Back to Natural Math® workshops

October 29th, 2003
Art and Mathematics

 


Workshop participants with their creations

This teacher workshop was done in collaboration with The Scrap Exchange, a creative reuse shop in Durham, North Carolina. Participants were learning how to help children use scrap materials in rich acticities combining art and mathematics.

 

Wearable art
 

Even the most unusual materials inspire people to create something they can wear. Insulation tube jewelry, spare key necklaces, or scrap theater costumes make people smile. Students can also think about deep issues such as symbolism in clothes, or different styles and traditions.


Insulation necklace, earrings, and a ring.

Is this hat casual or formal? Interestingly, the question can be asked about a hat made from scrap insulation and pieces of lace, just as well as about a real hat. Children interpret symbols expressed in any materials, traditional or not. This can be used to introduce algebraic ideas:

  Algebra Clothes
Concrete, real

3*2=6

6 is an even number, because it is a product of a whole number 3, and 2

This "real" hat is a fancy, dressy hat
Symbolic

k*2=m

"k" (a symbol for a number) is a whole number

"m" (a symbol for a number) is an even number, because it is a product of a whole number and 2

This "symbol of a hat" is a fancy, dressy hat

 


Accessorizing! A belt, a bracelet, a head band...

 


...And a beatiful fan...

 


...And a veil...

 


...and a hair decoration!

 

Masks and constumes are very special. They mean taking on a role, pretending to be someone else, hiding, secrecy. Anybody can be under a mask. Isn't mask much like a variable? Any number can be under a "mask" of a variable in an equation. Who is this mysterious Mr. Ex in X+2=5? Only solving the equation will unmask him!


A model for a costume for a Sheakspearian play. What queen will wear it?

 


A composite mask made out of simple shapes.

 


A beautiful mystery mask.

 

 
Metaphors

Mask - unknown, a variable

Symbols in clothes - symbols in mathematics

 

Group projects
 

Sometimes individual projects come together because of a common theme. Here workshop participants who created "wearable art" from an insulation belt to a shiny key necklace join forces for a "fashion show."

 

Sometimes a "frame" or a stage or another conceptually empty space may inspire several people to fill it up with their creations. An empty bulletin board with some pushpins may inspire children to draw for an art exibit. Whenever they have a free moment and an idea, children will keep working on filling a prepared space for a group project. For example, children can create sculptures of plants and animals for a habitat, or a fill a garage and a race track waiting for models of made-up vehicles. Such a project can keep growing for weeks, which also helps students who need more time to plan their work.


Workhop participants set their "people" to ride on an empty "parade float."
A model car, created by other participants, is added to the parade scene.
And now there is royalty at the parade!

 

Some themes, such as clothes or human faces, are guaranteed to interest many students. A lot of workshop participants created portraits of people and animals. Here is our portrait gallery.


Note the pretty earrings!

 


Sad face - happy face. A mobile portrait!

 


Madonna of the shiny eyes, with child.

 


"What a big smile you have!"

 


All dressed up for a party.

 

It may be interesting to initiate a discussion of body proportions in portraits. What geometric shape can work for a torso - a cone, or maybe a cylinder? How long should the arms be?


The author dressed the sculpture in the same color. Note the conic shape.

 


A portrait of a student coming in for a detention.

 


A dancing model! A mobile, posable portrait.

 


A colorful inchworm can adorn a science room...

 


...Here is a friend to keep the creature company.
And to help students study patterns.

 


A bust portrait.
The mouth is made out of rope that is also used to attach the head to the body.

 


What a hairdo!

 


A magical flying creature.

 
Metaphors

Facial expressions - symbols (e.g. smile for "happy")

Similar forms - mathematical approximations

 

Guessing games: creativity, science, tolerance
 

With any art activity, students can be invited to play various "guessing games" or "naming games" that help with creativity, exchange of ideas, and tolerance to different means of artistic expression.

For example, a part of a drawing or a sculpture can be revealed. Each student can finish the scultpture in his or her own way. Then an exhibit of art that started from the same "seed" can be used for activities such as exploring different styles. A very similar game can be played with other subjects. For example: "I am thinking of a figure that has two parallel sides" - it can be a square or a hexagon or a rhombus or a trapezoid... A cooperative group project can be to come up with many different examples.


Here is a modernist-lookin mouse.
The shape is approximated by cones.
For a fun game, children can create their own versions of sculptures from a detail.
This can be a part of a mouse, a crawfish, a spaceship, or other things:

 

Another "creativity challenge" is to figure out how to use given materials to accomplish a goal. Such exercises are frequent in management courses!

 

How can we make these comb shapes work?

The problem is solved:

A partially restored to flesh dinosaur skeleton.
Children can be like scientists who restore extinct animals by their bones.

Another game is to take an already finished "abstract" piece of art, and to interpret it differently. It may be as simple as giving the piece a name, or as elaborate as writing an essay on its cultural significance.


Is it an alien ship? A carnival ride? A jellyfish?
Participants played "Name this sculpture!" with several creations.

 


A fancy example for our "Name this sculpture" game.
Metaphors

Finishing a sculpture from a detail - finding a mathematical object with given features.

Analyzing, naming "abstract" art - making connections and figuring out features of objects.

 

Modeling and working with shapes
To begin

Many workshop participants explored "making shapes out of other shapes" in their projects. Such ideas are widely used in subjects from architecture to 3-D modeling. For example, this Mayan pyramid is made out of flat square shapes of diminishing size:

In this classic toy, short cylinders of diminishing radii are used to approximate a cone:

And this illustration to a Russian children's book shows a horse made entirely out of marbles:

"Girl with a mandolin" is a cubist painting by Pablo Picasso. The artist created the portrait out of simple geometric shapes:


There is a mouse in the house!
How do you make a mouse out of cirlces?

 


A dressy top hat (a cylinder) for this character is made out of different circles.
Students can learn about cross-sections by approximating shapes.

 


A composition with several well-balanced parts.
Note the stable, bottom-heavy, conic-shaped base made out of circles.

 

What can you do with a sheer stocking?

You can create a doughnut (mathematically speaking, torus) shape by rolling it up.
Christmas is coming:

How about a hood ornament?

This vehicle is also a mobile sculpture. The sides can move up:

 


Colorful autumn trees are made of cones, "combs" and fabric.

 


"Would you like ketchup with your order?" Cylinder burgers and pizza segments:

 


A tribute to Twin Towers.

 


Weaving patterns on a transparent block.
Such crafts can be used to study number patterns.
If every third thread is of a different color, students can work with divisibility by 3.
Trying to use a finer mesh:

 


A robot made entirely out of different kinds of cylinders.

 


Bendable, colorful, patterned...

 
Metaphors Making sculptures out of simple shapes - mathematical approximation, 3-d modelling.