Early Childhood Math Practices

• Study notes for understanding early childhood math practices and processes, covering manipulatives, number sense, spatial sense, culturally responsive teaching, technology, and common misconceptions

Manipulatives Resource

• Locally sourced items can be used to teach math concepts
• Bottle caps can teach counting, patterns, sorting, comparing sets, repeating patterns, modeling addition/subtraction/multiplication/division, and fractions
• Stones (small, medium, large) can teach counting, comparing size/weight/sets, repeating patterns, modeling operations, fractions, bar graphs, and data summarization
• Sticks can teach base 10 concepts, measuring length, geometric patterns, and modeling multi-digit addition/subtraction
• Nuts from trees can be used for counting, comparing size/weight, measuring weight, comparing sets, repeating patterns, modeling operations, and data summarization
• Cut newspaper/magazine/catalog/greeting card strips can teach symmetry, properties of polygons, story problems, area models for fractions, and measuring length
• Rubber bands are good for counting and bundling sticks
• Colored paper teaches symmetry, polygons, area models for fractions, and measuring area
• Lines in sand help identify quantities with symbols and measure length
• Leaves teach counting, comparing size/weight, measuring weight, comparing sets, repeating patterns, operating, modeling fractions, and data summarization
• Paper cups teach base 10, counting, and measuring capacity
• Fabric squares can teach measuring area, symmetry, and polygon properties
• Empty soda cans/planks/blocks can teach counting, comparing sets, repeating patterns, modeling operations/fractions, measuring weight, polygon/3D shape properties, and decomposing 3D shapes into 2D components
• Counting cards 1-10 (paper squares) can teach counting, number identification, number properties (odd, even, etc.), and basic facts
• Coins are useful for concepts of money and for doing addition and subtraction of monetary values
• Learning clocks can teach about time, duration measurement, and time conversions
• Lotto games teach number identification, sorting, data gathering, and graphing (colors, numerals, pictures)

Rocking and Rolling. Nurturing Early Math Play and Discovery

• Infants and toddlers develop math foundations by understanding calculations, measurements, comparisons, and spatial relationships through exploration and movement.
• Early exposure to math vocabulary and play during toddler years correlates with better math knowledge later on
• Preschool math skills predict fifth-grade mathematics achievement
• Early math experiences can help address inequities in learning
• Teachers can introduce "big ideas" of early math by using simple activities as part of routines

Sets and Sorting

• This involves noticing item attributes (or features)
• Teachers can provide baskets of fabric swatches with different textures
• Describe the textures as babies explore, and group items into "soft" and "rough" piles

Number Sense and Counting

• Help toddlers grasp concepts by setting up activities such as a dinosaur egg hunt
• Hide plastic eggs around the classroom
• The teacher can ask them to collect one, two, or three eggs

Number Operations

• Teachers can plan a "one more" activity to introduce addition for young toddlers
• As children build a tower and place down two blocks, ask “Should we add one more?"

Shapes

• Give children the opportunity to explore both two and three-dimensional shapes by touching, manipulating, and combining them to make designs or structures to foster age-appropriate learning

Spatial Relationships

• Spatial relationships that infants and toddlers can grasp are On top, under, in, and out
• Give chunky blocks and a bucket so older babies can explore in and out by playing fill-and-dump
• For older toddlers, have a game involving “Teddy Bear and the Chair” where children are asked Where to position the items

Patterns

• Patterns can be found in children's songs and books
• Teachers may choose to sing songs, like Wheels on the Bus or Old MacDonald, or to share rhymes with clear patterns

Measurement

• Measurement is a diverse domain
• Includes temperature (hot or cold), distance, volume, and capacity
• Teachers can engage toddlers with water play and cups, modeling language like full, empty, almost full, and overflowing

Guiding Principles for Early Math Learning Experiences

• Goal is to provide repeated opportunities to explore math concepts through play
• Encourage children to be curious and explore, rather than focus exclusively on securing the right answer

Math Language

• Use math language to describe calculations (add to, take away), quantities (more, less, the same), and measurement (big, bigger, biggest)
• Also describe attributes of the world (color, shape, size) and point out patterns

Mathematize Interactions

• This means using math thinking and talk during play or routine activities
• When feeding the classroom fish, count how many fish are in the bowl
• During diaper changes, count baby toes or sing a song

Daily Instructional Routines

• These routines can help promote number sense and spatial sense

Number Sense Routines

• Walk & Count involves verbally counting while walking
• More or Less helps practice quantifying and identify items with more or less of a quantity
• Thumbs Up, Thumbs Down reviews previously learned math
• If I Have, You Have reviews math with a target number, where the target will need to be obtained by adding on to the known figure

Spatial Sense Routines

• I Spy helps students notice geometric objects around them using specific characteristics
• Sticks & Shapes lets students are building shapes with sticks based on characteristics provided

Culturally Responsive Teaching

• Culturally responsive teaching incorporates student well-being
• To be effective, it should include communication of high expectations, supports and scaffolds, regular math conversations, critical thinking, and empowered students

The Role of Technology in Early Childhood Learning

• Computers are increasingly prevalent in preschoolers' lives
• Comfort and confidence are seen in young children using software
• Children with disabilities can use computers to enhance mobility and control
• Research has dismissed concerns that computers might isolate children, and are actually a catalyst for social interaction

Teaching and Learning Mathematics

• Computers offer unique learning opportunities through exploration, problem-solving, and instruction
• Software aids mathematical idea development

Calculator Activities for Young Learners

• These can help teach various math concepts to young children

Activity Ideas

• Say It, Press It
• Oral Skips Count
• Broken Keys
• Broken Keys Extended
• Two Jumps to 10
• Three Jumps to 15
• Four Jumps to 20

Number Patterns

• This is useful for investigation of patterns using calculator tools

Misconceptions/Error Pattern

• The child skips numbers or goes out of order
• The child only count up to a certain point and then the numbers are random

Addressed Misconceptions

• Use numbers for practice and correct the puppet's mistakes
• Engage the children in practice counting for and backwards
• Prepare cards with numbers and have the children identify the items