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The main features of this file are:

Recommendation 1: Teach number and operations using a developmental progression.

Recommendation 2: Teach geometry numbers, patterns, measurement, and data analysis using a

developmental progression.

Recommendation 3: Use progress monitoring to ensure that math instruction builds on what each

child knows.

Recommendation 4: Teach children to view and describe their world mathematically

Recommendation 5: Dedicate time each day to teaching math, and integrating math instruction

throughout the school day.

Recommendation 1: Teach number and operations using a developmental progression.

Recommendation 2: Teach geometry numbers, patterns, measurement, and data analysis using a

developmental progression.

Recommendation 3: Use progress monitoring to ensure that math instruction builds on what each

child knows.

Recommendation 4: Teach children to view and describe their world mathematically

Recommendation 5: Dedicate time each day to teaching math, and integrating math instruction

throughout the school day.

1.
Teaching Math to Young

Children

Children

2.
This training provides five recommendations to

teach math to young children.

teach math to young children.

3.
Recommendation 1

Teach number and operations using a developmental progression.

Recommendation 2

Teach geometry, patterns, measurement, and data analysis using a

developmental progression.

Recommendation 3

Use progress monitoring to ensure that math instruction builds on what each

child knows.

Recommendation 4

Teach children to view and describe their world mathematically

Recommendation 5

Dedicate time each day to teaching math, and integrate math instruction

throughout the school day.

Teach number and operations using a developmental progression.

Recommendation 2

Teach geometry, patterns, measurement, and data analysis using a

developmental progression.

Recommendation 3

Use progress monitoring to ensure that math instruction builds on what each

child knows.

Recommendation 4

Teach children to view and describe their world mathematically

Recommendation 5

Dedicate time each day to teaching math, and integrate math instruction

throughout the school day.

4.
Recommendation 1

Teach number and operations using a

developmental progression.

Teach number and operations using a

developmental progression.

5.
Subitizing is the ability to instantly recognize “how many” in a small set.

To identify the number of things by quickly looking at them—not by

counting them one by one.

An example often used to explain this, is to think of dice – we immediately

recognize the number of dots without having to count each one individually.

To identify the number of things by quickly looking at them—not by

counting them one by one.

An example often used to explain this, is to think of dice – we immediately

recognize the number of dots without having to count each one individually.

6.
Meaningful Object Counting: Counting one-to-one and recognizing that the last word

used while counting is the same as the total.

Cardinality- Understanding that the last number word is the total of the collection.

A child who recounts when asked how many candies are in the set that they just

counted, has not understood the cardinality principle.

used while counting is the same as the total.

Cardinality- Understanding that the last number word is the total of the collection.

A child who recounts when asked how many candies are in the set that they just

counted, has not understood the cardinality principle.

7.
Counting-based comparisons of collections larger than three:

Once children can use small-number recognition to compare small

collections, they can use meaningful object counting to determine the

larger of two collections.

Once children can use small-number recognition to compare small

collections, they can use meaningful object counting to determine the

larger of two collections.

8.
Number-after knowledge: Familiarity with the counting sequence enables

a child to have number-after knowledge; to enter the sequence at any

point and specify the next number instead of always counting from one.

a child to have number-after knowledge; to enter the sequence at any

point and specify the next number instead of always counting from one.

9.
Mental comparisons of close or neighboring numbers:

Once children recognize that counting can be used to compare

collections and have number-after knowledge, they can efficiently and

mentally determine the larger of two adjacent or close numbers.

Once children recognize that counting can be used to compare

collections and have number-after knowledge, they can efficiently and

mentally determine the larger of two adjacent or close numbers.

10.
Number-after equals one more:

Once they can mentally compare numbers and see that “two” is one

more than “one” and that “three” is one more than “two” they can

conclude that any number in the counting sequence is exactly one more

than the previous number.

Once they can mentally compare numbers and see that “two” is one

more than “one” and that “three” is one more than “two” they can

conclude that any number in the counting sequence is exactly one more

than the previous number.

11.
What could our mathematical manipulatives be in the early years?

• Loose parts: Natural objects (stones, plant seeds, sticks, etc.) manmade

objects (bottle tops, keys, washers, buttons, etc.)

• Manufactured mathematical resources: Counters, blocks, interlocking cubes,

five and ten frames, mechanical clocks, pattern blocks

• Loose parts: Natural objects (stones, plant seeds, sticks, etc.) manmade

objects (bottle tops, keys, washers, buttons, etc.)

• Manufactured mathematical resources: Counters, blocks, interlocking cubes,

five and ten frames, mechanical clocks, pattern blocks

12.

13.
Recommendation 2

Teach geometry, patterns, measurement, and data

analysis using a developmental progression.

Teach geometry, patterns, measurement, and data

analysis using a developmental progression.

14.
Help children recognize, name and compare shapes, then teach them

to combine and separate shapes.

• Take children on shape walks and ask them to point out the shapes

they see.

• Ask children to bring in things from home that illustrates a particular

shape or locate shapes in the classroom.

to combine and separate shapes.

• Take children on shape walks and ask them to point out the shapes

they see.

• Ask children to bring in things from home that illustrates a particular

shape or locate shapes in the classroom.

15.
Identify patterns as well as, extend correct and create patterns.

• Introduce children to basic repeating patterns.

• Help children lean to extend patterns

• Introduce children to basic repeating patterns.

• Help children lean to extend patterns

16.
Promote children’s understanding of measurement by

teaching them to make direct comparisons and to use

both informal and formal units and tools.

• Children can compare objects as they sort, arrange and

classify them.

• Measurement using non-standard and standard tools.

teaching them to make direct comparisons and to use

both informal and formal units and tools.

• Children can compare objects as they sort, arrange and

classify them.

• Measurement using non-standard and standard tools.

17.
Help children collect and organize information, and

then teach them to represent that information

graphically.

then teach them to represent that information

graphically.

18.
• Math Room Quest

• Describe, Describe, Draw

• Interactive Word Walls (Subject)

Visual supports help make language and

mathematics more comprehensible.

• Describe, Describe, Draw

• Interactive Word Walls (Subject)

Visual supports help make language and

mathematics more comprehensible.

19.
Recommendation 3

Use progress monitoring to ensure that math

instruction builds on what each child knows.

Use progress monitoring to ensure that math

instruction builds on what each child knows.

20.
Use introductory activities, observations, and assessments to determine

each child’s existing math knowledge, or the level of understanding or

skill he or she has reached on a developmental progression.

• Use introductory activities to present a new concept to determine how much of the activity

children are able to do independently.

• Observe using a math activity that addresses a specific skill and observing how children try to

complete or solve the task.

• Use formal assessments to help teachers direct their instruction to particular goals.

The flow of progress monitoring.

each child’s existing math knowledge, or the level of understanding or

skill he or she has reached on a developmental progression.

• Use introductory activities to present a new concept to determine how much of the activity

children are able to do independently.

• Observe using a math activity that addresses a specific skill and observing how children try to

complete or solve the task.

• Use formal assessments to help teachers direct their instruction to particular goals.

The flow of progress monitoring.

21.
Tailor instruction to each child’s needs, and relate new

ideas to his or her existing knowledge.

ideas to his or her existing knowledge.

22.
Recommendation 4

Teach children to view and describe

their world mathematically.

Teach children to view and describe

their world mathematically.

23.
Uncommon technical terms

that are typically associated

with a specific domain.

Amino Acid, Peninsula

Array, equivalent,

Deliberate direct instruction

needed. It helps students build

a web of word knowledge.

Distribute, secure, contribute,

parallel, predict, contrast

Commonly used social

language. We generally acquire

these words through basic

interpersonal communication

or natural exposure.

bed, happy, sad, cold, hungry

that are typically associated

with a specific domain.

Amino Acid, Peninsula

Array, equivalent,

Deliberate direct instruction

needed. It helps students build

a web of word knowledge.

Distribute, secure, contribute,

parallel, predict, contrast

Commonly used social

language. We generally acquire

these words through basic

interpersonal communication

or natural exposure.

bed, happy, sad, cold, hungry

24.
Speaking and Listening strategies:

Anticipatory Guides

Think-pair-share

Gallery Walks

Anticipatory Guides

Think-pair-share

Gallery Walks

25.
Recommendation 5

Dedicate time each day to

teaching math, and integrate

math instruction throughout

the school day.

Dedicate time each day to

teaching math, and integrate

math instruction throughout

the school day.

26.
Plan daily instruction targeting specific math concepts and skills.

• Introduce a concept for the first time or illustrate a concept through an

example that is relevant to children’s everyday lives.

• Embed math in classroom routines and activities.

• Introduce a concept for the first time or illustrate a concept through an

example that is relevant to children’s everyday lives.

• Embed math in classroom routines and activities.

27.
• Highlight math within topics of study across the curriculum.

28.
Why We Need Math Read Alouds?

• One of the best ways to introduce a new math concept or math skill is by

using books, poems or songs. Math read alouds are a visual way to show

math concepts and the stories help promote a high level of student

engagement by sparking their imaginations.

• Math achievement when they enter kindergarten can predict reading

achievement.

• Foundational skills in number and operations sets the stage for reading skills.

• One of the best ways to introduce a new math concept or math skill is by

using books, poems or songs. Math read alouds are a visual way to show

math concepts and the stories help promote a high level of student

engagement by sparking their imaginations.

• Math achievement when they enter kindergarten can predict reading

achievement.

• Foundational skills in number and operations sets the stage for reading skills.

29.
Create a math-rich environment where children can recognize and meaningfully apply math.

30.
Use games to teach math concepts and skills and to give children practice in applying them.

These can provide an engaging opportunity to practice and extend skills.

These can provide an engaging opportunity to practice and extend skills.

31.