Educational research -- not to mention experience and common sense -- tells us that students learn best and make better sense of what they're learning when they can make connections with previous learning or with different areas of learning...
Carol Goodrow, a first grade teacher and an avid runner, knows about the value of making connections. She has connected her curriculum by integrating running into almost every subject area -- and her students are reaping the benefits.
Mrs. Goodrow's first graders at Parker Memorial School in Tolland, Connecticut, took off running in September. By May, Goodrow told Education World, all the students could run a mile, had completed a mile fun run, and loved to write about running. According to Goodrow, many of the students started writing in their journals after running practice. Even those who had been reluctant writers loved the running practices so much they wanted to write about them.
"Also," Goodrow added, "they couldn't have any Gatorade until they wrote in their journals."
But, as Goodrow told Education World, the benefits weren't limited to physical fitness and writing. She saw improvement in math skills as well. For example, during year-end benchmark testing, the class completed sections on numeration more quickly, yet scored as well or better, than past classes.
In addition, Goodrow reported that many students demonstrated a better understanding of fractions. "My fraction committee, a group of the most capable math students, computed the class's [running] mileage on their own, working with 1/2's, 1/4's and 3/4's. They represented the fractions by models, but they could also compute them in their heads."
One of the class's favorite activities, however, was their ongoing "Trek Across America." In this project, Goodrow, her class, their families, and runner Don Allison set off on a virtual race from Boston to San Diego. Each time the participants ran, they kept track of their distances in personal mileage logs. As they progressed along the trek's 3,252 miles, the students traced the route, exploring 14 key cities.
Reports of the trek, as well as many other class activities, can be found on the class's Web site, Kids Running.com. According to Goodrow, this site is built so that kids can be authors, columnists, and more. There are sections where teachers can use running-related data, such as the voting booth data bank, to build math lessons. "It's also a site," she said, "where kids can practice reading stories written by other kids. And of course it encourages fitness and healthy attitudes."
Education World asked Goodrow if she had any suggestions to offer other teachers on how they can make learning more relevant. "Choose something you love," she said, "and integrate it into your curriculum."
But first, you might want to choose some of the activities below and use them to integrate Math across your curriculum.
Another good source for ideas on integrating math is Carol Hurst's Math and Children's Literature site. Though geared toward students in Pre-K through Grade 2, many of the activities here can be adapted for use with older students. For example, the article Time and Time Travel Fantasies, reprinted from Teaching K-8 Magazine, recommends setting up a classroom clock display and allowing students to take the clocks apart (and, hopefully, put them back together again) as they learn to tell time. The site includes a list of books with time-related themes, which you can use to accompany and/or inspire the activities.
Extension: You might extend the activities with older elementary students by setting up a clock repair shop, rather than a display, and having students prepare estimates and invoices for needed repairs. Students might also prepare written reports about the ways in which people have told time throughout history. One interesting site about gnomonics, the art of telling time using the sun's shadow, can be found at Cannon-Mania. Scroll down and click Sundial to learn about the sun dial cannon.
At Mathematicians Commemorated on the Eiffel Tower, students in grades 3-12 will discover the names of French scientists and mathematicians that were placed on plaques in the Tower more than 100 years ago. Encourage students to visit The Official Site of The Eiffel Tower to learn more about this historic French landmark.
Extension: Following the tour, have each student return to the Mathematicians Commemorated on the Eiffel Tower site to read the biography of one of the mathematicians whose name is on the tower. Create a chart listing the name and major accomplishment of each mathematician. You might also encourage students to add to the chart the names of other mathematicians, some of whom might be found at Biographies of Woman Mathematicians.
After your middle- and high school students have toured the Eiffel Tower (see "History and Math" above) and perhaps helped build the Tower of the 3rd millenium, they may be ready to participate in Hands-On Bridge Building. This project, in which students use spaghetti, glue, and their knowledge of science and math to construct a weight-bearing bridge, begins with a lesson on scientific and mathematical vocabulary. Then, students create designs, reduce them to scale, prepare cost analyses, and build and test their bridges. The site includes quizzes, worksheets, and bonus and extension activities.
At The Stowaway Adventure, "stowaways" in grades 6-12 can plot latitude and longitude to locate the route of the ship they're hiding on. They use that information, along with their math knowledge, to determine the ship's speed, distance traveled, and projected destination. Those stowaways who enjoy their voyage can move on to the second leg of their voyage, where they use what they have learned to determine future destinations and view satellite images to predict weather and ocean conditions.
Extension: When students return from their sea voyage, ask them to plan a trip on land or in the air. Students should use a map to set their starting point and destination, decide on an appropriate mode of transportation, and determine a reasonable speed. Then have them calculate the distance they'll travel and the time the trip will take. You might also encourage students to identify some landmarks along the way and to write postcards about the places they "visit."
At Fat Counting, students in grades 1-6 study and discuss the food pyramid. Then they compare the foods on the pyramid to the foods they eat, keep a fat-counting diary, calculate the number of calories from fat they eat in a week, find their daily average of fat, and compare their fat intake with that of other students. The lesson is less self-sufficient than many others, but the site does provide links to all the necessary information and resources.
At Greeting Card Geometry Math, a unit you can use to teach geometry to students in grades 2-5, students learn to identify and create congruent, similar, and equivalent shapes and then they use those shapes to make a holiday greeting card. The lessons are simple, yet effective, and include creative extension activities.
Extension: As a follow-up, you might encourage older students to use geometric shapes, and any medium, to create a poster showing the relationship between math and art. Then invite them to visit the National Museum of American Art or another online museum or art gallery, and identify examples of math in the art they find.
The Music section of Online Math Applications is one of the best sites available for introducing students to music and its relationship to math. The rhythm page explains how different musical notes represent the rhythm, or time, of a piece of music, while pages on tone and tune provide a thorough discussion of pitch, frequency, and amplitude. The site explains the mathematical relationship of adjacent notes on a keyboard and the theory that ratio is essential to harmony. Here, students can rediscover the discoveries of Pythagoras and listen to the music of Mozart. The clearly written, easy-to-read information makes this is a site that's appropriate for students of all ages.
Extension: After students have explored the site, taken some of the quizzes, or submitted quizzes of their own, give them an opportunity to listen to a variety of musical styles. Discuss the rhythm, tone, and tune of each selection, then ask students to compose a tune of their own. You might also encourage older students to research the lives of some classical musicians to discover how many were also mathematicians. Students of all ages will enjoy making, and experimenting with, a monochord.
Article by Linda Starr
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