Math: Algebra & Functions Foundations and Framework ©2013 California Department of Education (CDE)...

Math: Algebra & Functions Foundations and Framework

©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)


Outcomes• Participants will become aware of key concepts to be

developed in the Algebra and Functions strand of the California Preschool Learning Foundations (PLF).

• Participants will become aware of key strategies in the California Preschool Curriculum Framework (PCF) regarding the development of Algebraic Functioning.

• Participants will consider how to support the development of the Algebra and Functions foundations for Children learning English as a second Language

• Participants will consider how to adapt curriculum to ensure access for children with varying needs.

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Button-Button Button-Button Choose Your Choose Your

ButtonButton



Two California Department of Education Resources

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Early Learning Development System

Start HereStart Here


Summary of Findings

Attending CPIN Math training sessions on the foundations and framework will help teachers meet

these outcomes.

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Rolling on to the Math Foundations

©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies,

California Preschool Instructional Network (CPIN). 05/2013 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)

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FoundationsFoundations

With appropriate supportWith appropriate support

After 1After 1stst or 2 or 2ndnd year of year of preschoolpreschool

At 48 and 60 monthsAt 48 and 60 months

High-quality programHigh-quality program



Domain Organization

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Algebraic Function Foundations

• Sort and ClassifySort and Classify

• Create and Understand PatternsCreate and Understand Patterns


Algebra and Functions Substrands and Foundations


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Connections to Kindergarten

Alignment Document

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http://www.cpin.us/


Early Intervention

Early intervention has positive outcomes for mathematics in kindergarten. The Outcomes of Early Intervention for Infants and Toddlers with Disabilities and their Families, July 2011

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The developmental The developmental continuum for data analysis continuum for data analysis

starts with classification starts with classification and counting and evolves and counting and evolves into data representation. into data representation.

PLF, Vol. 1, p. 162PLF, Vol. 1, p. 162



Museum Walk: Sorting ButtonsBegin By:

1. As a group sort your buttons as many ways as you can (remember to use attributes)

2. Record the ways you sorted.

3. You have 5 minutes and remember to keep your sorting a secret)

Next:1. Rotate Tables (to the

right).

2.Try and identify how the previous table group sorted their buttons.

3.Write your guess on a 3 by 5 card and leave face down.

4.Rotate Again.

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Button Sorting Wrap Up16

We practiced how to: We practiced how to: Engage children in conversations about their sorting and classifying. PCF, Vol. 1, p. 262

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Conversations Considering Dual-Language LearnersScaffold Scaffold communication by communication by combining English combining English words with some words with some type of body gesture type of body gesture or visual cue. or visual cue. PCF, Vol. 1, p. 199PCF, Vol. 1, p. 199


Talk About the Here and Now• Gives the child the chance to narrow down Gives the child the chance to narrow down

what the conversation is aboutwhat the conversation is about

• Allows child to focus in on a more restricted Allows child to focus in on a more restricted number of options to respondnumber of options to respond

• Share the same physical space and have Share the same physical space and have reference to the same informationreference to the same information

• Allows the teacher to provide some missing Allows the teacher to provide some missing vocabulary informationvocabulary information

✔ Stage 1: Home Language

✔ Stage 2: Observational/Listening

✔ Stage 3: Telegraphic/Formulaic

✔ Stage 4: Fluid Use


Teacher facilitation and modeling is Teacher facilitation and modeling is particularly importantparticularly important


Framework Strategies Curriculum planning

should offer children learning

opportunities that are attuned to their

developing abilities.

PCF, Vol.1, p. 2


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Teach this through using rhythmn sticks and music

Music is a highly social, natural, and Music is a highly social, natural, and developmentally appropriate way to engage even developmentally appropriate way to engage even the youngest child in math learning. the youngest child in math learning. (NAEYC The Patterns of Music 2013)(NAEYC The Patterns of Music 2013)


It may be It may be necessary necessary to make to make special special adaptations adaptations to create to create access to access to learning. learning.


1. Find your rhythm sticks

2. Decide how to create a gripper

3. Follow instructions on handout

4. Get ready to learn about patterns©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). (08/2013)

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Types of Patterns in Preschool

• Repeating patterns

• Growing patterns


Repeating Patterns

A certain sequencing of shapes, sounds, or other elements is repeated again and again.

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Growing Patterns

EXAMPLES: Patterns that change from one value to another in a predictable manner.

1 2 3 4 5

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Playing with Patterns

• Find the Playing with Patterns handout.

• Turn to page 268 in the PCF.

• Now you are ready to complete this handout.

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Playing with PatternsPatterns can be presented in different formats:

through movement, soundsound, language, objects, or

picturespictures.. Expressing patterns through different

modalitiesmodalities (kinesthetic, tactile, auditory and visualvisual)

provides different learning modes and facilitates

preschool children’s understanding of patterns. There

are numerous opportunities for children to duplicate,

extendextend, and create patterns through art, music,

movementmovement, literacy, and sciencescience. . PCF, Vol. 1, p. 268PCF, Vol. 1, p. 268

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Let’s try it!Let’s try it!

Rhythm patterns Rhythm patterns can be more can be more engaging than engaging than verbal patterns.verbal patterns.

(NAEYC The Patterns of Music 2013)(NAEYC The Patterns of Music 2013)



Let’s Think about Daily Routine Let’s Think about Daily Routine OpportunitiesOpportunities



Teacher can reflect on opportunities for classifying and

patterning in the daily routine• How could you How could you

integrate sorting and integrate sorting and patterning experiences patterning experiences into the children’s into the children’s current topic of study?current topic of study?

• How do you, or could How do you, or could you, organize your you, organize your classroom classroom environment to environment to facilitate classification facilitate classification activities?activities?


To be effective teachers should:• Respond to each

child individually• Build on the

children’s individual strengths

• Build on the children’s individual ways of learning

PCF, Vol .1, p. 236

Guiding Principle: Guiding Principle: Recognize and support the individualRecognize and support the individual


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Culminating Activity

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Thank you for fitting us intoThank you for fitting us into your schedule! your schedule!


Math: Algebra & Functions Foundations and Framework ©2013 California Department of Education (CDE)...

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