Challenge
Professor Lina Wu wanted to find a creative way to teach Calculus, to make materials more interesting, and to better engage her students.
Solution
Wu decided to use art as a tool for teaching Calculus, to further the idea that mathematics is fundamental to many ideas and processes in everyday life. She adopted Maple to implement her teaching method because it had the features necessary to allow her students to create and manipulate artwork using mathematics.
Result
Using Maple, students are able to create artwork and visualize the impact of the mathematics behind it. This approach allows students to apply Calculus in a way that helps them better understand key concepts. Wu has also seen greater student engagement in class, both with the materials and with each other.
Mathematics is more than a series of numbers, symbols and equations. It is at the root of many concepts that we encounter on a regular basis. Lina Wu, a professor at Borough of Manhattan Community College, The City University of New York (BMCC/CUNY), wanted to find a creative way to teach calculus and show students that math is not just numbers, but is fundamental to many ideas and principles in the universe. Wu chose to focus on art, challenging her students to identify mathematical elements in various pieces of art. Using Maple, she developed a method for teaching mathematics that tied in visual images.
While Wu was teaching at the University of Toledo, the math department introduced Maple to its faculty members. Maple has played an important role in her teaching and research since. In addition to her work as a professor, Wu is completing educational research on her teaching pedagogy of using a Project-Based Learning method that combines math, art and Maple technology. Maple’s visualization features, animated graphing tool and symbolic and numeric calculation tools make it ideal for Wu’s unique teaching approach. “So far I have created 6 Maple artwork projects in calculus courses,” she said. “These and other research projects have taught students how to apply their knowledge of math and Maple to create artwork.”
Wu, along with several colleagues, conducted a study on the value of using artwork to teach calculus. The study, published in the International Journal of Applied Research, was motivated by math anxiety in students, as well as various limitations to the current method of testing, specifically multiple choice tests. Wu wanted to design a mathematics curriculum to help students better understand mathematics and gain the ability to apply it to real-life situations. The study found that math concepts, such as numbers, shapes, patterns, groups and symbols, can often be seen in artwork, which makes it an ideal medium to explore mathematics. Using images to break up the abstraction of math subjects also helps alleviate students’ anxiety towards the subject.
Wu believes that visualization through artwork enhances students’ intuitive understanding of calculus concepts and theories. In Wu’s calculus class, students use their knowledge of various concepts to create art diagrams using Maple, which in turn helps improve their grasp of the materials. They visualize concepts through their designs and gain perspective on the impact of changing parameters.
Wu has her students view art at museums in New York City and identify pieces that may contain elements rooted in or related to mathematics. When students identify pieces, they then must explain how the artist applied math in their artwork. It’s not easy to find math in art, but it’s a fun challenge for students to get them thinking about math beyond the numbers, Wu said. She recently decided to take the idea one step further. “I thought it would be interesting to have the students create their own artwork using their knowledge of mathematics,” she said.
As a result of Wu’s course, students spend a significant amount of time and effort using math to create art, leading to better understanding of math concepts. Maple is valuable in this regard, as it allows students to visualize their artwork and make changes to their designs quickly. Students are able to apply all they have learned in math to produce a masterpiece of artwork they can be proud of. “There was no doubt in my mind that Maple would be the ideal technological tool for students to create images using math, she said. “The dynamic and interactive applications in Maple make it easy for students to communicate their math ideas through computerized programs. Visualization tools in Maple enable students to see how changes in the math impact their artwork.”
During these projects, Wu encourages her students to interact with each other, share ideas and have open discussions in the classroom. This provides Wu with an opportunity to engage with the students about project ideas and execution, how complex ideas use math and answer questions about Maple itself.
Wu’s research into her teaching method has been published in peer-reviewed mathematics journals and the artwork her students have produced in class has been presented at annual math conferences such as the AMS-MAA Joint Mathematical Meetings and MathFest. Students who participated in Wu’s pilot courses provided very positive feedback. They were able to learn calculus in a non-traditional way and, after completing the projects, they were impressed with the finished product. “They see themselves as artists and mathematicians, and are proud of their achievements,” Wu said. “My project-based teaching approach has ignited students’ desire to learn math. They use their math knowledge along with Maple to produce impressive artwork. With the many advantages that come with using Maple, it has become an important technological tool in my calculus teaching.”
Contact Maplesoft to learn how Maple can be used in your classroom.
