Supporting Early Math Skills: A Key to Kindergarten Readiness Day 2 The Visible Child Initiative August 18, 2015 Beth Menninga [email protected].

Supporting Early Math Skills: A Key to Kindergarten Readiness

Day 2

The Visible Child Initiative August 18, 2015 Beth Menninga [email protected]

Checking in with those who were here last time….

Did anyone try playing games?

Any other thoughts before we continue exploring other math domains?

Research based national standards say children need to learn about….

Charts & graphs

Patterns

Measurement

Shapes and spatial sense

Numbers and operations

using these mathematical processes

use math vocabulary and ask questions

In preschool math

is not focused on having the

“right answer”, it’s about

encouraging mathematical

thinking

Let’s sort!

Why sort?

Sorting teaches about…

•Similarities and differences (including matching)•Noticing attributes (that may help define something) such as size, color, shape•Sets (collections)•Comparing and ordering

Initially, children sort before they count the number of items in each group (Clements, 2003).

Children sort objects into groups before they can describe the groups with a label (Russell, 1991).

Sorting continuum of activities(The Early Math Collaborative, 2014)

Exact match• “Same” or “Different”• Socks, lotto games, some puzzles

Single sorts (one or two sets)• Making a set of objects with the same attribute/s• “what’s my rule?” • “Thing/not thing” sort

Multiple set sort• One attribute, many sets• Can be sorted multiple ways

Compare sets• More? less? the same? • Can be graphed or tallied

Shapes and Space

“The understanding of foundational concepts in three areas of geometry-- two- and three-dimensional shapes, spatial relationships, and symmetry and transformations – should be a focus of curriculum experiences for young children.” (National Council of Teachers of Mathematics, 2000)

SHAPES

•Physical knowledge of shapes•Language related to shapes

cube

SHAPES: stages

Informal deduction (6+ years old)

Form logical deductionsUnderstand why a square is always a rectangle but a rectangle is not

always a square.

DescriptiveNotice attributes of shapes Example: triangle has 3 sides and 3

“points”

VisualSee shape as a whole Example: rectangles look like doors

Van Hiele, 1986

Exploration with shapes helps children move from the VISUAL to DESCRIPTIVE stage

VISUAL DESCRIPTIVE

Making 2-D Shapes

•Make as many shapes as you can with the post it notes. Label them as you can

2- AND 3- DIMENSIONAL SHAPES

• Attribute – In Mathematics, the attribute is a characteristic to describe an object. The attribute usually refers to the shape, size or color.• Learning attributes of shapes:

• edge

• side/face

• angle/corner

• curved, straight

• flat (2 dimensional) and 3-dimensional

What Do Children Know About Shapes?

Interviews with 128 children ages 3 to 6 years• Most children (96%) know something about circles.• Most children (87%) know something about squares, and

“tilted squares.”• Children were less accurate (60%) identifying triangles.

Errors of omission (long triangles are rejected) and errors of inclusion (anything “pointy” is a triangle). • Children were less accurate (54%) identifying rectangles

(54%) (made errors of inclusion)

Clements & Sarama, 2000 TCM; Clements et al., 1999 Slide courtesy of M. Mazzocco, U. Of Mn.

What Do Children Learn about Shapes?

• Triangles: few gains from preschool to middle school• 60% of preschoolers accurate identifying triangles.• 64% of kindergartners, 81% of 6th graders

• Rectangles• 54% of preschoolers accurate identifying triangles.• 63 - 68% of elementary school children

• CONCLUSION: opportunity to teach about shapes in preschool; may have long term benefits

Clements & Sarama, 2000 TCM; Clements & Battista, 1992 Slide courtesy of M. Mazzocco, U of MN.

Teaching attributes

•Rectangles and squares•Triangles

RECTANGLES: Dos and don’tsDO SAY:• A rectangle has 4 sides

with opposite sides the same length• A rectangle has 4 right angles or corners• All lines are connected and straight• A square is a special kind of rectangle,

where are the sides are the same length

90° 90°

90°90°

RECTANGLES: Dos and don’ts

DON’T say:• Rectangles are long• All rectangles have 2 long sides

and 2 short sides• Rectangles are like any 3-D shapes

such as a shoe box

TRIANGLES: dos and don’tsDO say: • Triangles have 3 sides • Triangles have 3 points or corners• All sides of a triangles are straight• All sides of a triangles are connected• Triangles may vary in orientation,

size, symmetry or pointedness

TRIANGLES: dos and don’ts

DON’T say: • Triangles have 2 points on the bottom

and 1 on top• Triangles have a point in the middle• Triangles have a flat bottom• Triangles can be made from

any 3 line segments• Triangles are like the open triangle

used in music or cone-shaped clown hat

??

Improving Early Shape Understanding

• Use examples (“non-traditional”)• Watch out for misconceptions

“All diamonds are squares” (not true) “That’s a square, not a rectangle” (not true)

• Expand on what children know!• Ask about their reasoning: “How do you know?”• Attend to vocabulary – is it understood by

children? “side” “angle”

Clements & Sarama, 2000 TCM; Clements et al., 1999 Slide courtesy of M. Mazzocco at U. of MN.

SPACE: manipulating shapes

•Children:•Compare and match•Take apart and put together•Move and reorient•Understand and use positional words•Represent ideas and objects

SPACE

“Thinking spatially—that is, visualizing objects in different positions and imagining their movements—is important to young children’s development as mathematical thinkers” (Copley, 2010)

Let’s make a tangram

Link to online video clip instructions:http://earlymath.erikson.edu/tangram-puzzles-make-one-for-your-kids/

Can you make something that looks like…

OR

TRANSFORMATIONS

A transformation means that a shape has changed position while retaining the same size, angles, area and line lengths.

Symmetry

Symmetry refers to a similarity of form, arrangement, or design on either side of a dividing line or around a point.

Research says…

“Preschool children who hear their parents describe the size and shape of objects and then use those words themselves perform better on tests of their spatial skills.” (Pruden, Levine & Huttenlocher, 2011)

45 more words= 23% average increase on non-verbal assessment of spatial thinking

“Circle, triangle…”

“Edge, bent, corner…”

“tall, wide….”

Also….

•Children with more puzzle play developed stronger STEM centric concepts •Girls show greater benefit from spatial exploration activities • Girls have greater challenges solving spatial problems starting at age 4)• Adults tend to use more spatial language with boys(Levine et al, 2012)

Research says…

“Children who are skilled in understanding how shapes fit together to make recognizable objects also have an advantage when it comes to learning the number line and solving math problems.”(Gunderson et al, 2012)

What do we measure?

Which is bigger?

Which is more?

Which is heavier?How do you know?

How do we measure?

•Comparing•Ordering

Comparison strategies (Copley 2010)

Perception-based (visual)

Direct comparison

Quantitative (number)

Measurement Tools:

•For fairness andprecision we use units•Non-standard or•Standard

Patterns all around us

What is a Pattern?

•Repetition

•Equality & symmetry

•Analysis of change (what is the rule?)

Children Learning Patterns

• Sorting and Classification

• Recognition of a pattern

• Copying a pattern

• Extending a pattern

• Creating a pattern

Initially, children sort before they count the number of items in each group (Clements, 2003)

Children sort objects into groups before they can describe them with a label (Russell, 1991).

Patterns

•Repeating patterns

•Growing patterns

•Analyzing Change

Growing PatternsIllustrates plus-one patterns

Growing patterns

• Use songs and rhymes to teach a growing pattern• The Ants Came Marching One by One, The Little Old Lady Swallowed the Fly

• Read books with growing patterns• Mrs. McTats and Her Houseful of Cats• My Little Sister Ate One Hare

Describing Change

• Describe change in terms of numbers i.e. “How tall did the plant grow?”• Describe change in growth, i.e. bodies, trees, animals• Describe change in appearance• Change books:• Do You Know Which Ones Will Grow?• When I Was Little: A Four-Year-Old’s Memoir of her Youth

Charts, Graphs and Estimation: using data to find answers

What Skills are developed?

• Sorting • Counting• Collecting specific information• Looking for patterns and meaning• Estimation• One to one counting, quantification, set comparison, addition and

subtraction

What Does Research Say?Initially, children sort before they count the number of items in each group (Clements, 2003)

Children sort objects into groups before they can describe them with a label (Russell, 1991).

The normal developmental progression of graphic representation is concrete (i.e. using physical objects like toys, to make the graphs) to pictorial (i.e. using pictures of objects, like drawings of toys) to symbolic (i.e. using letters to present the color of toys, like b for a blue car and r for a red car) (Friel, Curio, & Bright, 2001)

Interactions are key during….

•Play•Games•Exploration

Families

•Math talk•Games provide a natural opportunity for math talk

Where’s the math in

family life?

at your tables

Brainstorm possible math activities for families

Some themes to remember….

CountingComparingOrderingComposing/decomposingRelationships between thingsAttributes: getting specific

Where are opportunities to

promote curiosity in the midst of

transition?

Some online early math resources

• Erikson Early Math Collaborative http://earlymath.erikson.edu/ • NAEYC articles on families and math http://

families.naeyc.org/learning-and-development/music-math-more/math-talk-infants-and-toddlers• www.Bedtimemath.org Ideas for families with children ages 3-8• http://

www.zerotothree.org/child-development/early-development/supporting-early-math-skills.html • http://

eclkc.ohs.acf.hhs.gov/hslc/tta-system/ehsnrc/cde/curriculum/nycuearlymathlear.htm