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The Alignment of Early Numeracy Skills

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### The Alignment of Early Numeracy Skills

Bethel P-3 Professional Learning Community

November 3, 2011

Julie Wagner

Elementary Mathematics Specialist

OSPI

Goals

Introduce participants to:

- Current research that supports a
P-3 numeracy alignment

- The Common Core State Standards domains and alignment of P-3
- Trajectories of learning
- Resources available

A Meta-Analysis

School Readiness and Later Achievement

Duncan, et al, Developmental Psychology, 2007.

The strongest predictors of later achievement are school-entry math, reading, and attention skills. Early math skills have the greatest predictive power. By contrast, measures of socio-emotional behaviors were generally insignificant predictors of later academic performance, even among children with relatively high levels of problem behaviors.

Review of Research

Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity

National Research Council, 2009.

The committee found that, although virtually all young children have the capability to learn and become competent in mathematics, for most the potential to learn mathematics in the early years of school is not currently realized. This stems from a lack of opportunities to learn mathematics either in early childhood settings or through everyday activities in homes and in communities.

Article by NCTM President

A Missed Opportunity: Mathematics in Early Childhood

Henry Kepner, NCTM Summing Up, February 2010.

Prior to kindergarten, many children have the interest and capacity to learn meaningful math and acquire considerable mathematical knowledge. Many early childhood programs do not extend children’s mathematical knowledge. Instead, they have these young students repeat the same tasks in varied settings without posing challenges that would push them to the next level.

Social Policy Report

Mathematics Education for Young Children: What It Is and How to Promote It

Ginsburg, Lee, & Boyd, Society for Research in Child Development, 2008

Cognitive research shows that young children develop an extensive everyday mathematics and are capable of learning more and deeper mathematics than usually assumed.

Typically, early childhood educators are poorly trained to teach mathematics, are afraid of it, feel it is not important to teach, and typically teach it badly or not at all.

What does all this mean?

Children can learn much about mathematics early in their lives.

The numeracy skills children walk into the door with in kindergarten predicts later achievement in math and reading.

Numeracy skills are often overlooked in child care settings through lack of precedence, neglect or fear.

If kindergarten teachers had students who had numeracy skills, achievement would increase dramatically.

The CCSS Document alignment

Design and Organization alignment

Standards for Mathematical Practice alignment

Make sense of problems and persevere in solving them

Reason abstractly and quantitatively

Construct viable arguments and critique the reasoning of others

Model with mathematics

Use appropriate tools strategically

Attend to precision

Look for and make use of structure

Look for and express regularity in repeated reasoning

Overview Page alignment

Domains, Clusters, Standards alignment

16

Common Core State Standards for alignmentMathematics - Domain Development

Kindergarten Standards alignment

- The Common Core State Standards in Mathematics at the kindergarten level include all of early numeracy…for a reason.

Common Core State Standards for alignment Mathematics - Domain Development

Pre-Kindergarten Mathematics Standards alignment

Number and Operation alignment

What does it mean to count?

Number and Operation alignment

Concepts in counting:

- Recognize counting words
- The sequence of numbers
- One-to-one correspondence
- Cardinality
- Reverse of cardinality

Number and Operation alignment

One-to-one correspondence

Children have to know sequence of numbers and remember the sequence and where they are in the sequence as they count in order to master one-to-one correspondence – assigning one, and only one, number to each object in a group.

Number and Operation alignment

Cardinality

Child moves from just saying the number sequence to understanding that the last number stated answers the question, “How many?”

Number and Operation alignment

Reversal of cardinality

Child can be asked to, “Give me eight blocks,” and is able to count out the correct amount. Why would this be more difficult?

Order of Counting alignment

- Small numbers first
- In a line
- In a circle
- In a pattern
- Scrambled

Counting Trajectory alignment

Counting Trajectory alignment

Learning and Teaching Early Math: The Learning Trajectories Approach, Clements & Sarama, 2009

Number and Operation alignment

Beginning components of operation

- Subitizing
- Comparison words
- Modeling

Number and Operation alignment

Subitizing

Knowing how many are in a collection without counting.

How valuable is this skill?

What is its role in operation?

Number and Operation alignment

Comparison words

Bigger, smaller

Longer, shorter

Less, more

Lighter, heavier

Comparison Trajectory alignment

Learning and Teaching Early Math: The Learning Trajectories Approach, Clements & Sarama, 2009

Comparison Trajectory alignment

Learning and Teaching Early Math: The Learning Trajectories Approach, Clements & Sarama, 2009

Comparison Trajectory alignment

Learning and Teaching Early Math: The Learning Trajectories Approach, Clements & Sarama, 2009

Operation (+/-) Trajectory alignment

Learning and Teaching Early Math: The Learning Trajectories Approach, Clements & Sarama, 2009

Operation (+/-) Trajectory alignment

Learning and Teaching Early Math: The Learning Trajectories Approach, Clements & Sarama, 2009

Shape (Geometry) alignment

- Recognition of basic shapes
- Application to world around us
- Classification and sorting

Trajectory for Shapes alignment

Learning and Teaching Early Math: The Learning Trajectories Approach, Clements & Sarama, 2009

Trajectory for Shapes alignment

Learning and Teaching Early Math: The Learning Trajectories Approach, Clements & Sarama, 2009

Trajectory for Shapes alignment

Measurement alignment

- Assigns a number to a measureable attribute of an object, usually length, weight, capacity or mass
- In the CCSS, connections between measurement and whole number operations and number line

Length Trajectory alignment

Learning and Teaching Early Math: The Learning Trajectories Approach, Clements & Sarama, 2009

Length Trajectory alignment

Learning and Teaching Early Math: The Learning Trajectories Approach, Clements & Sarama, 2009

A look at available resources alignment

Resources alignment

OSPI Website - Common Core State Standards

Common Core State Standards

Transition Documents

Learning Progressions (trajectories)

Arizona examples

Learning and Teaching Early Math: The Learning Trajectories Approach, Clements and Sarama (2009)

Early learning trajectories, pre-k standards

Sources of your own

Reflections and Questions alignment

Thank you for undertaking this important work! alignment

Office of Superintendent of Public Instruction

360-725-6233

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