Math & Dance: Help me brainstorm the essential qualities of action-oriented math ideas?

[Malke]

Good morning!

I've been active at the intersection of math, dance and learning for the past decade. Now, in the process of writing a book on the subject, I am experimenting with an idea that I hope will further deepen our understanding about how we can create meaningful overlaps between math and dance in the classroom. As part of this experiment I am hoping to benefit from the insights of math educators and mathematicians like you! Later, I will take these ideas to the dancers and work the process from the other direction.

Specifically, I've recently been inspired by Anna Sfard's 1991 article on reification as well as her subsequent related writings on metaphor and the "embodied character of abstract thinking." [Sfard 1994]  It has helped me refine my inquiry into what kinds of math the body can best express. I have recently begun collecting examples of action-oriented math concepts and, more importantly, what mathematicians and math educators see as their essential qualities.

To me, "action" can mean a few things. For example, iteration directly implies an activity or process. On the other hand, gradient refers to an object, but there was some kind of process involved in its creation. 

Here is the list so far.  What I am looking for is a deeper sense of how these ideas work and how they are applied.  What are the quintessential actions, functions, roles, movements, or personalities of these ideas related to the contexts in which they are used and why?  Are there one or two you really love? What really interests you about those actions/ideas? Can you think of any other ideas to include?

Iteration
Transformation
Function

Operation
Gradient
Algorithm
Pattern
Circumscribe
Dilate
Qualitative
Inverse
Relation
Construct
formal grammars in CS
convolution
iterative functions
matrix factorization
differential
integral

Many, many thanks for any help you can provide! Let me know if I can clarify anything.

All the best,

Malke
www.malkerosenfeld.com
www.mathinyourfeet.com

[Maria Droujkova]

On Wed, Feb 19, 2014 at 10:41 AM, Malke <mjr...@gmail.com> wrote:

Here is the list so far.  What I am looking for is a deeper sense of how these ideas work and how they are applied.  What are the quintessential actions, functions, roles, movements, or personalities of these ideas related to the contexts in which they are used and why?  Are there one or two you really love? What really interests you about those actions/ideas? Can you think of any other ideas to include?

I decided to look for PERSONALITIES, because that request for math ideas surprised me the most, at one of my favorite places, the tvtropes.org wiki. Here are a few math tropes about movement and characters:

http://tvtropes.org/pmwiki/pmwiki.php/Main/MirrorMatch (symmetry --> a fight with yourself, inner conflict)

http://tvtropes.org/pmwiki/pmwiki.php/Main/MirroredConfrontationShot (symmetry --> opposites)

http://tvtropes.org/pmwiki/pmwiki.php/Main/BigShadowLittleCreature (scale --> putting on airs, pretending)

Here is a bigger list of Stock Pose tropes that may prove useful: http://tvtropes.org/pmwiki/pmwiki.php/Main/StockPoses

Cheers,
Dr. Maria Droujkova

moebiusnoodles.com
919-388-1721
~~*~~*~~*~~*~~*
 

[Malke Rosenfeld]

Thank you Maria!  These will help my dancer friends begin to understand how to translate math *ideas* into choreography.  We may not want all our dances to be story-based, but having a well-defined personality for a few ideas (scale and reflection) may help them expand their interpretation of other, perhaps more abstract (to them) ideas.

Thanks again!!

Malke
www.malkerosenfeld.com
www.mathinyourfeet.com

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[Patrick Vennebush]

www.scottkim.com

Scott and two others used to do a math/dance performance. One of the others was Dr Schaeffer (sp?) but that's all I remember about him. Would be worth contacting Scott. He's a great guy, would be willing to help.

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