7/22/2016

1

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

7/22/2016

2

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)

7/22/2016

3

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

7/22/2016

4

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?

7/22/2016

5

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

7/22/2016

6

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

7/22/2016

7

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

7/22/2016

8

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/

7/22/2016

9

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

7/22/2016

10

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

7/22/2016

11

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 ?

7/22/2016

12

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

7/22/2016

13

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

7/22/2016

14

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

7/22/2016

15

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

bhardingbuehler@psesd.org ksoltman@psesd.org