Math in Art
An Elementary Festival
John Golden
Grand Valley State University
Credit Where Credit is Due
• Susan Walborn, originator and motivator.
Instructional leader and teacher extraordinaire.
• Barbara Todd, inspirational principal with unhesitating
support
• Dana Bradt, PTA leader and grant administrator
• Amy Archangeli and Joanne Pereira,
our great art interns
• Teachers and Staff of Aberdeen/Shawnee Math/Tech
Academy, a GRPS elementary school, especially
Mike Klann and Chris Strevel
The Idea
Susan’s idea:
Students in each grade would take part in a math
lesson whose output is a piece of art. Each class
would select three pieces to send to a school wide
show where the ten best would be selected at a
school wide festival. With families invited. And
math/art activities to try on the spot.
My response:
Wow!
Second Year
Or
“How Crazy Were We?”
We applied for a
community foundation
grant to really put the
festival on. All of the
previous were kept, plus an
Artist-in-Residence, a mini
Art Fair for the festival
night and a mural generated
by the students guided by
the artist in residence.
Goals and Objectives
• Reach all students, including those who have not
been successful in mathematic
• Connect mathematics with art – Get students to
ask: “What else does math connect to?”
• Increase awareness of art as a possible
occupation
• Provide opportunity for significant mathematics
and real art
Artist to Mathematics
Some projects were inspired by the
artist first.
•Alexander Calder
•Piet Mondrian
•Andy Warhol
Calder
• Grand Rapids has a
large Calder statue
(stabile) providing a
local link.
• Lots of obvious
math. Really.
– Balance
– Variety of shapes
Constant Area and the Mean
• 3rd graders had to design five shapes with
an area of 10 square units. These were cut
out and then transferred to heavy
cardboard.
• Used weights (poster putty on paperclips)
to solve the problem of finding a balance
point for multiple objects, essentially
constructing the mean.
After finishing their projects,
students displayed them
anonymously and evaluated
them on a rubric for the math
invovlved and for the artistic
impact. Universally students
were impressed by originality.
Mondrian
• Connection
with jazz
• Are you
kidding –
look at all
those
rectangles!
Golden Rectangle and Fibonacci
• Mondrian viewed proportionality as one of the
keys to visual harmony. Students investigated
the Golden Rectangle by constructing a
rectangular spiral.
• By studying the data in the rectangular spiral
students discovered multiple instances of the
Fibonacci sequence.
Square
added
Fifth grade students constructed
the rectangular spiral on graph
paper, then collected data and
found patterns, including the ratio
of long to short.
Short Long
side side
1x1
1
1
1x1
1
2
2x2
2
3
3x3
3
5
5x5
5
8
8x8
8
13
This was the project that
convinced us of the artist in
each student. We expected
students to mimic the spiral
motif, but they took amazingly
independent and free direction
with the projects.
Warhol
•Repetition with
variation
•Patterns
•Image decomposition
into regions
This filled a number of gaps – we had no
information technology involved, no pop art and no
photography before this project was developed.
The math link came when I
made a connection with a
freeware program I use for
image editing. There’s a feature
that takes the RGB information
for color in a picture and
permutes it.
6th grade
students
investigated
combinations
and
permutations,
deriving the
underlying
factorial
patterns.
The only
problem was
that they
turned out so
visually
impressive…
…that they
completely
dominated
the school
wide show!
Math to Art
Other projects started with the
mathematics and led to an art project to
investigate.
•Shape recognition and use
•Polyhedra
•Fractals
Shape Recognition
For a project accessible to kindergardeners in terms of
math and art. Shape recognition despite orientation and
size was perfect material and Susan had the idea to use
them to make…
Students chose a shape for the face,
painted it, and then chose shapes
for the features. Shapes of the
same type had to be colored the
same color. Artistically they
investigated the emotion their
masks showed.
How do
kindergardeners
vote?
Polyhedra
• 3rd graders investigated polygons, then extended
the properties to three dimensions.
• They used polytiles to design a sculpture, then
partially disassembled it to make a plan for a net.
• Students then laid polygon templates out (with a
larger scale) to make a net for a cardboard
sculpture.
• They folded up the cardboard net to make a
sculpture.
Aside from the sculpture
aspect, students learned
about graphic design,
analyzing how packages are
decorated with repeated
geometric designs.
Fractals
Susan had already been investigating origami
fractals with several classes, but felt strongly that
festival projects should not overlap with other
work. Investigating fractals led us to the idea of
Sierpinski carpets – connecting immediately with
textile art.
4th graders investigated
•recursion,
•generation by motif
•exponential number patterns
Other!
Students learned about Jackson Pollack
and created abstract works based on
topology and the Jordan curve theorem.
2nd graders
looked into
kaleidoscopes
and investigated
rotational and
reflectional
symmetry.
Then they used MIRAs,
precut shapes from
origami paper and
hinged mirrors to make
their own kaleidoscope
design, which was
displayed in embroidery
hoops.
Frieze!
1st graders worked on an ancient art
form already loaded with math –
friezes.
They studied translations and
rotations as well as several types of
visual patterns.
Festival Day
Festival Day
Festival Day
Eric Pichado
-the Artist in
Residence