Chance (Probability) Operations in Dance Composition - Grade Eight

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Chance (Probability) Operations in



Dance Composition

-

Grade Eight




1


Ohio Standar
ds
Connection


Fine Arts
-

Dance


Historical, Cultur
al and
Social Contexts


Benchmark C

Research a recognized
contributor to dance (e.g.
choreographer, dancer, or
educator) and trace the
development of the
individual’s work to its
hi
storical and cultur
al
influences.


Indicator 5

Research a historically
significant choreographer
and describe his or her
contribution to dance
histor
y.

Lesson Summary
:

What is the relationship between choreographer Merce
Cunningham and the mathematical co
ncept of probability
or chance oper
ations?

In this lesson, students investigate modern
-
dance
choreographer Merce Cunningham’s historically significant
contribution to dance
-
making history. Specifically, students
explore and practice Merce Cunningham’s chor
eographic
use of chance operations (probability), through kinesthetic
and movement explor
ation.


Experiences with chance operations (probability) in dance
transfer to everyday life and help students to develop a
perspective on real
-
life situations for whic
h the answers are
not known or will not be known until after decisions are
made.


Estimated Duration
:

10 Lessons, 45
minutes each.

Commentary
:

Merce Cunningham originated
chance operations

(probability) in dance composition. Cunningham is a
second
-
generat
ion modern dancer and choreographer who
followed modern dance pioneers such as Ruth St. Denis,
Ted Shawn, Charles Weidman, Doris Humphrey and
Martha Graham.

Cunningham’s life and work are highly
楮晬略湣e搠dy⁅a獴敲渠灨楬潳潰oyⰠf
J
C桩hgⰠ灲潢a扩b楴yⰠ
c桡湣
e⁡湤⁣潬oa扯牡瑩潮.


Chance Operations

are philosophically grounded in the
Eastern teachings of the
I Ching
.
They reflect a deliberate
move away from an exclusive reliance on standardized
choreographed movements, often found in stylized dance
forms such a
s ballet, towards a choreographic structure
where certain elements of spontaneity and chance are built
into the dance composition and performance
.

Having
dancers throw large, foam number cubes

and then perform
jumps according to the numbers that appear on
the cubes
(probability) is an example of a chance operation.
Consequently, no two performances are the same.



Chance (Probability) Operations in



Dance Composition

-

Grade Eight




2


Commentary
: (Continued)

At all levels, the subject of probability (chance operations) is best introduced and
developed through hands
-
on activit
ies and experiments.

Pre
-
Assessment
:

Assessment Envir
onment



Divide students into small groups of three to four students
.



Present the following pre
-
assessment questions verbally, or visually with an overhead
projector or in a handout:

a.

What do you think of
when you hear the words, “modern dance?”



In your mind, what is modern dance?

c.

Who is Merce Cunningham?

d.

What is Merce Cunningham’s relationship to the Eastern teachings of I Ching and
c桡湣e灥r
a瑩潮猿



What is Merce Cunningham’s living contribution to the p
牥獥湴慴楯渠潦潤e牮r
摡湣e?⁔漠瑨 ⁳瑵 y映 潤o牮⁤r湣e?



What is a chance oper
ation?

g.

What is a choreographic process?

h.

What is a choreographic device?

i.

What is Eastern philosophy?

j.

Who was John Cage?

k.

What is the relationship between Merce Cunningham and Joh
n Cage? Elaborate.

l.

What inspired Merce Cunningham and John Cage in their work? Where did they
often find their artistic inspiration?

m.

Discuss each question and record responses on chart paper
.



Have each group select a team reporter. Randomly request student

responses and
record all variations and interpretations of responses on a chalkboard or with another
visual aid. All responses are considered “understandings
J

J
process” and
扲b楮獴潲浩湧⁲
e獰潮獥献



Repeat this approach with each question. Use attribute w
ebs, lists, Venn diagrams and
concept maps, as needed.


Scoring Guidelines
:

This inquiry
-
based approach to pre
-
assessment will reveal what students know about
modern dance, choreography, the choreographic process and choreographers, and their
collaborators

such as Merce Cunningham and John Cage. The pre
-
assessment also shows
if students know specific dance vocabulary, including probability, I Ching, chance and

compositional devices. Student responses will indicate if students have already studied
significan
t people in dance and selected dance compositional devices, particularly from a
living history perspective. Student responses should be used to guide instruction.



Chance (Probability) Operations in



Dance Composition

-

Grade Eight




3

Post
-
Assessment
:

Students will:



Compose a choreographic study using one or more chance operations.



Share dance phrase(s) with peers.



As a group observe, identify and discuss what chance operations c
horeographers have
used.



View selected DVD or VHS documentaries based on the life and work of Merce
Cunningham. See list of resources.



Consider the relationships between the students’ compositional study using chance
operations and Merce Cunningham’s chore
ography using similar choreographic
processes. Identify the similarities and differences and speculate about why differences
exist.



Reflect on the effectiveness of chance as a choreographic device and the overall
choreographic processes and group dynamics
used to create a dance study. Record their
reflections in journals.



Write one
-

to two
-
page papers summarizing the significance of Cunningham’s work in
relation to their own experiments as dance makers.


Scoring Guidelines
:

Student mastery of chance operati
ons (probability) in dance composition is assessed using
scoring rubrics
. See

Attachment A,
Student Assessment Rubric
,

and

Attachment B
,

Dance
Journal Rubric
.


Instructional Procedures
:

Session One


Background

Physical Warm
-
Up

1.

Explore locomotor and nonlo
comotor movement and dance phrases within the
Cunningham canon using a teacher
-
directed instructional strategy.


Thinking Warm
-
Up

2.

Lead the class in a discussion, or allow students to work in small groups, using the
questions from the pre assessment. See At
tachment C,
Answers to Pre
-
Assessment
Questions
.

3.

Share Attachment B,
Dance Journal Rubric,
and
discuss the criteria.

4.

Give an overview of the lesson and the connections between the physical war
m
-
up and
the discussion.

5.

Direct students to write their first jo
urnal entries. Pose open
-
ended questions as prompts
for student reflection, but encourage students to write their feelings about the lesson study
and any questions they might have as they reflect on the lesson’s introduction.


Session Two

Conducting a Cha
nce Operation

6.

Recall Session One’s instruction.



Chance (Probability) Operations in



Dance Composition

-

Grade Eight




4

7.

Sit together in the floor in a circle. Ask students in what ways they can move through
space (locomotor); in what ways they can move in their self
-
spaces (nonlocomotor
).

8.

Write their responses on a ch
alkboar
d.

9.

Invite individual students to write each movement listed on 3
-

by 5
-
inch index car
ds.

10.

Fold each card into quarters and place each one into a large bag. Shake the bag to mix the
car
ds.

11.

Randomly draw six locomotor and six nonlocomotor movem
ents. The first six locomotor
and nonlocomotor movements randomly selected will be used in this lesson.

12.

Ask:



What is a chance oper
ation?



How did we use a chance oper
ation today?



Are there any movements not selected that you personally love to perfor
m? If
so,
which one(s)?



Why would a choreographer choose to leave out a favor
ite movement(s)?



Why would a choreographer consciously choose to wor
k this way?



How can using chance operations serve a purpose in choreogr
aphy?

13.

Hand out a sheet of unlined, 8½ by 1
1
-
inch paper to each student. Instruct students to
fold their papers into three columns by four columns. They should see 12 boxes on the
single sheets of paper. Have them write a
different

locomotor

movement,

from the class
selections, in each of the six b
oxes. In the remaining six boxes, write six
nonlocomotor

movements fr
om the class selections.

14.

Tell students to cut or tear apart each of the movements, then take all 12 of the
movements and tightly crush each one into a ball. Each student stores his or

her 12
movements in a small plastic bag to use in futur
e classes.

15.

Direct students to write their journal entries reflecting on how the thinking exercise
relates to mathematics and if it has components of probability and chance. Tell them to
provide ex
amples.


Session Thr
ee

Using Chance as a Choreogr
aphic Device

16.

Sit together in a circle. Review Session Two’s instr
uction.

17.

Stay in the circle formation. Have the students randomly place their 12 dance movements
on the floor in front of them. Ask stu
dents to recall the definition of chance procedures or
operations used in the last session. Ask students to consider how they can use their 12
pieces of paper to create chance procedures, and what procedures they must follow to
maintain the integrity of th
e exercise.

18.

Have each student randomly select the 12 pieces of paper, one at a time, keeping them in
the order in which they were chosen, and keeping them folded until all 12 pieces have
been selected. When all 12 pieces of paper are selected, students

unfold each paper,
maintaining the
randomly selected

order. Students write or notate the order of their 12


Chance (Probability) Operations in



Dance Composition

-

Grade Eight




5

movements

by writing the number of the movement on the back of the piece of paper to
create movement sequences, dance combinations or dance phrases.

The 12 pieces of
paper are placed back in the plastic bag.

19.

Tell students to practice the movements of their 12
-
part dance phr
ases.

20.

Ask:



What does it feel like to have a
predetermined order
?



If you had a choice, would you change the sequence of mov
ements?



If you changed the order, would it still be a chance oper
ation?



Are most of your locomotor movements at the beginning or end of the phr
ase?



Do you like your phr
ase?



Do you feel limited or freed by the compositional structure of this exercise?

21.

R
ecall the main points of today’s session. Direct students to make journal entries that
include, but are not limited to, reflecting on what went well today in the chance
operations, what didn’t go well, what was easy, what was cha
llenging and why.


Session
Four


Independent and Group Choreography

22.

Sit together in a circle. Review Session Three’s instruction. Have students use their 12
movements to review the sequences they developed through chance selections.

23.

Have students practice their movement phra
ses alone.

24.

Tell students to share their movement phrases with partners. They should determine how
the two movement phrases are similar and how they are different, and if there are any
extra movements and why.

25.

Divide the class into two groups. Have
students share their movement phrases with the
members of their groups. They should observe the phrases and respond orally to what is
viewed. Ask them what they think of this choreogr
aphy method.

26.

Recall the main points of today’s session. Tell students

to write journal entries about
what they learned in class today.

27.

As homework, ask students to practice their movement phrases.


Why would a choreographer such as Cunningham consciously choose to work through
random ordering of movement and chance proc
edures?


Session Five

Determine Use of Space, Facing and Timing through a Chance Operation

30.

Sit together in a cir
cle. Review today’s session.


Physical Warm
-
Up

31.

Have students practice their movement phrases until they
move fluidly and fully.

32.

Dire
ct them to move through their phr
ases using a slow tempo.

33.

Direct them to move through their phr
ases using a fast tempo.

34.

Direct them to move through their phr
ases at a medium tempo.



Chance (Probability) Operations in



Dance Composition

-

Grade Eight




6

Body of the Session

35.

Have students repeat their movements from s
low to fast to medium to develop fluid
transitions between the movement phrases. This is similar to developing three sentences
into a meaningful paragraph.

36.

Have students choose partners and share and teach their three movement phrases with
each another
.

37.

Tell student partners to discuss and demonstrate the similarities and differences between
their dance phrases.

38.

Ask students to use what they know about the compositional components of space, facing
and timing to create duets or other dances for t
wo people. With their partners, have them
use chance operations to shape their own and each other’s use of space, facing and/or
timing. Give them coins, number cubes, playing cards or other devices to determine
chance procedures. Ask them how this use of c
hance operations changes their
choreographic experiences, and whether chance enhances or hinders their creative
pr
ocesses.

39.

Tell them to be prepared to share their

duets in the next session.

40

Direct students to write journal entries reflecting on the ses
sion’s collaborative process
and other points that came up during the work session. Have each student describe his or
her creative process and his or her partner’s creative process, and how a chance operation
was used in the duet.

41.

Review the main points of

today’s session with the students Ask:



Are there one or two kinespheres in your

duet?



Do you and your partner share the same kinespher
e?



Is there a common front in your duet? Why? Why not?



How are the rhythms similar? Or, are they distinct from one anothe
r
?



Is there a common front in the dance classr
oom?



How does this affect the performance of your movement phrases?


Session Six

Sharing the Movement Phrases with Others

42.

Sit together in a circle. Review Session Five’s instruction.


Physical Warm
-
Up

43.

H
ave students move through their phrases beginning slowly, then using a quick tempo
and
, finally, with a medium tempo.


Body of the session

44.

Ask student to share duets. Invite two groups to perform simultaneously and sequentially.

45.

Through a whole
-
cla
ss discussion, compare and contrast the varying degrees of chance
procedure
s in each dance movement study.



Chance (Probability) Operations in



Dance Composition

-

Grade Eight




7

46.

Review the main points of today’s session. Allow time for journal entries. Tell students to
include their thoughts about sharing the dance moveme
nt phrases they created through
dance operations.


Session Seven

Learning Centers


Writing in the Content Area

47.

Sit together in a circle and explain what the students will be doing in today’s session.

48.

In small groups, have students write brief sum
maries of what they have learned to date,
using the title, “A Chance Oper
ation is… Got Cunningham?”


Session Eight


Review Previous Study of Chance Operations in Dance Composition

49.

Sit together in a circle. Review and discuss the first three pre
-
assess
ment questions.

50.

In small groups, ask students to discuss the relationship between Merce Cunningham’s
choreography and the mathematical concept of chance operations.

51.

Direct students to write journal entries that examine this perspective theoretical
ly and
how they and their partners applied it to their duets.


What is the relationship between choreographer Merce Cunningham and the
mathematical concept of chance operations?


Session Nine

Revisiting the Essential Question

52.

Lead the class in discuss
ing pre
-
assessment questions four through six . Ask students
what the relationship is between choreographer Merce Cunningham and the mathematical
concept of chance operations.

53.

Allow time for journal entri
es. Ask:



How has your perception of using chance ope
ration
s in dance composition changed?



Will you use this compositional device in your next choreographies? Why? Why not?


Session 10

Predictions and Inferences

54.

Sit together in circle. Have students think about what questions they would ask Merce
Cunnin
gham if they had the opportunity, and why
they would ask those questions.

55.

Tell students that John Cage died in 1992, but if he were alive today, working as a
composer and experimenting with new and innovative sound (music), what tools
(electronic, comp
uter, technology) would he use that weren’t available during his life?

56.

Ask students if computers, technology and the advancement of science would have
affected Merce Cunningham’s work in a progressive way. Using dance software
programs show
how and why

this could happen.

57.

Ask students how they can apply what they learned in this lesson to mathematics class.
Do they think mathematicians would approve of the application? Do they approve of this
application? Why or

why not?



Chance (Probability) Operations in



Dance Composition

-

Grade Eight




8

58.

Ask students again what t
he relationship is between choreographer Merce Cunningham
and the mathematical concept of chance operations.


Differentiated Instructional Support
:

Instruction is differentiated according to learner needs, to help all learners either meet the
intent of the

specified indicator(s) or, if the indicator is already met, to advance beyond the
specified indicator
(s).



Some students may need to repeat the chance operations numerous times to begin to feel
kinesthetically that their new movement possibilities are deve
loping into dance phr
ases.




You can take more time to assist students as they physically explore and accurately
arrive at their own compositional designs, allowing those with varying physical
perceptions of chance operations to develop their performances o
f dance phrases
accurately and at their

own paces.



Students may choose to compose solo or small group chance
-
oper
ation studies.


Extensions
:



Extend the content into real
-
world applications such as problem
-
solving techniques or
chaos versus or
ganization.



Co
mpare modern dance choreographers to other modern performing and visual artists
such as composer and musician John Cage or visual artists such as Jasper Johns, Robert
Rauschenberg, Jackson Pollack or Andy Warhol.



Make interdisciplinary connections between
modern dance and other arts disciplines such
as music and visual art and to movement and cultural studies.



Use extension questions to promote higher
-
order thinking. See Attachment D,
Extension
Questions: Higher
-
order Thinking.


Home Connections
:

Students
are encouraged to practice movement phrases outside class as they are shaped and
reshaped throughout the chance operation(s) dance composition lesson.


Interdisciplinary Connections
:

Science

Scientific Inquiry

Benchmark B:

Analyze and interpret data from s
cientific investigations using appropriate mathematical
skills in order to draw valid conclusions.


Set up a chance operation using locomotor and nonlocomotor movement as the variables.




Chance (Probability) Operations in



Dance Composition

-

Grade Eight




9

Scientific Ways of Knowing

B
enchmark A:

Use skills of scientific inq
uiry processes (e.g. hypothesis, record keeping, description and
explanation).


Use text and motif notation to record and notate the movement sequences.


Benchmark C:

Give examples of how thinking scientifically is helpful in daily life.


Use a chance oper
ation to set up, construct and perform a movement sequence.


Mathematics

Data Analysis and Probability

Benchmark B:

Evaluate different graphical representations of the same data to determine which is the most
appropriate representation for an identified pu
rpose.


Benchmark E:

Evaluate the validity of claims and predications that are based on data by examining the
appropriateness of th
e data collection and analysis.


Maintain the integrity of a chance operation; avoid tainting the results.


Benchmark H:

Use
counting techniques, such as permutations and combinations, to determine the total
number of options and possible outcomes.


Determine the probability of drawing a specific movement.


Mathematical Processes

Benchmark A
:

Formulate a problem or mathematical
model in response to a specific need or situation,
determine information required to solve the problem, choose a method for obtaining this
information, and set limits for an acceptable solution.


Compose a chance operation movement sequence, and record the

results on separate sheets
of paper.


Interdisciplinary Extensions
:

Lesson extensions may include, but are not limited to these studies:



Modern and post
-
modern visual art and music of the 20
th

Centur
y;



Chance (Probability) Operations in



Dance Composition

-

Grade Eight




10



Subject
-
specific vocabulary words such as dance, visu
al art, music, movement, reading
and language ar
ts, and humanities;



Modern dance and choreography in philosophy or

humanities;



History

dance, modern and post
-
modern art, music, and humanities thr
ough the ages.


Materials and Resources
:

The inclusion of a s
pecific resource in any lesson formulated by the Ohio Department of
Education should not interpreted as an endorsement of that resource, or any of its contents,
by the Ohio Department of Education. The Ohio Department of Education
does not

endorse
any part
icular resource. The Web addresses listed are for a given site’s main page;
therefore, it may be necessary to search within the site to find the specific information
required for a given lesson. Please note that information published on the Internet change
s
over time; therefore, the links provided may no longer contain the information related to a
given lesson. Teachers should preview all sites before using them with students.


Note: Some Web sites contain material that is protected by copyright. Teachers
should
ensure that any use of material from the Web does not infringe upon the content owner's
copyright.


For the teacher:

chart paper, markers, overhead projector, overhead markers,
chalkboard, chalk, pencils, student dry
-
erase boards and markers,
pencil
s, blank paper, small plastic bags


For the student:

paper, eraser and pencil


Vocabulary

The following list defines terms as they are used in this lesson:




chance operations

a dance composition device invented and used by
Merce Cunningham that often util
izes coins, cards or
the
I Ching

as tools to determine chance procedures.
Chance is a compositional device; a choreographic tool
used in dance making



choreographic device

an artistic contrivance in a choreographic work used to
achieve a particular effect;

in this lesson, 12 slips of
paper used to perform one or more relatively simple
tasks



choreographic procedure

an act composed of steps; a course of action; a set of
established forms or methods for dance making



choreography

the art of symbolically represe
nting movement through
dance; the composition and arrangement of movement
and dance phrases



Chance (Probability) Operations in



Dance Composition

-

Grade Eight




11



collaboration

working with others in an artistic endeavor resulting in
a new and innovative work of art.



compositional device

the manner in which parts are used, co
mbined and
related; for example, the use of 12 slips of paper
transferred and used in this lesson to create a movement
phrase.



compositional procedure

the arrangement of choreographic parts to form a
whole; the process of creating structure and
organizatio
n.



Cunningham technique

a highly physical modern dance and choreographic
style that emphasizes unique connections between the
back and legs; a series of codified back exercises
strengthens the technique; a technique that explores the
possibilities of human

movement potential



essence

the main idea communicated in and through the
choreogr
aphy



event

a Cunningham choreographic technique that uses
specific sections from the past and present repertoire of
the Merce Cunningham Dance Company



kinesphere

t
he space a
n individual occupies



legacy

something, usually valuable, received from an ancestor
or predecessor; Cunningham’s use of chance operation
is a legacy to the modern dance movement



locomotor

Moving thr
ough space



modern dance

a formalized dance technique that
evolved in the 1920s;
first
-
generation modern dance pioneers include Ruth St.
Denis, Ted Shawn, Charles Weidman, Doris Humphrey
and Martha Graham



nonlocomotor

not moving through space; stationary



probability

a math concept that depicts the number of ways a
n
event can happen over the total number of possible
events



somatics

the body as experienced from within; wholeness and the
rediscovery of the unity of body, mind and spirit; the
inner and outer relationships and dynamic interactions
between the whole self

and other individuals and
groups, both public and private, and all the issues
arising from these relationships and interactions



somatic forms and techniques

procedures and methods that reflect wholeness and
body, mind and spirit integration, such as Barte
nieff
Fundamentals®, Laban Movement Analysis and yoga,
which were used in this study



Chance (Probability) Operations in



Dance Composition

-

Grade Eight




12


Resources
:

Atlas, Charles.
Merce Cunningham: A Lifetime of Dance
. DVD. An American Masters
Broadcast Production, New York: Thir
teen/WNET, 2000.


Caplan, Elliot.
Cage/Cunn
ingham
. VHS. Kultur International Films: Cu
nningham Dance
Foundation, Inc.


Copeland, Roger.
Merce Cunningham: The Modernizing of Modern Dance
: New York:
Routledge Taylor and Francis Gr
oup, 2004.


Cook, Christopher. “Forms of Life.”

Dance Now
: Summer 1997.


Fetterman, William. “Merce Cunningham and John Cage: Choreographic Cross
-
Currents.”
Choreography and Dance: An International Journal

4.3 (2000).


Lesschaeve, Jacqueline.
The Dance and the Dance: Merce Cunningham in Conversation with
Jacqueline Lesschaeve
. London: Marion Boyars Publishing, Ltd., 1991.


Shulte, Albert, and Stuart Choate.
What Are My Chances? Book B
. Palo Alto, CA: Creative
Publications, 1977.


---
. “What is Probability?” In
What Are My Chances? Book B
. Palo Alto, CA: Creative
Publications,
1997. P. 30.


---
. “Probability Practice.” In
What Are My Chances? Book B
, Palo Alto, CA: Creative
Publications, 1997. P. 31.


---
. “Sums for Two Number cubes.”,In
What Are My Chances? Book B
, Palo Alto, CA:
Creative Publications, 1997. P. 38.


---
.
“Multi
ple Coin Tosses.”
In
What Are My Chances? Book B,

Palo Alto, CA: Creative
Publications, 1997. P. 42.


Sontag, Susan.
Dancers on a Plane: Cage, Cunningham, Johns
. New York: Alfred A. Knopf
Publishing, 1990.


Starr, Frances.
Merce Cunningham: Changes Notes o
n Choreography.

New York:
Something Else Pr
ess, Inc., 1968.


Unrau, Sharon.
Children’s Dance: An Exploration through the Techniques of Merce
Cunningham
. Diss. The Ohio State University, 2000.




Chance (Probability) Operations in



Dance Composition

-

Grade Eight




13

Unrau, Sharon.
Place
. VHS. New York: New York Library for the P
erforming Arts, 1998.


Vaughan, David.
Merce Cunningham: Fifty Years
. Italy: Aperture Press, 1997.


Vaughan, David (Ed). “
Merce Cunningham: Creative Elements
.”
Choreography and Dance:
An International Journal
, 4.3 (1997).



Attachments:

Attachment A,
Stude
nt Assessment Rubric

Attachment B
,
Dance Journal Rubric

Attachment C,
Answers to Pre
-
Assessment Questions

Attachment D
, Extension Questions: Higher
-
order Thinking



Chance (Probability) Operations in



Dance Composition

-

Grade Eight




14

Attachment A

Student Assessment Rubric


*Bloom’s levels of higher
-
order thinking skills;

**
Renzulli’s creative thinking areas: fluency, elaboration, visualization,


intuition and originality.



Criteria

4

3

2

1

Level of

higher
-
order* and creative
thinking**

Strong evidence
of analysis,
synthesis and
creative
thinking.

Evidence of
application
and
analysis levels;
some creative

thinking.

Does not go beyond
comprehension and
application levels;
limited creative
thinking.

Does not go beyond
knowledge and
comprehension levels;
lacks creative thinking.






Written report

“A Chance Operation is…


t Cunningham?”

E捨慮捥 op敲慴楯nF

Eone
J

瑯 two
J
p慧攠p慰敲F


fn捬cd敳emany
r敬敶慮琠
慤d楴楯n慬a慮d
v慲楥i r敳eur捥s
r敧慲d楮g
Cunningham’s
work㬠
楮nov慴av攠
捨慮捥
movemen琠
phr慳攻⁲敬敶an琠
d整慩氠楮 v敲b慬a
慮d wr楴瑥t
r敳eons敳㬠
楮form慴楯n
suppor瑳 瑨es楳.

fn捬cd敳⁡琠汥as琠
4 慤d楴楯n慬a慮d
v慲楥i r敳eur捥s
r敧慲d楮g
Cunningham’s
work㬠somewh慴a
楮瑥t敳瑩ng
捨慮捥
movemen琠
phr慳攻⁳am攠
r敬敶慮琠t整慩氠in
v敲b慬a慮d
wr楴瑥n
r敳eons敳㬠楤敡s
慮d 楮form慴楯n
捬敡r.

fn捬cd敳⁡琠汥as琠t
慤d楴楯n慬ar敳eur捥s
bu琠t
o v慲楥iy of
sour捥s r敧慲d楮g
Cunningham’s work;
汩瑴汥ld整慩氠慮d 捬慲楴y
楮 捨an捥 movem敮琠
phr慳攻bv楯us g慰s
楮 楮forma瑩tnI 捨an捥
op敲慴楯n 慮d
movemen琠thr慳攮


乯 慤d楴楯n慬a
r敳eur捥s r敧慲d楮g
Cunningham’s work;
楮捯mp汥瑥lprodu捴猻
污捫 of d整
慩氻a
楮form慴楯n and
捨慮捥 op敲慴楯n 慮d
movemen琠獥tuen捥
捯nfusing 慮d
d楳org慮楺敤.


䵥捨慮楣猠is敤 楮 ch慮捥
op敲慴楯n

楮 d慮捥 phr慳as

Emovem敮琠楮ven瑩tn and
p敲forman捥 pr慣瑩捥t

䙥w minor
敲rors 楮 捨慮捥
pro捥dur攠慮d
subs敱u敮琠
movemen琠
phr慳


卯m攠敲rors 楮
捨慮捥
pro捥dur攠慮d
subs敱u敮琠
movemen琠
phr慳攮

卥p敲慬a敲rors 楮
捨慮捥 pro捥dur攠慮d
movemen琠thr慳攬
wh楣h 慤v敲s敬y
慦f散瑳 th攠
p敲forman捥 of d慮捥
phr慳攮

䵡ny 敲rors 楮 ch慮捥
pro捥dur攠慮d
movemen琠thr慳攬
wh楣h 慤v敲s敬y
慦f散t
s th攠
p敲forman捥 of th攠
d慮捥 phr慳a


††
䭮ow汥lge

Ed楳捵ss楯nsI ref汥捴lv攠
pr慣瑩捥t 橯urn慬awri瑩tgF

䑥mons瑲慴敳a
und敲s瑡nd楮g
of 慬氠汥獳on
捯n捥p瑳.


䝲慳as mos琠key
汥獳on 捯n捥p瑳.

䝲慳as key 汥獳on
捯n捥p瑳 慴a愠gen敲慬a
汥l敬eof und敲s瑡nding
.

i楴i汥lor no 敶楤敮捥
of und敲s瑡tding
汥獳on 捯n捥p瑳.



Scale: 4
-

Exemplary; 3
-

Proficient; 2
-

Basic; 1
-

Limited



Chance (Probability) Operations in



Dance Composition

-

Grade Eight




15

Attachment B

Dance Journal Rubric



Merce Cunningham’s Chance Operations in Dance Composition

May be used by both the teacher and the stu
dents

to check progress and assess reflections.


Criteria

4

3

2

1

Records movement
analyses with regard to
chance operations used
in composing and
performing a dance
phrase(s). Dance
movement vocabulary;

spatial, rhythmic

and dynamic intention;
dramatic
intent and
other important
features are observable
contributions.

Always
demonstrates
highly accurate
and detailed
analyses of
chance
operations used
in composing
and performing a
dance phrase(s).

Often demonstrates
somewhat accurate
and descriptive
analys
es of chance
operations used in
composing and
performing a dance
phrase(s).

Sometimes
provides accurate
and descriptive
analyses of chance
operations used in
composing and
performing a dance
phrase(s).

Rarely provides
accurate and
descriptive analyses
of

chance operations
used in composing
and performing a
dance phrase(s).


Records thoughtful
responses to individual
dance learning
(artistic, aesthetic,

Cultural, and
traditional

processes and
practices) associated
with chance operations
in dance composi
tion.

Always offers
thoughtful
responses to
learning (artistic,
aesthetic,

Cultural, and
traditional

processes and
practices)

associated

with chance
operations in
dance
composition.


Often offers
thoughtful
responses to
learning

(artistic, aesthetic,

cultural, and
traditional

processes and
practices)
associated

with chance
operations in dance
composition.


Sometimes
provides thoughtful
responses to
learning

(artistic, aesthetic,

cultural, and
traditional

processes and
practices)
associated

with c
hance
operations in dance
composition.


Rarely provides
thoughtful responses
to learning (artistic,
aesthetic, cultural,
and traditional

processes and
practices) associated

with chance
operations in dance
composition.


Records journal entries
over

time

that reflect

personal

growth and
understanding.

All entries
provided over

time reflect

attention to
personal

growth and
understanding.

Frequent entries
provided over

time reflect

attention to
personal

growth and
understanding.

Sometimes offers
ent
ries that reflect

attention to
personal growth
and understanding.

Rarely offers entries
that reflect attention
to personal growth
and understanding.

Scale

4

Highly cogent and reflective






2 Rarely cogent and infrequently reflective

3

Fairly cogent and
a reasonably responsive reflective


1 Sometimes cogent and not reflective




Chance (Probability) Operations in



Dance Composition

-

Grade Eight




16

Attachment C

Answers to Pre
-
Assessment Questions


1.

Who is Merce Cunningham?

What continues to be his contribution to the visual and

performing arts?

Examples include his pa
st and ongoing integration with significant
visual arts such as Robert Rauschenberg, Jasper Johns, Isamu Noguchi, Andy Warhol
,

among others; and musicians

and
composers such as John Cage, Kronos Quartet,
Radiohead
,

among other
s.


2.

What is Merce Cunningha
m’s relationship to chance operations?

Mathematically
,

the

chance operations or probability of an event can be defined as:



number of ways the event can happen

total number of possible events



Beginning in 1951, with his
16 Dances for Soloist and Co
mpany of Three
, Cunningham
decided to determine the arrangement of sequences by tossing coins, to make impersonal
and more objective decisions, rather than structuring the dance according to the
subjective dictates of his own instincts or taste. In most of

Cunningham’s early works,
chance operations ordered sections of the dance, instead of assembling the movement
steps and phrases as found in later works. Early chance works often had multiple
sections or suites of movement. When computer software for dance

became available,
Cunningham used chance operations to assemble movement combinations for his later
works.


3.

What is Merce Cunningham’s living contribution to the presentation of modern

dance
?
Merce Cunningham continues to fracture every rule while subs
tituting

his own systems
and credos about the very nature of how dance is created and performed. Cunningham
has created more than one hundred dance works, and for the

last fifty years has always
been considered “of the moment.”


4.

What is Cunningham’
s contribution to the study of movement?

Cunningham’s technique
incorporates a wide range of dynamic nuances and rhythms. In the Cunningham
technique, accentuation, dynamism and the power to change direction quickly is required.
Cunningham movement usuall
y is taught through layering in class and in choreographic
settings. The dancers first learn the locomotor patterns and directions. The arms and
focus are added after the dancer understands where the movement takes place and in
which direction to perform t
he movement. Layering is a common practice with
Cunningham since 1991 and many of the teachers influenced by LifeForms™, (Cook
1997)
.



Chance (Probability) Operations in



Dance Composition

-

Grade Eight




17


Attachment C

(Continued)

Answers to Pre
-
Assessment Questions


5.

What is a chance operation? What is a choreographic pro
cedure? What is a choreographic
device?

Using random selection devices number cubes, coins, sticks, cards or I Ching to
construct dance compositions is an essential element of Cunningham’s techniques.
Chance operations involve randomly selecting, by variou
s means, the elements of each
dance. Another element is his collaborations with artists, designers and composers, most
notably John Cage, Jasper Johns and Robert Rauschenburg and Andy Worhol.
Collaboration has its own meaning for Cunningham, as he readily
explains. “In
performance, dance and music and design exist in the same space and take up the same
amount of time, but from different points of view.” (Christopher Cook, “Forms of Life,”
Dance Now
, summer 1997, p. 64).


6.

Who was John Cage? What is Cage’s

legacy to Cunningham’s use of
chance operations
?

Why should we care
?
John Cage, born in Los Angeles in 1912, had studied with Richard
Buhlig, Adolph
Weiss, Henry Cowell, and Arnold Schoenberg. Cage already had radical
notions about music. During a residen
cy at the Cornish School, John Cage was a
substitute teacher for two weeks in dance composition where he met Merce Cunningham.
Cunningham says this time was
,

“a revelation



suddenly there was something very
precise and very strict to work with. He simply
made us make things




you had to think
about it, not just have some feeling about what you were going to do next, but think about
it, and that was an extraordinary experience” (Merce Cunningham:
Fifty Years,

1997,
Vaughan, p. 17)
.

Cage himself would say o
f these classes that he was trying to arrive at
,

“A way in which dance and the music could be composed at the same time rather than
one waiting for the other to be finished or before you fitted the music to the dance or
fitted the dance to the music. So I
was teaching the dancers to compose, using percussion
instruments” (p. 17)
.

Cage sought other forms of musical composition. What interested
him most was rhythmic development, rhythm defined as the relationships of sounds and
silences.


7.

What is the relat
ionship between Merce Cunningham and John Cage?
Cunningham and
Cage were the first performing artists to
consciously separate the music from the dance.
In addition, their collaboration with

prominent visual artists was significant. They
worked together for

more than

forty years, challenging common practices in dance and
music aesthetics and performance.


8.

What inspired Merce Cunningham and John Cage in their work? What inspired them as
artists
?
They were inspired by

Eastern philosophy, the I Ching and Zen
, in addition to
numerous personal

and professional conversations, collaborations and experiences with
artists, friends
,
art and philosophical writings.



Chance (Probability) Operations in



Dance Composition

-

Grade Eight




18

Attachment D

Extension Questions:

Higher
-
o
rder Thinking


1.

Is it common practice for an artist to app
ly mathematical thinking in his or her creative work?
If so, is it a conscious or unconscious practice of the artist? Is this practice common in the
arts, more specifically dance? Does the integration of mathematical thinking, in this case
chance operation
s, compromise or enhance the original theory, application and body of
knowledge? Can a choreographer successfully maintain the integrity of a mathematical
application integrated into his or her work? Is mathematical thinking a creative process?
Provide exa
mples to support your answer
.


2.

What are the pros and cons of transferring these findings in mathematical inquiry to
choreography? Does it enhance or hinder a choreographic process? Give specific examples of
past and current choreographers who used mathe
matical theories and practices in positive or
negative scenarios in their wor
k.


3.

As a mathematics student, does movement exploration help you reach a deeper somatic
(mind
-
body) understanding of this specific mathematical concept? Provide specific person
al
examples to support a response. Can movement be used as a learning tool in all academic
curriculums? Why or

why not? Explain.


4.

How can various modes of inquiry and documentation including performance, written, and
oral responses help you reach a deep
er, more informed understanding of Merce Cunningham
and his integration of chance operations? Explain.