Before you get comfortable… Please take a jaunt around the room and add your information to the...

Before you get comfortable…

Please take a jaunt around the room and add your information

to the Daily Data charts that are posted.

©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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Mathematical ReasoningFoundations and Framework

Volume 1


Outcomes• Participants will become aware of key concepts to be

developed in the Mathematical Reasoning strand of the California Preschool Learning Foundations (PLF).

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

• Participants will consider how to support the development of Mathematical Reasoning 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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Can you put the puzzle together?Can you put the puzzle together?

Preschool Math: Preschool Math: Guiding PrinciplesGuiding Principles


Two California Department of Education Resources


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Early Learning Development System

Start HereStart Here

Summary of Findings7


Domain Organization


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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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Connections to Kindergarten

Alignment Document


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http://www.cpin.us/

Map of the Foundations11

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

FoundationsFoundations

With appropriate supportWith appropriate support

After 1After 1stst or or 22ndnd year of year of preschoolpreschool

At 48 and 60 monthsAt 48 and 60 months

High-quality programHigh-quality program


MathematicalMathematical Reasoning

• ThinkThink

• Reason logicallyReason logically

• Apply math Apply math knowledgeknowledge

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

Mathematical Reasoning is woven through:

• Five math strandsFive math strands

• Daily routineDaily routine

• Teacher interactionsTeacher interactions


Hearing From the ExpertsDr. Clements Says

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“Children like to play with Math.”

Clements, D.H. & Sarama, J. “Creative Pathways to Math,” Scholastic Early Childhood Today Journal, 2003.


http://youtu.be/EYaLrPNtD8I

Research BiteRecent Research indicates that school-entry math skills have the greatest predictive power for later achievement in school, compared with reading, attention skills, and social development.Duncan et al. 2007


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From longitudinal research we know:

Children learn from:Children learn from:– Generalizing solutionsGeneralizing solutions

– Repeating activitiesRepeating activities

– Practicing mental actionsPracticing mental actions

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The Framework:

“…presents strategies and information to enrich learning and development opportunities for all of California’s preschool children.”

PCF, Vol. 1, p. v


Practicing with Vignettes• Turn to page 286 in the PCF.• What opportunities do you see for:

– Generalizing– Repeating– Practicing mental representations

• What other math did you see happening?– (number of steps, etc)


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Universal Design for Learning

• Multiple means of representation

• Multiple means of engagement

• Multiple means of expression


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In Volume 1, Discover Ideas

for:

• EnvironmentsEnvironments

• Building on children’s Building on children’s playplay

• MaterialsMaterials

• Teacher-guided Teacher-guided learning activitieslearning activities


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Research Bite

The number of distinct mathematics activities in which children engage is just as important as total time on task in supporting their learning of mathematics.

Sarama, J., Clements, D.H., Wolfe, C.B., & Spitler, M.E. (2012). Longitudinal evaluation of a scale-up model for teaching mathematics with trajectories and technologies. Journal of Research on Educational Effectiveness, 5, 105-135.

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

Studies, California Preschool Instructional Network (CPIN). (08/2013)

Let’s Watch: Mathematical Reasoning


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Children eagerly engage in Children eagerly engage in mathematical reasoning when: mathematical reasoning when:

• The context is The context is familiarfamiliar

• The problem is The problem is meaningfulmeaningful

• They have an They have an existing knowledge existing knowledge basebase


One More Time• What did you see?• How did that relate

to information on the previous slide?

• What did you notice that was important?

• How might you replicate it in your program?


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What Do the Mathematical Reasoning Vignettes Have in Common?

• Each person at the table chooses a strand card

• Read a vignette in your strand

• Discuss what the adults were doing

• Use Sticky wall (or use sticky notes)

• Are there some things in common?


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Guiding Principle

Provide an environment rich in language, and introduce preschool children to the language of mathematics

PCF, Vol. 1, p. 235


Minute to Win ItOpen-Ended Questions

• Get ready to write

• One minute on the clock

• When I turn the slide come up with as many open ended questions as you can that might be applicable to the photograph.


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Minute to Win It


Mathematically Reasoning Interaction Strategies

• Read handout and highlight something in each section

• Write one of the questions on a sentence strip

• You have five minutes


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Conversations Considering Dual-

Language Learners

Scaffold communication by combining English words with some type of body gesture or visual cue.

PCF, Vol.1, p. 199


Talk About the Here Talk About the Here and Nowand 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


Daily Data in Our DayDaily Data in Our Day


Create learning invitations with objects that Create learning invitations with objects that are relevant and meaningful to the children are relevant and meaningful to the children in your group. in your group. PCF, Vol. 1, p. 238PCF, Vol. 1, p. 238


Environment Materials


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An Few Ideas to Take Back

• What’s my cage?

• Mr. Fur Ball

• Daily Data


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Thank you for coming!


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