The quantity of a small set You perceive the parts and put together - - PDF document

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The quantity of a small set You perceive the parts and put together - - PDF document

Making Sense of Number Sense Definition Number sense is .good intuition about numbers Making Sense of Number Sense and their relationships . It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts


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Making Sense of Number Sense

Jennifer Jansen Mississippi Bend Area Education Agency

Making Sense of Number Sense

Definition

Number sense is “….good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms.”

(Howden, 1989)

Find someone whose card has the same quantity as yours

Introduce yourself to your number soulmate Ask your number soulmate…

  • What’s your favorite number?
  • Why?

Perceptual Subitizing

You perceive the three or four dots intuitively & simultaneously. You “just know.”

Conceptual Subitizing

You perceive the parts and put together the whole All of this happens quickly and often is not conscious - it is still subitizing

A Big Idea

The quantity of a small set can be intuitively perceived without counting.

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Learning about Number from Mitsumasa Anno

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How many fives do you see? Number is Complex!!! A Big Idea

Numbers are used many ways, some more mathematical than others.

Uses of numbers

  • Nominal or categorical numbers
  • Referential numbers
  • Cardinal numbers
  • Ordinal numbers

A Big Idea

Quantity is an attribute

  • f a set of objects.

A Big Idea Quantity is an attribute of a set of objects.

3 elephants

3 mice

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A Collection Can Have Many Attributes

  • Pink color is an attribute
  • Round shape is an attribute
  • Nice smell is an attribute
  • Quantity is another attribute:

there are THREE roses in this collection

A Big Idea Quantity is an attribute of a set of objects. A Big Idea Quantity is an attribute of a set of objects.

Numerosity

  • The quantity of things in a set
  • The “three-ness” of 3
  • Separate from number words and written
  • symbols. Words and symbols these vary

between languages – numerosity does not.

  • Humans seem to be biologically programmed

to automatically perceive the numerosity of small sets. (The Early Math Collaborative, 2014)

Numbers: Nouns or Adjectives?

Counting, determining & naming quantity, telling “how many” ... all of these use number as an adjective, not a noun. Are there 3 dots? 3 fingers? 3 inches? 3 tenths?

Big Ideas of Number Sense

Developmental Levels for Recognizing Number and Subitizing

  • Name groups of 1 or 2, sometimes 3 (2 yrs)
  • Match small collection (no more than 4,

usually 1-3) (3 yrs)

  • Instantly recognizes collections up to 4 and

verbally names the number of items (4 yrs)

  • Instantly recognizes collections up to 5 and

verbally names the number of items (5 yrs)

  • Verbally labels all arrangements to 5 (5 yrs)

(Clements & Sarama, 2014)

Developmental Levels for Recognizing Number and Subitizing

  • Verbally labels arrangements to 6, then up to

10, using groups (5 yrs)

  • Verbally labels structured arrangements up to

twenty using groups (6 yrs)

  • Uses skip counting and place value to verbally

label structured arrangements (7 yrs)

  • Uses groups, multiplication, and place value to

verbally label structured arrangements (8+ yrs)

(Clements & Sarama, 2014)

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Video Analysis: Focus on the Child

While watching, consider:

  • Children’s understanding
  • Children’s learning
  • Evidence of thinking
  • Additional opportunities

Recognizing Quantity Child 1, preschool Recognizing Quantity Child 2, preschool Matching Quantity Child 3, preschool Comparing Quantities Child 4, preschool Comparing Quantity Child 5, kindergarten Estimating Quantity Child 9, preschool Estimating Quantity Child 3, preschool

Developing Visual Number Sense Through Models

Dot Cards

Developing Visual Number Sense Through Models

Number Cards

Developing Visual Number Sense Through Models

Dice

Developing Visual Number Sense Through Models Developing Visual Number Sense Through Models

Counting Frames or Rekenreks

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Where’s the MATH? Number All Around the Classroom

In Art In the Block Area In the Book Area In Dramatic Play

Where’s the MATH? Number All Around the Classroom

At Snack Time During Transitions Transition Activity Attendance Routine

Why focus on developing number sense?

Hierarchical Inclusion Because each number names a quantity one greater than the number before it, each number includes all the quantities named by those earlier numbers.

(Kamii & Joseph, 2004)

Number Sense

  • Solid number sense is key to mathematically

healthy development & practice.

  • Number sense is not static. It continues to

deepen & build as new relationships amongst more numbers are established.

Poly-ominoes

Dominoes (2-square shape)

Poly-ominoes

How many ways?

  • Tri-ominoes (3-square shapes)
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SLIDE 7

Poly-ominoes

How many ways?

  • Tri-ominoes (3-square shapes)

Poly-ominoes

How many ways?

  • Tetromiones (4-square shapes)

Poly-ominoes

How many ways?

  • Tetromiones (4-square shapes)

Poly-ominoes

How many ways?

  • Pentominoes (5-square shapes)

Poly-ominoes

How many ways?

  • Pentominoes (5-square shapes)

Mathematics All Around: Exploring Number

Subitizing is foundational.

  • Subitizing relies on visual patterns.

– Not all arrangements of a number are equally easy to “see.”

  • How is subitizing different than counting?

– Label small sets with number, without enumerating.

  • How does subitizing support counting?

– Authentic reasons to count small sets. – When counting, restate the last count word to emphasize cardinality: “1, 2, 3, ... 3 cups.”

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Mathematics All Around: Exploring Number

Subitizing is foundational (continued).

  • Subitizing & counting build understanding of

cardinality.

  • Expect children to subitize small sets; avoid

“counting to be sure.”

Mathematics All Around: Exploring Number

Children learn about quantity even without exact numbers.

  • “Which pile has more?”
  • “Put one napkin on each plate.”

Smaller numbers are easier than larger.

  • With infants and toddlers, talk about “1” and “2” and “1

more” and “2 more”

  • With preschoolers, spend a lot of time exploring “3” and “4”

and “5” Fingers are great tools for understanding small numbers, then building to 5 & 10. Children need repeated exposure to amounts in order to associate number name and quantity.

Video Analysis

Number Arrangements

  • About the Children
  • About the Teacher
  • About the Activity

How might this experience connect to other math?

Finding Math in Great Books

Mouse Count by Ellen Stoll Walsh Ten Black Dots by Donald Crews Count and See by Tana Hoban Splash by Ann Jonas 1, 2, 3 to the Zoo by Eric Carle Five Creatures by E Jenkins The Doorbell Rang by Pat Hutchins Ten, Nine, Eight by Molly Bang

Making Connections to the Big Ideas of Number Sense

Iowa Early Learning Standards

  • Standard 7.1.PS Children understand counting, ways of

representing numbers, and relationships between quantities and numbers.

  • Benchmarks: The child…

7.1.PS.1 recognizes small quantities (1-5) without counting them (subitizing). 7.1.PS.4 makes sets of 6-10 objects and describes parts. 7.1.PS.5 uses language such as more, less or the same amount to compare quantities. 7.1.PS.6 identifies numerals to 10 by name.

(Early Childhood Iowa, 3rd ed., 2018, p. 202)

Making Connections to the Big Ideas of Number Sense

(Heroman et. al., 2010, p. 107 )

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Making Connections to the Big Ideas of Number Sense

(Heroman et. al., 2010, p. 108 )

Making Connections to the Big Ideas of Number Sense

NAEYC Early Childhood Program Standards & Iowa Quality Preschool Program Standards

  • Standard:

– Curriculum

  • Criterion:

– Children are provided varied opportunities and materials to build understanding of numbers, number names, and their relationship to object quantities and to symbols.

Resources

Early Math Collaborative. (2014). Big Ideas of Early Mathematics. Boston: Pearson. Early Math Collaborative website www.earlymath.erikson.edu Follow on Facebook, Twitter, YouTube Young Mathematicians website http://youngmathematicians.edc.org/

Questions???

Contact Information: Jennifer Jansen jjansen@mbaea.org