Drawing Art into the Equation: Aesthetic Computing Gives Math a Clarifying Visual Dimension
An evolving teaching method applies the theory and practice of art to computing and problem solving.
Teaching math at a high-risk juvenile detention facility in Marion County, Florida, Debra Hamed was more used to having assignments crumpled up than eagerly completed. Then she heard about something with a slightly puzzling name: aesthetic computing.
Aesthetic computing is a curricula-blending approach that applies the theory and practice of art to computing and problem solving. Hamed tried it in her History of Math class. Following the aesthetic method, Hamed asked the students to create a piece of artwork or a poem that conveys the ideas behind key mathematical pioneers -- people such as Pythagoras, Ptolemy, Leonardo da Vinci, and Fibonacci.
Hamed was amazed at the results.
The students not only grasped the innovations they were illustrating, but "because they were successful," Hamed adds, "it provided them with enthusiasm when they saw the same concepts in the textbook."
Of course, you don't have to go to a juvenile detention center to find students with a strong aversion to math. Many teens and preteens struggle to make sense of geometry and the abstract symbols, terms, and logic of algebra. And because they don't see the subject as relevant, students say they have little motivation to figure it out. "'When will I ever use this?' That's their mantra. They just don't see any need for it," says Bunny McHenry, a Marion County high school teacher who attended the workshop with Hamed.
In the Los Angeles Unified School District alone, 44 percent of ninth graders enrolled in beginning algebra during the fall 2004 semester failed. Because passing the course is required for graduation, many take it and flunk again. With each failing grade, a student's motivation and prospects for earning a diploma get dimmer.
Aesthetic computing attempts to reach those frustrated by traditional math instruction by presenting abstract mathematical concepts in a more creative and personal way. Students break down difficult mathematical concepts, such as algebraic equations, into their basic parts, figure out how those parts relate to one another, then re-create the equation creatively. For example, a standard equation for graphing lines on a slope such as y = mx + b might become a hamburger, with y representing the whole burger, m referring to the meat, and x standing in for spices. Multiplication is indicated by the fact that the meat and spices are mixed together, and b is added to represent hamburger buns.
Students then write a story about the burger or draw a picture of it. (See "Five Easy Steps to Aesthetic Computing," in the sidebar below.) Not only does the process enable students to understand the equation in a more meaningful way, the art and stories they create can later guide and inspire them when they need to solve the same equations using standard notation later on.
This type of visual approach is not only fun but also increasingly necessary in a world in which everybody needs to have some basic understanding of mathematical concepts -- not just to graduate but to thrive after graduation. "Students learn in lots of different ways," says Cathy Seeley, president of the National Council of Teachers of Mathematics. In fact, representing mathematical concepts in multiple forms is among the NCTM's five content standards for teaching K-12 math. According to the NCTM, "Representations are necessary to students' understanding of mathematical concepts and relationships. Representations allow students to communicate mathematical approaches, arguments, and understanding to themselves and to others. They allow students to recognize connections among related concepts and apply mathematics to realistic problems."
Paul Fishwick, the University of Florida computer science professor who developed the aesthetic-computing method, says his inspiration came from popular culture. He wanted to do for math what the 1982 Disney film Tron did for computer science. With its then-cutting edge graphics and its action-heavy plot about a hacker overriding a malevolent operating system, it made a previously dry and impenetrable field of study visual and exciting. "If we have the capability of doing some of these fantastic things with technology, such as the immersive environments and 3-D graphics for entertainment purposes, why are we still programming and doing math by scratching with pencil on paper, much the same way we did 2,000 years ago?" Fishwick asks.
Surprisingly, aesthetic computing requires no expensive software or even a computer. It's so flexible, in fact, that it can be used just as effectively for learning basic middle school prealgebra as university-level programming courses. Says Jodee Rose, a former art and math teacher who developed a middle school lesson plan for teaching the method, "It's low tech, but it's high tech ideas, because it's working through computer language, which kids are going to need to learn eventually." Rose, who lost her job when her school's art department budget was cut, hopes it might provide an opportunity for kids to create art as part of an academic discipline.
Reaching students who aren't naturally drawn to math, whether they're phobic or simply more artistically inclined, isn't the only benefit of the method. Fishwick notes that aesthetic computing "provides a continuum for the constructivist, concrete-object approach to mathematics" many teachers use in the early grades -- for example, using three apples to explain the number three. Unfortunately, he says, this approach typically stops after fourth or fifth grade.
For Katrina Indarawis, who developed a high school lesson plan for aesthetic computing, it's a less intimidating way of introducing new concepts in math. "I thought it would really help students not be so scared of some of the math notations," she says. "It helps them break it down and turn it into something they like." Obviously, aesthetic computing is no cure-all. "You still have to teach the same concepts, but it may reinforce those concepts, because they're using it in a different way," says McHenry. She plans to try the method in her classroom during the next school year.
The New Math
The aesthetic-computing method is still new. No formal studies have confirmed its usefulness. Nor is there much in the way of materials that would help teachers who want to try it out. Hoping to address these problems, Fishwick is trying to attract more researchers to study the method and to raise money to put on additional workshops.
For teachers who don't want to wait, the lesson plans developed by Rose and Indarawis, thanks to a National Science Foundation grant, are now available through Fishwick's Web site, as are several articles on aesthetic computing, links to free software developed by students of Fishwick, and a discussion area. In addition, MIT Press is publishing Aesthetic Computing, a book Fishwick contributed to that discusses the more theoretical aspects of the method. He's also working on a more advanced computer tool that helps students simulate the process (and a student of his is developing an academic video game that will use these methods and problem-solving tools) -- anything, he says, to help get more kids to make a personal connection to math.
"Now that we're recognizing how important math is, we have to expand the ways we teach so we can allow people who learn in different ways or have strengths in different points into math," says the NCTM's Seeley. Fishwick believes aesthetic computing could grow into one of those entry points.
Debra Hamed, for one, is a true believer: "I'm fired up to teach math again."
Jenn Shreve wrote "No Train, No Gain: Educators Poorly Prepared for ELL Instruction" in our November 2005 issue.
Five Easy Steps to Aesthetic Computing
1. Students begin by breaking down the mathematical expression they're working on into an "expression tree." Like a sentence diagram, it helps them understand the components of an expression -- in this case, individual parts of the equation, what each one does, and how they relate to one another.
2. Based on their diagram, students make a list of all the parts of the equation (constants, variables, and operations) as well as hidden meanings such as the "argument of" relationship (for example, 1 and 2 are arguments of + in the expression "1 + 1 = 2").
3. They then brainstorm ideas they'd like to use to reexpress the elements of the expression tree creatively. Once they've chosen a theme, they come up with a means to express it -- for example, as a drawing, a story, or a sculpture.
4. Now it's time to put things together. The parts of the equation listed in step 2 are paired with the creative objects brainstormed in step 3, keeping in mind that the metaphor needs to function in the same way as the equation. So, for example, two objects that are multiplied would be combined, just like meat and spices. Once students have worked these details out, they can use their list (from step 2) to make a key, linking the parts of the equation with their language counterparts ("y = meat; x = spices").
5. When the standard equation and its more creative expression are mapped out, it's time to build the new, creative version.
From lesson plans found in Paul Fishwick's report "Introduction to the Aesthetic Computing Method for Teaching Algebra in Middle and High School."