Reading Math

You may have heard this complaint or even made it yourself: “These tests are more about reading than they are about math!”  Students are increasingly asked to understand and apply math to situations, rather than just perform an operation on numbers. This involves reading the math text that sets out the problem scenario.

Add to that the inherent difficulty of math vocabulary, where a word can mean one thing in a mathematical context and another in everyday settings.  Symbols, another part of vocabulary, can look alike but have different meanings, or different symbols can represent the same operation (for example, *, x, and · for multiplication).

And there’s the textbook, usually opened only for the problem sets, since most students are alienated by its language and its very format.

How can we help middle school students learn to read the math they need for today’s tests and high school courses?  Far from expecting teachers to stretch their class time to include yet more content, I’d like to offer online resources that can enrich math instruction as teachers help their students better understand the content they are already tackling.

Reading in the Mathematics Classroom
Written by Diana Metsisto, a middle school mathematics coach, this online chapter involves both the “why” and the “how” of integrating reading in the teaching of mathematics. She offers a number of concrete classroom strategies.

Unlocking the Mystery of Mathematics: Give Vocabulary Instruction a Chance
Math teacher Bizzie Cors realized that her students needed to “construct meaning for all vocabulary terms and connect to prior knowledge as well as to new concepts and algorithms.”  This led her to create a new process to teach vocabulary development.  Described here is what she calls the “sticky-note chain” process; its final product is a graphic organizer complete with sticky notes, connections, and problems created by the students themselves.

A Maths Dictionary for Kids
This animated, interactive mathematics dictionary for kids explains over 500 common mathematical terms in simple language. Each term is illustrated and, often, accompanied by an interactive applet that makes visual and immediate the definition of the term.

Getting to Know Your Middle Grades Mathematics Textbook
This article by Diane Kahle, an experienced teacher of middle school mathematics, shares general tips, small group and whole class ideas for textbook reading, and a ten-question scavenger hunt to help students learn how to find information in their mathematics textbook.

Books can be used to teach actual math concepts. For ideas, spend a few minutes at the Mathematics Bookshelf.

Please comment on these resources and offer your own ideas on teaching students to read math.


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 10/10/2011.

Writing Math

As in other subjects, writing forces us to order our thoughts, make them clear to others. In mathematics, writing, as difficult as it is, helps students organize their understandings of concepts and set out for themselves their reasoning about a problem and its solution.  As stated in the Principles and Standards for School Mathematics, “students who have opportunities, encouragement, and support for writing, reading, and listening in mathematics classes reap dual benefits: they communicate to learn mathematics, and they learn to communicate mathematically” (National Council of Teachers of Mathematics 2000).

Writing comes easily to few of us, and that includes our students. These resources offer practical advice learned from the experiences of teachers in the classroom.  If you would, share with your colleagues your ideas on using writing as a teaching/learning tool by commenting on this blog post.

A Case for Using Reading and Writing in a Mathematics Classroom
Speaking from her own experiences as a math teacher, Sarah Kasten tells how — and why — she introduced reading and writing in her classroom. She shares how she directed her classes to do 5-minute, impromptu writing assignments, explain their problem-solving process, or even explain a new concept and create their own example problems. 

 Writing in Mathematics
A brief teacher-to-teacher article on getting started with writing in math class — moving from think-pair-share to a less-known model: think-write-pair-share.  A set of helpful links to other teachers’ experiences is given.

Math and Communication
You’ll find solid tips on encouraging and supporting math talk in this brief piece by well-known math teacher Kay Toliver.

Adapting Literacy Strategies to Improve Student Performance on Constructed-Response Items
This article discusses ways of adapting various reading strategies to help students improve their answers to extended-response questions on the mathematics portion of high-stakes tests. A practical article directed to teachers.  

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 4/14/2012.

Reading and Writing Mathematics

Reading the math textbook or handouts or extended response problems presents built-in challenges. The vocabulary of mathematics can be confusing, with some words meaning one thing in a mathematical context and another in everyday settings. Symbols can look alike, and different symbols can represent the same operation (for example, *, x, and • for multiplication). Graphs vary in format, even when representing the same data. Writing is valued as a way of communication in most school subjects, yet rarely in math. If students can learn to explain their thinking in solving a math problem (using drawings or tables or graphs as well as words), they acquire a means of setting out their work logically and refining their thinking as they communicate their understandings.

Far from expecting teachers to stretch their class time to include yet more content, a new Explore in Depth publication from the Middle School Portal, Reading and Writing Mathematics, offers resources that can enrich math instruction as teachers help their students better understand the content they are already tackling. Each section of the publication contains articles, many by teachers, who share their experiences, rationale, and classroom methods. Each section also offers lesson plans or activities appropriate for middle school students. Enjoy the challenge of opening your students to mathematical communication!

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 4/14/2012.

Math Students Collaborating Nationwide, Even Worldwide!

There are middle school projects that gain impact through collaboration with students outside your own classroom, such as estimating the average amount of water used per person per day. This problem takes on deeper relevance when averages are compared to those of classrooms around the country and the world. Other projects, such as finding the circumference of the Earth, require data input by geographically distant schools. 

To connect with and collaborate with classrooms interested in the same project, you can make use of online sites, even though you work in an offline classroom. You need Internet access to register for the project (free registration!), to find suggested teaching procedures, and to submit and retrieve data from other schools. But you can be offline while teaching the lessons, collecting and analyzing data, and presenting results. 

The Internet-based projects below are excellent samples of what’s available online for the offline classroom. If you know of similar projects, please share via this blog! 

Down the Drain: How Much Water Do You Use?  

In this project, 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 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.

RoadKill 

If your school is located among rural roads, you and your students can collect roadkill data in your community for analysis and compare your data to other areas participating in the project. The site provides a detailed protocol for monitoring and reporting roadkill, a method of reporting data through the web, and access to data collected by all participants. The project crosses many disciplines, including environmental science education and data analysis.

The International Boiling Point Project

Students around the world boil water to discover what influences its boiling point. Is it room temperature, elevation, volume of water, or the heating device used? All you have to do is boil a bit of water, record a bit of information, and send it along to the site for inclusion in the database of results.

The Noon Day Project: Measuring the Circumference of the Earth 

 In the course of the project, students learn about Eratosthenes and his experiment, and then do a similar experiment themselves by collaborating with other schools. They learn the “why” of the measurements they’re taking, collect the data as precisely as possible, and submit their findings to the central site. By collaborating with a classroom in another state or even another country, they actually determine a good estimate of the Earth’s circumference. The site provides detailed instructions, activities, and reference materials.

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.

Measuring a Solid

Many students never really understand volume or surface area, although they can memorize the formulas and even apply them on tests. These resources have been selected with an eye to helping students enter into the concepts of volume and surface area through practical problems, hands-on experiences, and applets they can manipulate to actually see how these measurements are affected by change in a figure’s dimensions. Please add your ideas on how to teach these concepts in the comments section.

Keeping Cool: When Should You Buy Block Ice or Crushed Ice?
Which would melt faster: a large block of ice or the same block cut into three cubes? The prime consideration is surface area. A complete solution demonstrates how to calculate the surface area of the cubes as well as the large block of ice. Related problems involve finding surface area and volume for irregular shapes and examining the relationship between surface area and volume in various situations.

How High? Geometry (Grades 6-8)
Using an excellent online simulation, students pour a liquid from one container to a container of the same shape, but of a larger size. Students choose from four shapes: rectangular prism, cylinder, cone, and pyramid. The smaller version of the selected shape is shown partially filled with liquid; the base dimensions of both containers are given. Using this information, students use a slider to predict how high the liquid will rise when poured into the larger container. On “pouring” the liquid, students can compare their prediction with the results. Multiple problems are available for each of the shapes.
 

Popcorn: If You Like Popcorn, Which One Would You Buy?
Students are directed to use popcorn to compare the volumes of tall and short cylinders formed with 8-by-11-inch sheets of paper. A simple but visual and motivating way of comparing volume to height in cylinders! The solution offered explains clearly all the math underlying the problem.
 

Surface Area and Volume
With this applet students explore both rectangular and triangular prisms. They can set the dimensions (width, depth, and height), observing how each change in dimension affects the shape of the prism as well as its volume and surface area. This is a quick way to collect data for a discussion of the relationship between surface area and volume or have students practice computing these measurements.
 

Pyramid Applet
This applet allows students to set the width, height and length of a pyramid. They then see the initial cutout (the net) and watch it fold into the pyramid specified. For better viewing, the pyramid can be rotated. At this point, the surface area and the volume are shown. No activities accompany the applet, except for the challenge to try to minimize the surface area while maximizing the volume.
 

Three Dimensional Box Applet: Working with Volume
With this applet, students create boxes online; for each box, its dimensions, surface area, and volume are displayed onscreen.  Since various sizes of boxes can be created, data can be quickly collected and the relationship between volume and surface area explored.  A visual and “hands-on” experience!
 


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 11/10/2011.