artistic pathways to early math - university of oregon...explore mathematical dimensions of their...
TRANSCRIPT
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Artistic Pathways to
Early Math
Presented by Beverly Harding Buehler & Krissy Soltman
Starting Strong Conference August 1, 2016
Walk the Line
• Where would you place yourself on the
line according to how strongly you feel
about this statement:
“I’m good at math”
Strongly
Agree
Strongly
Disagree
Now, introduce yourself and share with those near you
why you chose to sign up for this session.
Neutral
Walk the Line
• Where would you place yourself on the
line according to how strongly you feel
about this statement:
“I’m good at the arts!”
Strongly
Agree
Strongly
Disagree
Now, introduce yourself and share why your position
did or did not change.
Neutral
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Learning Objectives
1. Be introduced to arts-infusion as a proven
strategy to engage early learners in
mathematics and close the opportunity
gap.
2. Review recent research on developing
operations and algebraic thinking with
Pre-K children.
3. Engage in research-tested arts infused
Pre-K math lessons and reflect on
applications to their learning settings.
Success Criteria
1. I understand how arts infused math helps
close the opportunity gap for children of
color and poverty.
2. I can explain why knowledge of problem
types is important for developing
children’s early math skills & practices
3. I know one way I can improve children’s
understanding of operations through the
arts
Numeracy is…
“…a term that refers to all the
mathematics that young students
learn including number,
operations, and geometry and
measurement concepts.”From the introduction of
Learning Pathways in Numeracy: Addressing Early Numeracy Skills,
OSPI (2014)
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NAEYC Position Statement 2010Children Are Young Mathematicians
“Throughout the early years of life, children notice and
explore mathematical dimensions of their world. They
compare quantities, find patterns, navigate in space,
and grapple with real problems such as balancing a
tall block building or sharing a bowl of crackers fairly
with a playmate. Mathematics helps children make
sense of their world outside of school and helps them
construct a solid foundation for success in school.”
video
School Readiness and Later AchievementDuncan, et al, Developmental Psychology, 2007.
The strongest predictors of later
achievement are school-entry math, reading,
and attention skills. Of these, early math
skills have the greatest predictive power.
Fall WaKIDS Data 2015
N = 58,656 or 74% of Kindergartners in WA
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Fall WaKIDS 2015 by
Race & Ethnicity
N = 58,656 or 74% of kindergartners in WA
Closing the Gap through Arts
• What common ground do the
arts share with Math concepts
and thinking strategies?
• How do these shared concepts
and thinking practices support
P-3 alignment in our efforts to
close the opportunity gap?
CONCEPT
• Is it broad and abstract? Can it be represented by one or two
words?
• Is it timeless – carries through the ages?
• Is it universal – carries across cultures?
• Can it be represented by different examples with common
attributes?
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Arts Infused Teaching – (Shared Concepts)
Teaching is defined by a concept authentically shared by both
subjects. The concept means the same thing in both
disciplines.
e.g. Fractions mean the same thing in dance and visual arts
as in math.
Arts Infused Concepts in CCSS Math
Arts ConceptsDance
• Sequence, beat, shape,
repetition, balance,
levels, accumulation
Music
• Rhythm, pattern, tempo,
note value, pitch, volume
Visual Arts
• Shape, scale, proportion,
balance, pattern, space,
symmetry
CCSSMath
• Shape
• Equivalency
• Fractions
• Addition, subtraction,
multiplication, division
• Pattern
• Repetition
• Place value
• Scale
• Symmetry
Dancing Trapezoids in Kindergarten
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Performance Based Assessments
in Math
Which part is bigger?
How do you know?
Arts Infused Learning Closes the Gap
21st Century Skills
•Creating
•Critical Thinking
•Collaborating
•Communicating
•Growth Mindset
•Perseverance
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Constructing and Deconstructing
Dancing Puzzle Shapes
Target: Demonstrates addition by constructing a puzzle shape with a group.Criteria: Adds a shape by dancing in when given a numerical cue, and
freezing over, under, around, through or beside four other dancers.
Target: Demonstrates subtraction by deconstructing a puzzle shape with a group.
Criteria: Takes away from a shape by floating away when given a
numerical cue.
Target: Solves addition and subtraction equations that correspond to the number of dancers.
Criteria: Adds and subtracts to show how many dancers are in each
puzzle shape.
WA State Standards Domains
Early Numeracy Support
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Young children and operations
• Early numeracy skills are foundational to supporting
operations
– Counting sequence
– Subitizing
– Comparing
– Visualizing/
physicalizing math
Building Conceptual
Understanding
Which of these did you notice?
– Count sequence
– Subitizing
– Comparing
– Visualizing or physicalizing math
http://earlymath.erikson.edu/mouse-collections-preschool-storytime-game/
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Traditional Ways of
Looking at Operations
• Addition – join together
situation – in all, all
together
• Subtraction – take apart –
how many left
• Limits children in what they
are able to do later.
Four structures of problem types
• Join Problems
• Separate Problems
• Part-Part-Whole Problems
• Compare Problems – usually one
number larger than another
Cognitively Guided Instruction
CGI CCSS
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Get away
from having
words
determine
operation
• Aidan had 4 marbles in
her marble bag. After
school, she found some
more marbles that she
had misplaced and put
them in her bag. When
she counted all of her
marbles there were 6 in
all. How many extra
marbles did Aiden find
and put in her bag?
Maggie had a large
collection of stuffed
animals. She gave away
2 of her favorite animals
to her little sister, Grace.
Maggie still has 8 stuffed
animals left in her
collection. How many did
she have before she
gave the animals to
Grace.
Problem Type activity
• Identify each of the problem types
• Use manipulatives to act out each problem or
• Draw a picture to represent the problem
• Fill in the grid with numbers
• Write an equation, draw a box to represent
the unknown
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Initial/Change/End
Add to/Result Unknown
The toy store has
5 puzzles on a
shelf. The owner
added 2 more to
the shelf. How
many puzzles are
on the shelf?
Start Change Result
5 + 2 ?
Start/Change/End
Add to/Change Unknown
The toy store has 5 puzzles on the shelf. The owner added puzzles until there were 7 puzzles on the shelf. How many puzzles did the owner add to the shelf?
Start Change Result
5 + ? 7
Start/Change/End
Take from/Result
UnknownThere were 7 puzzles on the shelf at the toy store. A customer bought 2 puzzles. How many puzzles are left on the shelf?
Start Change Result
7 - 2 ?
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Start/Change/End
Take from/Change Unknown
There were 7 puzzles on the shelf at the toy store. A customer bought some puzzles. After this purchase 5 puzzles were on the shelf. How many puzzles did the customer buy?
Start Change result
7 - ? 5
Put together/Take Apart
Total Unknown
The toy store has two kinds of puzzles. Currently, there are 5 animal puzzles and 2 transportation puzzles. How many puzzles are currently on the shelf?
Part Part Whole
5 + 2 ?
Put Together/Take Apart
Both Addends Unknown
A toy store has 5 puzzles. How many can be put on the red shelf and how many on the blue shelf?
Part Part Whole
? ? 5
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Teaching Sequence
Always begin with
“What’s happening in this situation?”
1.a) Join (result unknown) b) Part-part-whole
(whole unknown) c) Separate (result unknown) –
These can be directly modeled
2. Join (change unknown) and Part-part-whole
(part unknown) Children first learn a and b above
with “counting on”. They then learn c as “counting
on” (11-6 becomes 6+=11) or counting back.
Teaching Sequence cont.
3. Start unknown – use communtivity +6=11
becomes 6+=11 and count on or reversal
to change -6=5 becomes 6+5=
Other considerations
• All problem types should be covered by
the end of first grade
• For the youngest kids use physical objects
related to the problem vs. general math
manipulatives
• Provide opportunities for children to
create, use, share and explain different
strategies
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Consider the situation
Use context students are familiar with…what might
happen in the classroom?
With your table group
brainstorm how you
can incorporate these
problem types iinto
your classroom
routines and activities
Be ready to share
Equations in Collage Quilts
Visual Arts & Mathematical Operations
Target: Shows and writes equations using a grid.
Criteria: Fills grid squares with one color horizontally to represent a
number, uses two different colors in each row below it to show pairs of
numbers that add up to 4, and writes corresponding equations.
Target: Shows and writes equations using collage grids.
Criteria: Glues paper squares in one color horizontally to represent five, glues two different colors in each row below to
show pairs of numbers that add up to 5, and writes corresponding equations.
Extension:
Target: Arranges collages to show addition and equivalency.
Criteria: Combines 5’s collages with a partner and writes equations for a sum of 10; combines collages in group quilts and
counts/writes equations.
Untitled #2, Agnes Martin, 1985, Seattle Art
Museum
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Blocks, Annie Mae Young, 2003, Seattle Art
Museum
Reflection…
Share 1 take away from your learning today?
Thank You!
Please Complete your Evaluations
Beverly Harding Buehler Krissy Soltman