
March 2011, Volume  16, Issue  7

Problem Solving around the Corner
April 2011, Volume  16, Issue  8

Tailoring Tasks to Meet Students’ Needs
May 2011, Volume  16, Issue  9

Article and Reflection Guide – Technology
Technology Enhances Student Learning across the Curriculum
Several forms of technology that can enhance basic understandings and skills of middle school mathematics concepts are discussed, including technologies such as Calculator Based Ranger (CBR), Spreadsheets, and Geometer’s Sketchpad. February 2004, Volume 9, Issue 6, pp. 344-349

Collecting and Analyzing Real Data

Data collection and analysis can be an avenue into meaningful mathematics, science, and problem-solving skills needed by students in the twenty-first century. And an answer to the student question, Why do we have to study math? can be found when teaching mathematics with a real-world statistics approach. Below are digital teaching resources that demonstrate how data and statistics are a vital part of learning mathematics in a meaningful context. The resource activities are often interdisciplinary, which makes them time-consuming to prepare, as additional expertise is often needed. But the payoffs can be huge: student engagement, in-depth learning, and a real-world context for learning mathematics.

One approach is to look at situations in your community or larger world issues and have the students frame questions to investigate. Students may develop a passion for scientific inquiry when a topic can be analyzed with numbers. Requiring quality work and including a component about sharing results with the community will add value to an interdisciplinary contextual learning experience. Teachers may want to enlist a community person to provide additional expertise. Whether thinking small activity or big project, be ready to be surprised at what the data analysis reveals!

Analyzing Numeric and Geometric Patterns of Paper Pool
Look out, pool sharks! Begin the study of data and statistics with this super student exploration where data are collected and analyzed while students apply mathematical topics studied in grades 6 and 7: factors, multiples, rectangles, and the meaning of being relatively prime. In the Paper Pool applet, a ball is hit from the lower left-hand corner of a grid-lined pool table at a 45-degree angle. Students modify the size of the rectangular pool table and observe how the ball always travels on diagonals of the grid squares. After gathering and organizing data, students look for patterns to predict the corner pocket into which a ball will fall and the number of side hits the ball makes as it moves on the table to a corner pocket. The goal is to determine how the number of hits, final pocket, and number of squares crossed depend upon the relative lengths of the sides of the pool table. Sounds like fun, doesn’t it?

Junk Mail (a mini project)
No one is immune from receiving junk mail, but just how much of it is really finding its way to your address? In this simple activity, data collection and analysis are a key part of a project to learn about the importance of recycling. For one week, students count and record the number of pieces of junk mail received in their homes. The display and organization of the data can be modified to address the data and statistics topics the class is working on.

WWW—Wonderful Web Weather
Just how on-target are those weather forecasters we watch and listen to? In this webquest, students work in groups to track online weather reports for several locations over the course of three days and determine the accuracy of forecasts. Students develop an understanding of how weather can be described by measurable quantities, such as temperature, wind, and precipitation as they find and compare weather data found on the Internet, chart and graph data, and present their conclusions about forecasting. This straight-forward activity is suitable for students who are just beginning their work with data and statistics.

The Global Sun Temperature Project
With this free online collaborative project, students measure the temperature and record the minutes of sunlight for one week. Data are collected on the web site, and average daily temperatures and amount of sunlight are compared. Students draw conclusions about how the distance from the equator influences temperature. If you like this collaborative project, be sure to check out Down the Drain: How Much Water Do You Use?, another collaborative data project from the Center for Innovation in Engineering and Science Education (CIESE).

The Gulf Stream Voyage
If ocean travel is your passion, this site offers a way to spend time at sea without ever leaving your classroom. Here is a science project that uses actual data to help students investigate the science and history of the Gulf Stream. Math students can greatly benefit from the opportunity to collect data and draw conclusions based on the data. In the lesson called Current Now, students use real-time data and satellite images to determine how the Gulf Stream moves in the course of a year. In another activity, students use data about water temperature obtained from ships and buoys to determine the course of the Gulf Stream.

Boil, Boil, Toil and Trouble: The International Boiling Point Project
Be part of an annual event: Enroll your class in this free Internet-based collaborative project. Students discover which factors–room temperature, elevation, volume of water, or heating device–have the greatest influence on boiling point. Students boil water, record their data, and send it via email to be included in the site’s database of results. Student activities focus on analyzing the compiled data to find answers to questions about how and why water boils.

Backyard Birding—Research Project
Birds are everywhere, and here are ideas for creating a data collection project. Work with a science teacher and, possibly, an industrial tech teacher to expand this multiweek activity into a cross-curricular project to help students see how data analysis can support an understanding of nature.

Population Growth
These nine online lesson/activities investigate population growth and its impacts. Students use archived census and demographic data from the U.S. Census Bureau to model population growth and examine how population change affects the environment. Teachers will want to carefully review this resource to choose the activities most appropriate for their students’ mathematics background. Linear, quadratic, and exponential functions are used in some lessons.
We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 4/07/2012.

Amazing New Collection of Hands-on, Interactive Resources

The Lawrence Hall of Science at the University of California, Berkeley, has launched an online collection of hands-on, interactive resources to help informal educators in nonclassroom settings, such as museums and science centers, engage school-age children in science, mathematics, engineering, and technology learning. The web site is called howtosmile.org.

The web site provides both an enhanced faceted and a visual search capability; list-making features that provide a public or private online space to collect favorite activities and add teaching tips and ideas on how to use an activity; user-contributed videos, and other creative community functions that encourage users to rate and comment on activities. Some activities are available in Spanish. Special activity collections target those with limited mobility and individuals who are vision impaired. Built using open source tools, howtosmile.org also includes an open infrastructure to allow institutions to contribute links to useful activities and a free widget to embed howtosmile.org search results on any web page.

We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 4/12/2012.

Crippling with Compassion?

Strange title? It comes from teacher Ellen Berg’s article in Teacher Magazine, Teaching Secrets: Don’t Cripple With Compassion. From her perspective, “One of the major issues with American teachers especially is our predilection to rescue kids instead of letting them struggle with the content a bit. In essence, we’re too compassionate.” It is second nature for us as teachers to help our students, but do we rush in on rescue missions too often and too soon?

Berg writes, “I get how difficult it is to step back and let them struggle, but I also know that it’s in the disequilibrium that kids have to make sense of things and that’s when the learning happens. If we do it for them, why would they be persistent with a problem or give it more than 30 seconds? And how can they become confident, self-directed learners if we don’t ever let them have that experience? Finally, why would they ever believe that they are able to figure it out if we show them by our actions that we don’t believe they can, either?”

Thinking of how we math teachers might challenge students to tough thinking, I looked around for problems that would work in middle school classrooms. Here are a few below, but please share any of your favorites from the classroom in the comments section.

Balanced Assessment

A set of more than 300 assessment tasks actually designed for off-the-wall thinking. Most tasks, indexed for grades K-12, incorporate a story problem and include hands-on activities. Some intriguing titles include Confetti Crush, Walkway, and Hockey Pucks. Rubrics for each task are provided.

Understanding Distance, Speed, and Time Relationships

In these two lessons, students use an online simulation of one or two runners along a track. Students control the speed and starting point of the runner, watch the race, and examine a graph showing time versus distance. Students can use the activity to come to conclusions on the distance, speed, and time relationship. They can also use it to consider the graphical representation and the concept of slope.

Measuring the Circumference of the Earth

Through this online project, students learn about Eratosthenes and actually do a similar measurement that yields a close estimate of the earth’s circumference. It’s a challenge! Even with access to only one computer, students can obtain data from other schools that lie approximately on their own longitude. Careful instructions guide the students in carrying out the experiment and analyzing the data collected. The project also provides activities, reference materials, online help, and a teacher area.

Down the Drain: How Much Water Do You Use?

Students first collect data from their household members and their classmates and then determine the average amount of water used by one person in a day. They compare their average to the average amount of water used per person per day in other parts of the world. Through the Internet, they can collect and share information with other students from around the country and the world. A teacher’s guide is included as well as guidelines on how students can publish reports, photos, or other work directly to the project web site.

Accessing and Investigating Population Data

In these activities, students use census data available on the web to examine questions about population. They also formulate their own questions. For example, in one section they analyze statistics from five states of their choice, develop specific research questions using the data, and create three graphs to compare and contrast the information.

The Handshake Problem

This two-lesson unit allows students to discover patterns in a fictional but real-world scenario: How many handshakes occur when the nine Supreme Court justices shake hands with each other? Students explore—through a table, a graph, and finally an algebraic formula—the number of handshakes in any size group. A second pattern is explored, that of triangular numbers; again, students generalize the pattern with variables. The lessons are well illustrated and include background information for the teacher.

These problems require patience and analytical thinking, even the easiest of them. I would not give such problems without having prepared my students with the needed tools to do them, if not before they start the work, then as they’re doing it. As Ellen Berg put it, “I’m not talking about failing to scaffold instruction or give kids input. Of course we want to do that. What I’m talking about is resisting the urge to fix things for them instead of asking more questions to get them thinking. I’m talking about sometimes just telling them, ‘I know you can do this,’ and walking away.”

Another teacher who feels that we need to help math students less is Dan Meyer, a high school math teacher. This 11-minute talk, Math Needs a Makeover, begins with: “I teach high school math. I sell a product to a market that doesn’t want it but is forced by law to buy it.” From there he moves to actual examples of textbook math versus ways to present real, hard thinking problems. Worth watching!

Citation: From Teacher Magazine [Teacher Update], Wednesday, May 26, 2010. See  http://www.edweek.org/tm/articles/2010/05/26/tln_berg_compassion.html?tkn=URPFzAhx52nB4%2FOp1kNYkfQZs6eV8MJI9rtk&cmp=clp-edweek

We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 4/12/2012.

Linking Math to Real Problems

Why bother with statistics in middle school? One answer: data analysis is one of the NCTM Standards and an 8th grade Focal Point. But even more important, in my experience, is that statistics links math to real problems.

Working Hours: How Much Time Do Teens Spend on the Job?
This activity challenges students to interpret a bar graph, showing only percentages, to determine the mean number of hours teenagers work per week. A more complicated and interesting problem than it may seem at first glance!

Train Race
In this interactive game, students compute the mean, median, and range of the running times of four trains, then select the one train that will get to the destination on time. Their goal is to find the most reliable train for the trip.

The Global Sun Temperature Project
This web site allows students from around the world to work together to determine how average daily temperatures and hours of sunlight change with distance from the equator. Students learn to collect, organize, and interpret data. You will find project information, lesson plans, and implementation assistance at the site.

Down the Drain: How Much Water Do You Use?
In this Internet-based collaborative project, your students share information about water usage with other students from around the country and the world. Based on data collected by their household members and their classmates, students will determine the average amount of water used by one person in a day. Students must develop a hypothesis, conduct an experiment, and present their results.

100 People: A World Portrait Detailed Statistics
You’ve heard the idea before: What if the whole world were represented by 100 people? It is mind-boggling, for example, to realize that 61 would be from Asia and only 5 from North America. This page gives a full list of the data collected, links to a lesson plan and to commentary on the statistics. Excellent for an interdisciplinary project!

If you’d like to focus attention on measures of central tendency, these last two sites help explain the mean and the median though interactive online practice.

Plop It!
Users click to easily and quickly build dot plots of data and view how the mean, median, and mode change as numbers are added to the plot. An efficient tool for viewing these statistics visually.

Comparing Properties of the Mean and the Median Through the Use of Technology
This interactive tool allows students to compare measures of central tendency. As students change one or more of the seven data points, the effects on the mean and median are immediately displayed. Questions challenge students to explore further the use of these measures of center; for example, What happens if you pull some of the data values way off to one extreme or the other extreme?

Join your colleagues in discussing these and other middle school issues at the Middle School Portal 2 (MSP2) social network. Hope to “see” you there!


We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 11/29/2011.