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The Choreography of Calculus: Using the Arts to Comprehend Content

| Jim Moulton

I recently attended the Juice Conference here in Maine on the effort to power up the state's creative economy. The discussions focused on how craftspeople -- potters, weavers, dancers, musicians, metalworkers, woodworkers, and their ilk -- contribute to the bottom line. As I listened, it occurred to me that the conversation -- and the definition of "creative economy" -- needed to be far deeper, far more foundational than that. We must be more creative in how we think about creativity.

Which brings me to the title of this post. As I sat in a session about how K-12 schools can best support the development of young adults and prepare them to drive the creative economy, it struck me that the room consisted mostly of art, music, and dance teachers or practitioners. There is little need to convince them of the power of the arts in developing agile minds, so I asked the question, "Rather than thinking about how to get more respect and encouragement for high-quality arts instruction in schools, what about supporting creative thinking by looking for ways that the arts can become a formal part of mathematics, science, language arts, history, and so on?"

Then I blurted out, "What if we asked students to demonstrate their foundational understanding of calculus not only by solving algorithms using it but also by choreographing a dance that shows deep understanding of what calculus means?"

My memory of calculus, based on two courses -- one in high school and one in my freshman year of college -- is that it is all about approaching curves and points and never really getting there: closer, always closer, but never arriving. Whoa. That sounds like a ballet I once saw. Or was it a poem I read? Or a song I heard?

So, I wondered, would a student who choreographed and performed that mathematical dance develop a kinesthetic, a body memory he or she would never lose? And would a learner who mastered the algorithms and the dance be better prepared to apply calculus not only to mathematical problems but also to complex human or mechanical ones? And isn't the latter -- the ability to resolve complex issues -- what an economy needs to be creative? It seems to me that the creative thinking that comes so naturally to the arts could well serve students in other content areas.

What I want to know is, has anyone tried this? Has anyone asked students to create a jingle for the Continental Congress or to write the algorithm for gossip? Are students anywhere demonstrating their understanding of mitosis on stage, in character, through dialogue, showing that those phases can be modeled in human relationships?

And about that choreography: Does anyone have some ideas?

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Comments (10)

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Christina B. (not verified)

Of course we've thought of it!

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Being an art educator we are taught to use disciplinary based projects in our curriculum. "We" don't necessary have a problem doing this. Artists and musicians, etc. know how to incorporate the main disciplines in their lessons. We can easily teach about math and history and language within our curriculum. I think the main discipline teachers should incorporate more visual and audio into their curriculum. I was and still am a visual learner. I loved when my teachers asked us to do a visual project. I knew I would get a great grade. I believe fine arts should be incorporated more in the main discipline subjects!

Adam Voss (not verified)

I also am a K-8 art teacher

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I also am a K-8 art teacher and I have been meet with teachers who don't want to collaborate with me also. After talking this situation over with my schools leadership team, they have given me access to the classroom teachers lesson plans, so that I can see what they are teaching and I can teach something related in my art class.

Anonymous (not verified)

Art in a High school Math Classroom

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As I high-school math teacher I have spent a significant amount of time developing projects that incorporate art into my subject. I have found that most students enjoy this, and sometimes these projects are the only things they like doing all year. I must admit I had never thought to incorporate music or dance into my curriculum, but I have frequently made use of the applications of math to art. In my geometry class we have discussed and made mandalas, studied angle and segment bisections with origami, and created posters that focused on the relationship of polygons' angles and transformations to tessellations. In precalculus we have used string art to study conic sections and created graphs of trigonometric functions using spaghetti. I don't know if this is the most in-depth use of art in a math curriculum but it has been the best I have been able to come up with. With the diverse group of students my school services I have to find different methods of presenting my material.

Erin (not verified)

Music in other settings

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I agree with your comment about using the arts throughout the school setting. My students, elementary aged, sometimes wonder why they are supposed to come to music class. They think it doesn't count. I always counteract with a few questions. I ask them, do you watch TV? Do you listen to the radio in the car? Do you play video games? What they don't realize is that music is in their everyday lives all the time. If they took away the music, they might find these everday activities boring. I know that a long car ride without music would feel like it lasted even longer.

I know of teachers in my school that allow students to listen to music during activities. I believe that music is calming, no matter what you like to listen to. I always feel better if I have music to listen to and I know that I work better with that in the background.

It is very sad that students aren't taking the arts more seriously. They are just as important as their other subjects. They get to learn history in our classes to add to what they're already learning in their everyday subjects.

I read an article called "Brain Research and Education: Fad or Foundation?" by Pat Wolfe, Ph.D. In this article he discusses how the outside world shapes our brain (Wolfe, 2003). Take away the arts and it seems that our brain is void of that shape. We need to allow students to have a well-rounded education so that they can experience all types of learning and lessons.

John Wells (not verified)

Multiple Intelligence Curriculum: Engaging Students in New Ways

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I have worked as both a middle school and high school teacher over the course of my short career as an educator. Currently, I am a tenth grade English Language Arts teacher. As I have developed in my field, I have fully embraced Howard Gardner’s theory of Multiple Intelligence and have been lucky enough to incorporate his thoughts into my curriculum. When I reflect to my days as a young student going through the daily eight periods, I can remember few of the actual lessons that were taught to me; this is most likely due to the monotony of daily routines and worksheets that seemed to dominate my adolescent experience. However, not all of my lessons were forgotten.

Personally, it is my belief that students are often not able to incorporate the content of the days’ lesson unless it maintains a particular level of “connectivity” to their personal lives. Speaking through the lens of a high school educator, the concept of “self-absorption” seems to dominate the minds of the youth; while this may not be true for all, most students demonstrate many behaviors and attitudes that display quasi-selfishness that is all too typical of this age group; I admit to suffering from this fault as well when I was coming through my formative years. Due to this fact, lessons must be geared towards the personal interests and value systems that our students hold dear.

In order to reach students and make learning a meaningful experience, we must recognize that students “do learn from reading and hearing, but the strongest connections are often made through concrete experience. Which do you think would make the most lasting changes in the brain, reading about an experiment someone conducted or performing the experiment yourself?” (Wolfe, 2003, p. 4). By getting students out of their traditional roles of sitting quietly, taking notes, and filling out worksheets, we will inspire learning that will actually mean something to our students; though they may not remember the content of the days’ lesson ten years from now, they will remember the activities they engaged in.

I try to apply this concept to my classroom. Although I still value traditional classroom activities such as notes and worksheets, I intersperse the work with theatre arts, music, games, as well pop cultural links and references. By making the content of my lessons different from the norm, my students remember more information, perform new skills proficiently, and are engaged in a learning experience that may potentially stay with them for a lifetime.

Resources:

Wolfe, P. (2003, Fall). Brain-compatible learning: Fad or foundation? Retrieved May 24, 2007, from http://www.mcli.dist.maricopa.edu/forum/fall03/brain.html

Britta Overson (not verified)

Teaching Comprehensively

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I find it slightly amusing that this blog and the correlating comments are from teachers in the arts. As a music teacher, this concept of using multiple teaching strategies correlating with the different subjects is intuitive. In fact, it is part of our National Standards for Music Education. The learner should understand relationships between music, the other arts, and disciplines outside the arts as well as understand music in relation to history and culture (MENC, 2005).

In order to teach comprehensive musicianship the teacher must take an interdisciplinary approach. They should not only learn how to perform on their instrument, but also be able to create, compose, conduct, listen to, and discuss music ("Comprehensive Musicianship through Performance," 2007). I firmly believe this concept would benefit the “traditional” classroom. Instead of merely learning how to perform (on the test), the learner can create (through the subject), listen to (experts), discuss the (concept), and compose (their own research)… you get the idea. Teachers need to be more creative if they would like to teach to this generation.

Beyond intuition, brain research supports the idea that the more ways we introduce material to the students the more opportunities they have to store that information (Wolfe, 2003). It stands to reason that creative projects that force students to activate multiple parts of their brain reach more students than the activity of taking notes, studying, and regurgitating for the test can.

I will end with the question: how can we get teachers to integrate this concept into their classroom?

MENC: The National Association for Music Education. (2005) "National Standards for Music Education." http://www.menc.org/publication/books/standards.htm

Comprehensive musicianship through performance. (2007.Retrieved January 26, 2008, from http://wik.ed.uiuc.edu/index.php/Comprehensive_Musicianship_through_Perf....

Wolfe, P. (2003, Fall). Brain-compatible learning: Fad or foundation? Retrieved January 19, 2007, from http://www.mcli.dist.maricopa.edu/forum/fall03/brain.html

Anonymous (not verified)

Arts inside the classroom

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I have been teaching preschool for several years and have never done the same thing once. By following and helping the children find answers to their questions the day to day activities are encaging and unique. As Loris Mallaguzzi describes in his poem, children have "100 languages" to express themselves. My classroom has an open art area where the children are able to create items to add to play, or to express their ideas. We use music, pictures or dramatic arts to tell stories. All of these meet the different learning methods of children. The arts are key in my philosophy of education, yet I am too worried that they are not encouraged in older schools. The confusing part; children we are conforming today are wanted as the creative employees of tomorrow.

Anonymous (not verified)

Children have different languages to express knowledge

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I have been teaching preschool for several years and have never done the same thing once. By following and helping the children find answers to their questions the day to day activities are encaging and unique. As Loris Mallaguzzi describes in his poem, children have "100 languages" to express themselves. My classroom has an open art area where the children are able to create items to add to play, or to express their ideas. We use music, pictures or dramatic arts to tell stories. All of these meet the different learning methods of children. The arts are key in my philosophy of education, yet I am too worried that they are not encouraged in older schools. The confusing part; children we are conforming today are wanted as the creative employees of tomorrow.

Elizabeth Ballard (not verified)

As a K-8 art teacher, I

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As a K-8 art teacher, I constantly attempt to work with classroom teachers to reinforce their curriculum through mine. It stands to reason that the more diverse ways a child can receive information, the more likely he is to retain it. Yet, I find most classroom teachers see it as a bother to let me know what is planned for their classrooms. I often find that I have a great Native American lesson plan for 2nd grade, but am teaching it two months too late. I have one or two supportive teachers that want to wrap their brains around Problem-Based Learning and incorporating as much as possible into the art classes, but most find it inconvenient.

The arts are all about creative thinking. If American businesses are looking for workers that can think outside the box for the 21st Century, they need to be adding arts programs to the schools and finding teachers that are willing to combine several curricula at once.

Sarah Clum (not verified)

Using Arts to Comprehend Content

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Jim Moulton,

As an art teacher, currently at the middle school level, I frequently incorporate core class (math, language arts, and history) assignments and work with other teachers on collaborative ideas. I think in Pennsylvania the teachers are expected, or encouraged, to do this (at least in my area). I just read an article about “Brain compatible learning” that stated “When you recall information, you have to reconstruct it. Since memories are constructed, the more ways students have the information represented in the brain (through seeing, hearing, being involved with, etc.), the more pathways they have for reconstructing, the richer the memory. Multimodal instruction makes a lot of sense” (Wolfe, 2003). I agree that learning a subject in as many different methods as possible is a great way to commit something to memory. I still remember the song my 8th grade math teacher made us memorize. I wish he had used this method more often. Please keep encouraging your teachers and students to collaborate!

Reference Article: Wolfe, P. (2003, Fall). Brain-compatible learning: Fad or foundation? Retrieved May 24, 2007, from http://www.mcli.dist.maricopa.edu/forum/fall03/brain.html
Reprinted with permission. From the December 2006 issue of The School Administrator

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