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I was a math kid. I did well in class, but the type of math I loved came from doing things I enjoyed. I loved reading the stats on the back of my baseball cards (I understood how great Mickey Mantle’s .298 lifetime batting average was). I helped my father measure down to the sixteenth of an inch as we worked on projects. I liked figuring out discounts at comic book stores. Only later, when I began teaching, did I realize that my most meaningful understanding of math came when it was part of other things that interested me. After all, that’s how math occurs in real life.
Teachers who intentionally bring math into other subject areas, or who bring other subjects into math, love the results. Audrey Trapolsi, an early childhood teacher in Chapel Hill, North Carolina, says, “I love cross-curricular integration. I think it strengthens all the areas of study by applying them in new ways. Applying a new skill within a different content area strengthens and deepens the skill.”
Kevin Costley, an associate professor of early childhood education at Arkansas Tech University, agrees. In his recent research, he found that “students in integrated curriculum courses perform better than [those] in nonintegrated courses…[showing] increased critical thinking skills, self-confidence, and love for learning.”
And what about math achievement specifically? In a 2015 article on Mindshift, KQED’s education news site, Katrina Schwartz found that great things were happening with math and the arts at the Integrated Arts Academy at H. O. Wheeler School in Burlington, Vermont. The school was failing before it became an arts-integrated magnet school in 2009, Schwartz reported, with only 17 percent of its third graders proficient in math. But by 2014, “66 percent met and achieved the standards.”
“Not only is achievement better,” says IAA principal Bobby Riley, “but students’ ability to collaborate and cooperate is enhanced. During integrated arts times, discipline referrals drop to basically zero.”
Both the research and educators’ personal experience make one thing clear: Integration helps to make math meaningful. Kids can relate to it, and may even decide it’s fun. Read on for tips on how to make math a companion to any subject, from writing to social studies to music.
Social Studies Loves Stats
Jo-Ann Trifiro, a fourth-grade teacher at Millstone Township Elementary School in New Jersey, uses math to help her students better appreciate and understand the differences between life in the 1800s and today. She does this by creating a simple chart or table in which key facts tell an important story about what life was like more than 130 years ago: Using multiplication, students figure out how much money a typical worker would make in a week, a month, or a year. The numbers help them better understand just how hard life was back then.
Planners and architects creating spaces for communities also use math in their work. Michael Jackson, a social studies teacher at Community Middle School in Plainsboro, New Jersey, helps students experience this in a project where they design schools that meet the needs of their community. Using centimeter graph paper and Cuisenaire rods, they determine a perimeter and then manipulate the rods to explore all of the possible arrangements to meet the area requirements while accommodating the needs of the school community.
The Art of Mathematics
Judy Klima, the integration arts coach at IAA, brings math into a study of famous artists. She begins by showing kindergartners Vincent van Gogh’s painting of sunflowers. They discuss their observations of the painting, including the colors, composition, and parts of the flowers. They then count the petals. Next, using large art paper and tempera paints, students create their own sunflower paintings and check to see if their number of petals match up with the original.
Another early elementary activity that brings together math, art, and, yes, space aliens comes from my book Special Delivery: Putting Math to Work. Shapey is an alien who wants kids to help him make a portrait of himself for his mom. He describes himself as symmetrical, made up of four rectangles, five triangles, and so on. Students create a portrait of Shapey out of construction paper, using their geometry knowledge and their own creativity. The complete lesson plan, including a letter from Shapey, can be found here.
To really empower kids in math, have them write their own math word problems. First, lay out specific criteria. In a second-grade class they might be: “Write a word problem that makes us add, makes us regroup, uses two double-digit numbers, and has one distractor.” (A distractor is an incorrect answer on a multiple-choice test.) Students write the problem and the solution. Emphasize that they should take care with punctuation, clarity, spelling, and other ELA standards.
Explaining one’s thinking in math is difficult for many students. Often they don’t know how to begin, so ask them to imagine that a new student has joined their class and doesn’t know anything about the topic they’re studying (e.g., adding with regrouping). They’re to write down a step-by-step instruction guide or how-to booklet on whatever the math concept is, or another of their choice. These are fun to publish and can be saved in a math resource writing center.
Music and Numbers
Patterns are foundational for math and for systems of notation, like those found in music.
To demonstrate the power of patterns, take your kids to the theater with Cyberchase for Real, a video showcasing the off-Broadway production Stomp, where the dancer-drummers make rhythm-infused music with everyday objects like brooms, garbage can lids, and tin cans. After students watch the video, have a volunteer clap out a pattern and then invite other students to repeat it. Challenge everyone to record and explain the pattern using letters, numbers, or symbols, then try other clapping patterns and compare notation systems with others.
To practice ordinal numbers and serial order with young students, recite “There Was an Old Lady Who Swallowed a Fly” together. Make simple cutouts of the items the old lady swallows. As you sing, pause at each new item and have volunteers place the cutout on the board in linear order. Number the items, and write the ordinal words first, second, third, and so on beside each item.
Reading Grids and Graphs
Diana Kaiser, a fifth-grade teacher at John F. Kennedy Elementary School in Jamesburg, New Jersey, uses a variety of charts for organizing data about book characters. For example, Kaiser has students create a grid for analyzing character traits while reading Because of Winn-Dixie, by Kate DiCamillo. “After analyzing their findings,” she says, “I encourage them to write a composition comparing these characters by citing examples from the book.”
Trapolsi, the early childhood teacher, uses chart paper to record events in fairy tales and fables. (Older kids can do this themselves.) She draws a line graph and annotates it as she reads. As the tension in a plot rises, so does the line on the graph. At the resolution of the story, the tension is gone, and the line returns to 0. Students see change over time recorded in a simple, understandable form, and they see how a line graph can describe how a favorite story is constructed.
Getting Physical With Math
Beverley Lynk, a first-grade teacher at Town Center Elementary School in Plainsboro, New Jersey, helps her students learn about shapes by physically experiencing them. When a shape—for example, a triangle—is introduced, students use their bodies to form it. The characteristics of the shape are reviewed on the board (closed figure, three straight lines, three corners), and students check their “work” (i.e., bodies) to make sure the shapes they’re making meet the criteria. She takes photos of the student shapes and compiles them in a class geometry book.
To build on Lynk’s idea, IAA’s Riley shares a lesson called “dancing geometry.” Fourth graders come up with singular moves for geometry terms: polygon, perpendicular, intersecting, obtuse angle, quadrilateral, and so on. Teachers choose one or two moves to combine to create one dance move for each word. Later, students find three or four terms to combine with transitions into a movement phrase that has individual and group moves. Now that’s truly math in action!
Bob Krech is a math consultant and author. He is a former elementary teacher and math supervisor and a recipient of the Presidential Award for Excellence in Math and Science Teaching.
Photo: Courtesy of Judy Klima