Addressing Early Numeracy Concepts and Skills in WashingtonSTARTING STRONG AUGUST 2015

TACOMA, WA

IntroductionsAmanda Baumgartner -Regional Math Coordinator ESD 123

Rachel Eifler -Early Numeracy Consultant ESD 101

Remy Poon - Pre K – 5 Math Systems Consultant ESD 121

Dawn Sparks - Regional Math Coordinator ESD 105

Julie Wagner - OSPI Early Numeracy Champion

Welcome….

Why was the math book sad?

What’s the king of the pencil case?

Heard about the new mathematical plant?

What does the 0 say to the 8?

What do you get if you divide the circumference of a jack-o-lantern by its diameter?

Thinking about Our Experience

What was your education in mathematics like?

Stand by the number that represents your experience.

"Boy, Girl Standing" by pixabay.com is in the Public Domain, CC0

Meaning and Sense-MakingInformation is most likely to get stored if it makes sense and has meaning.

It makes sense if the learner can understand the mathematical content based on previous experience.

It has meaning if it is relevant to the learner.

Of the two, meaning has the greater impact on the probability of retention.

How the Brain Learns Mathematics, Sousa (Year)

Children Are Young Mathematicians

“Throughout the early years of life, children notice and explore mathematical dimensions of their world. They compare quantities, find patterns, navigate in space, and grapple with real problems such as balancing a tall block building or sharing a bowl of crackers fairly with a playmate. Mathematics helps children make sense of their world outside of school and helps them construct a solid foundation for success in school.”

6

NAEYC Position Statement 2010

What do you

see?

What does it

mean?

What

considerations

might be made?

Overview of the Three ModulesC o u nt i ng a n d C a rd i na l i t y

O p e rat i on s a n d A l ge b ra i c T h i n k i ng

G e o m e t r y

Counting and CardinalityThe Counting and Cardinality module helps participants understand what children must learn in order to learn the counting sequence and understand the quantity associated with each number. Subitizing, which helps children know quantity without counting it, can begin with small numbers. Comparing quantities creates a later need for operation. Participants will explore each of these topics by doing hands-on activities associated with each.

Operations and Algebraic Thinking- blurb

GeometryThrough the geometry module, participants will explore the early learning pathways for geometry and develop a deeper knowledge of how children progress in their understanding of geometry and spatial sense. Participants will engage in hands on activities that can be easily replicated in the classroom to further develop students' understanding of geometric concepts. Handouts of ideas, activities and resources will be provided.

Digging into the Modules

Counting and Cardinality

Counting and Cardinality –Overview from Standards

The counting sequence underlies all of mathematics and is a first step in a child's understanding of mathematics. The pathway goes from:

◦ saying the counting words to counting out objects.

◦ subitizing to single-digit arithmetic fluency.

◦ counting to counting on.

◦ comparison by matching to comparison by number to comparison involving adding and subtracting.

Learning Pathways in Numeracy ActivityWork at your tables to put the math progression statements in order:

◦ Counting

◦ Subitizing/Early Operations

◦ Comparing and Ordering

At your tables…

Learning Pathways in Numeracy

Counting and Cardinality Domain

How do the Learning Pathways in Numeracy help us work with students?

There are general progressions of learning at early stages in numeracy.

Observation will help teachers see whether children are progressing or stagnant in their learning.

If a child is unable to do a task, the teacher can go back and find where he needs to build knowledge in order to progress.

Teachers need to know where a child is so she can take him further.

Common Core Domains

How many do you see?

How many do you see?

What patterns did you see?

How is this image different from the previous one?

Perceptual vs. Conceptual Subitizing

Perceptual – Being able to tell the number of objects in a small collection without counting them.

Conceptual – Seeing the parts in a collection and joining them to make a whole without counting them.

Subitizing lays the groundwork for operations, counting on, and base-ten understanding.

Build Subitizing with CardsDawn has the idea – will do this

Subitizing –Why teach it?Children can visualize quantity without counting.

Subitizing helps children understand part-whole relationships.

Understanding part-whole relationships supports addition and subtraction operations.

Practice with subitizing activities makes it easier to count and work with numbers.

Operations and Algebraic Thinking

Overview from Standards OA

Activity:In-Out Shake and SpillObjective:

Practice finding combinations of numbers within 10

Materials:

Shake and Spill Recording Sheets

2-sided colored counters

Paper Cups

Activity: Five Octopi

1 octopus, 2 Octopi, 3 octopi, 4 octopi, 5,

5 octopi swimming in the sea,

Everyone’s swimming, happy as can be.

Oh, no! Here comes a shark. Black ink’s a’ coming…Some run hiding…everyone’s running.How many octopi do you see?

Reflecting on the Activities: Shake and Spill & Five Octopi

• Where does this activity fall on the Pathway (Learning Pathways…)?

• How can this activity be adapted to meet the needs of your students (interventions and extensions)?

• What can be assessed from this activity (formative assessment)?

Geometry

GeometryGeometric and spatial thinking are important in and of themselves, because they connect mathematics with the physical world…

They are also important because they support the development of number and arithmetic concepts and skills. Thus, geometry is essential for all grade levels.

Geometry involves: Geometric shapes, their components (e.g., sides, angles,

faces), their properties, and their categorization based on those properties.Composing and decomposing geometric shapes.Spatial relations and spatial structuring.

Common Core Writing Team (2013)

3-D Shapes What do the Washington State Learning Standards say?

K.G.A.3Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid").

K.G.B.4Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describetheir similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length).

K.G.B.5Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

"3D_Shapes " by 2dand3dshapes.wikispaces.com is in the Public Domain, CC0

“Children need to hold and manipulate objects before they work with paper representations of objects. The same is true as children explore geometric shapes. Building with three dimensional shapes, rolling them down ramps, tossing them as targets, and modeling three dimensional shapes with clay are all good beginning activities for children. Three-dimensional shapes should be used to introduce the two-dimensional shapes, for example, by making block prints in water, paint or clay. The resulting prints can be identified as the more common two-dimensional shapes (e.g., a cube makes square prints, a square pyramid makes four triangle prints and one square print.)”

COPLEY, J.V., JONES,C.,& DIGHE, J. (2010) THE CREATIVE CURRICULUM (R) FOR PRESCHOOL, VOLUME 4: MATHEMATICS (5TH ED.) WASHINGTON, DC: TEACHING STRATEGIES, LLC.

Begin with Three-Dimensional Shapes

Transform

Students use play dough to create three-dimensional shapes

As you watch this video reflect:

• Where does this activity fall on the Learning Pathways in Numeracy document?

• How are the CCSS-M standards addressed?

https://www.youtube.com/watch?v=1nD1R5D69nQ

Learning Pathways in Numeracy

Learning Pathways in Geometry Geometry consists of three categories:shapes

spatial relationships/structuring

geometric measurement

Mystery Bag Directions: One person from the group will place his or her hand inside the “mystery bag” and feel the shape. Describe the attributes that you feel (polygons within, faces, vertices, etc.) See if the group can guess your shape.

•What can you assess from this activity?

•Where is it in the learning pathways document?

Wrap Up

Summary of Modules and Work Research and purpose

3 modules experience

What are the three modules?

Counting and Cardinality

Operations and Algebraic Thinking

Geometry

Work to be continued….For us:

•Develop more modules e.g. Measurement/Data

• Extend the 3 hours modules to the 6 hours modules

For you:

• Come and invite others to attend the courses

offered at your local ESD.

Tips•Count everything: model counting objects by pointing to each object as you say the numbers

•Use number vocabulary as much as possible: instead of saying “Please put those balls away,” say “Please put those 2 balls away.”

•Use geometric vocabulary and help children understand shapes using both two and three dimensional objects. For example, explain, a cylinder is like a can, a ball is called a sphere.

Tips•Encourage children to work puzzles. Let children figure out where the pieces go and use terms such as turn, slide and flip to help them decide how to place the pieces.

•Embrace block play in daily routines.

•Let children figure things out for themselves as much as possible. I know it’s hard! We want to rescue our children and it’s difficult to see them struggle, but struggle is how we learn and how we develop problem solving skills.

•Most importantly, make it fun and be positive about math!

Contacts HandoutContacts for EL Coordinators◦ Contact of Regional Math Coordinators

Information about each module

Reflection1. What is something you learned or will take away

from this presentation?

2. What questions do you still have?

3. What will you need to further implement this work?

Thank you! Please leave your evaluations at the door.