Marx Brothers Math: Transformation & Reflection

I'll wager that each one of us looks into a mirror at least once a day. Surprisingly, what we see in the mirror is up for some debate; at least that's been my experience when talking with fourth graders about the subject of reflection.  The result of these conversations is that I now firmly believe that when we use movement to explore the concepts of transformation and reflection, we gain a truly three-dimensional understanding of the subject.  Here's a little peek into how it all goes down:

Me: "What do you see when you look in the mirror?"
4th Grader: "Myself."
Me: "But is it really you? There's only one of you!  There's no one else like you in all the world.  You are an original!"
Different 4th grader: "It's your reflection!"

Later, after my 'magic wand of transformation' has turned the entire class into multiple reflections of me and they've had a chance to experience what it's like to exist on the other side of the mirror, I ask:

Me: "How many of you think it would it be fair to say that your reflection is doing the same thing as you?"
Half the class raises their hands.
Me: "Or, is your reflection doing the opposite of you?"
One third of the class raises their hands.
Me: "Or, how many of you think it might be both, the same and the opposite?"
One or two hands shoot up, other hands raise and lower tentatively.

We work through answering this question in class using our creative dance work.  In lieu of this experience here is a video clip for you from the Marx Brothers movie 'Duck Soup' (below).  I find this video to be simultaneously fun, highly entertaining, and instructive about the process of reflection.  Remember that transformation is essentially about change, and I assert that movement is a particularly effective way to make the process of change visible.

A few things to consider before watching the video, below:

Most of the time we are looking into a mirror straight-on. We brush our teeth, wash our faces, or comb our hair, all while looking at our faces and the fronts of our bodies. In this orientation is easy to think that the reflection is doing the same thing as us.

But remember, the mirror can reflect all sides of our bodies.  As you watch this video you will see Groucho and Harpo directly facing the "mirror" but also walking along the length of the mirror (shoulders to the mirror line) and turning toward and away from the mirror. There's even a fun bit where their bottoms are closer to the mirror than their heads!

In Math in Your Feet, children reflect their dance patterns by deciding who will dance the original pattern and who will reflect that pattern; the reflection changes the original pattern in small but very important ways.  Based on the narrative arc in this particular video, Groucho is the homeowner (original) and Harpo an interloper (reflection).  As you watch, ask yourself:

When is the reflection doing the same thing as the original?

When is the reflection doing the opposite of the original?

I'll give you a couple examples to get you started. When Groucho first sees his 'reflection' in the 'mirror' they both move in toward the mirror and then away from the mirror. In this case they are doing the same thing. Then, still facing each other, Groucho's right hand goes to his chin, but it is his reflection's left hand that goes up. Both hands go up to the chins, but they are using opposite hands.

One more example: At 0:35 Groucho turns away from the mirror over his right shoulder, for a total distance of 180°. Harpo also turns 180°, but over his left shoulder.

How many examples of same and opposite can you find? Can you find any mistakes? I had a hard time tracking if they were using opposite rights and lefts in their footwork, for example. Have fun and don't forget to try out some of the activities listed below when you're done watching!



How'd you do? Ready for a little application of the concepts?

Try this at home:
Put a line of tape on the floor. This is your mirror, otherwise known as a line of reflection.
Decide who will be the original and who will be the reflection.
To start, the reflection has to be the same distance from the mirror line as the original.
Move slowly at first so the reflection has a better chance of accuracy.
Most important: don't forget to experiment with having different sides of your body be 'reflected' in the mirror.

Extra challenge:
Make up a short piece of choreography with a variety of moves and levels (high, medium and low).  In Math in Your Feet, the foot based patterns are units of four steady beats.  See if you can make a four- or eight-beat combination of moves using your whole body. 
Both people practice doing this choreography congruently (everything the same).
Then, do the choreography with the line between you. The original needs to move slowly while the reflection figures out what parts of the choreography needs to change (hint: everything is the same except the reflection uses opposite rights and lefts).
When you're well-practiced and have it a tempo that both people can do comfortably, show off your work!

Extra, extra challenge:
Perform your choreography with your partner first congruently (everything the same) and then reflected (opposite rights and lefts).
If you want a triple challenge, change roles and have the other person become the reflection.