(This is not a trick question, but you will have to read below to find the answer!)
One of the founding principles of Boston Arts Academy (BAA) involved interdisciplinary teaching and learning. The paint on the walls was barely dry in 1998 as we tried to discern what it meant to teach “interdisciplinarily.” Was that even a word? What did it look like? Was there a right and a wrong way to do it?
Should we have interdisciplinary courses? Yes, we said – we wouldn’t teach English and History separately, but rather, we would teach Humanities. How would we integrate the arts into our academic courses? And did that make the curriculum interdisciplinary or integrated? Were we encouraging our students to develop interdisciplinary understanding or merely providing them with integrated or infused experiences?
At BAA, we have spent years in professional development discussions and workshops trying to define the terms and the experience so that faculty, students, and parents would know what interdisciplinary understanding (IU) meant. We spent one year pairing up departments so that teachers could develop interdisciplinary units together. For example, world languages paired with theatre, dance with math and so on. Some interesting projects emerged, but the effort seemed forced. Teachers never had enough time to work together. They didn’t know if efforts would meet any external criteria for what constituted IU. We felt we needed more of an academic framework to support our endeavors. After over a year of working with Project Zero (PZ), particularly Veronica Boix Mansilla and her colleagues, we adopted their definition for interdisciplinary understanding: The ability to integrate knowledge and modes of thinking from two or more disciplines to generate a new insight.
Further, PZ suggested that “students build and demonstrate interdisciplinary understanding when they can bring together concepts, methods, or languages from two or more disciplines. For example, to explain a phenomenon, solve a problem, create a product, or raise a new question in ways that would have been unlikely through single disciplinary means.”
BAA’s journey, looking for ways to increase interdisciplinary understanding, has been fraught with tensions. We are hypercritical of our forays into this IU world. Is a dance using video cameras increasing students’ knowledge of technology and choreography, or is it just a cool way to explore new ideas? Does the study of architecture in visual arts class meet the standard for IU? What about a plie done in Spanish class? The answers are both yes and no depending on the viewer, the learner and the purpose of each class or lesson. It is also perplexing to think that we need two teachers from distinct disciplines working together to enable pure interdisciplinary learning.
The other day I walked into a math class, where students learn hula dancing in order to demonstrate their understanding of trigonometric and other mathematical functions. One might say this is “a lot of hogwash”, or that “this is what’s wrong with education today”. But I was blown away by how describing functions kinesthetically could deepen students’ understanding of math as well as their appreciation for an ancient art form.
The classes of both Ms. Wallace and Mr. Lonergan had combined in the assembly hall for “Function Hula” class. As students entered, Mr. Lonergan, dressed in his best Hawaiian shirt, distributed lei to the grinning students. Some kids had dressed specially for the day, as “Function Hula” has become a staple of the curriculum and an event to look forward to. Ms. Wallace stood at the front of the room in a traditional hula skirt adjusting the music. Suddenly, music filled the room. Students took their seats, fiddled with their lei and took out their notebooks.
Mr. Lonergan began class by greeting the students in traditional Hawaiian, “Aloha. Today is Math Hula Function Day and we are your Kuma Hulas, your master teachers.” Some students murmured a muted “aloha” back. Mr. Lonergan continued energetically, “To be successful today, you need to have done your homework.” Students rustled a little more intently in their backpacks looking for their homework papers. “Remember to incorporate at least one of the challenge problems into your dance. For example: -y= square root of x+ 8-2, and its parent function. Which families will you use? See #1 on the handout—you must use at least five—linear, quadratic, cubic, exponential growth, exponential decay, absolute value, square root, trigonometric, or reciprocal. And, you have to use at least three of the function transformations listed: horizontal, vertical, reflection, or dilation.” There were no cries of “What’s going on?” in the assembled group of students, just nervous excitement and “When will we begin?”
The video screen lowered and Mr. Lonergan said, “We are going to an unusual place—Disney’s Lilo and Stitch—to learn about Hawaiian music and dancing.” “Oooh, I love that movie,” one student said, balancing her saxophone case on her lap. Mr. Lonergan continued, “I know you may have learned in Humanities classes about the racism and classism in Disney movies; but this time Disney was actually trying to be culturally accurate. They filmed live hula dancers and turned those dances into animated sequences. Even Ms. Eriksson [another math teacher who is of Hawaiian descent] has assured me that this clip is completely authentic. We will watch it a couple of times, Ms. Wallace will review the symbols and dance moves, and then you will have a chance to practice before you create your own Hula functions. Got it?” There were nods all around. Mr. Lonergan grinned. He clearly loves this day!
The film began and someone in the class began to snort with laughter. I couldn’t tell who was tittering, but Mr. Lonergan immediately stopped the film. “Remember Ms. Wallace and I are your kuma hulas, your master teachers, and that is a serious responsibility for us. We are learning an ancient art form and we will be respectful of it.” I noticed that Amber was shooting a disapproving look at one of her classmates and wondered if he was the joker. Amber was dressed in Hawaiian attire and clearly eager to begin her own choreography. The film began again and this time everyone was quiet.
A few students got up from their seats and began moving in sync with the dancers on the screen. Ms. Wallace then brought two students to the stage. “Here are the terms on the white paper,” she indicated to the easel. “We are going to show you each move again and its correlation to the symbol. Just so you get the basic moves.” More students got up to practice with them. Tizi joined Ms. Wallace on stage and moved rhythmically to the music. “I know it’s not bachata or salsa, but the hips are sort of the same,” she said, smiling. “It’s just coordinating the hands with the hips that is hard.”
Mr. Lonergan took the stage again. “Here’s an example of how to do a dilation and horizontal translation.” With his arms raised in a V shape he moved them in closer to his head and then sank down, bending his knees in a staccato expression for eight counts. Next he moved six steps to the left. “So what equation do you think I just did?” A number of students guessed correctly. “So that is the challenge for you. How will you demonstrate these functions with movement? You may use music or perform without music. You may also create your own chants. Remember that for extra credit your group can include a storyline/theme that is told through your hula.” Students broke into groups, having been instructed to mix majors (i.e. not all dancers together). Ms. Wallace and Mr. Lonergan joined in.
When I returned an hour later for the final performance, I was enthralled by the creativity, clarity, and precision of each group. Some had grabbed drums from the music room. Others put together costumes. All used individual methods to express complex functions using hula dancing. While the study of hula dancing didn’t occupy as much class time as the study of functions, this one-day foray into an unfamiliar art form truly engaged every single math student. I am convinced that the kids will never forget these mathematical functions. It is easy to memorize and then promptly forget something as abstract as a formula, but when your body owns the movement of the equation, it will stay with you forever.
The PZ definition of interdisciplinary understanding serves a useful purpose in connecting us to a larger academic context and conversation. Ultimately however, teachers must continue to explore various ways to incorporate IU. I am grateful to Mr. Lonergan—the creator of this unit—and his partners on the math team, Ms. Wallace, Ms. Erikkson, Mr. Bobrow and Ms. Mandell, for continuing to push the envelope on our assumptions about what kids can do and the multiple ways they can learn.
There are just so many ways to learn math! Appreciate the post.
I agree! Glad you enjoyed the piece… I’d be interested to hear your innovative teaching and learning strategies for math as well!