Oregon Early Childhood Foundation: Ages Three to Five - Mathematics

Overview

Young children grow up developing an informal knowledge of mathematical relationships and concepts that are broad and complex. Their early learning experiences are the gateway to “Mathematical Literacy” and provide the foundations for development of the knowledge and skills needed to participate effectively in mathematical situations relevant to real life situations.

Mathematics helps young children begin to make sense of the world in which they live. Children are observers. They tend to make comparisons, and see similarities and differences in toys, objects and materials. As they proceed in development, they increase their ability to organize information. Learning to recognize and create patterns, categorize, predict and use data to solve problems helps children learn about numbers, space and time.

Play provides an opportunity for developing children to explore and construct mathematical ideas and gain an understanding of mathematical concepts. Simple activities like playing in the sandbox, building in the block area, and cooking lead to an understanding of volume, measurement, weight, classification, seriation and conservation, and offer opportunities to create and solve problems. Playing with number and counting games as well as manipulating shapes and puzzles are also significant to the child’s later success using math. Each is an engaging activity that allows children to develop the thinking skills they will use throughout life. Children learn the use of mathematics to describe and/or explore relationships within their environment. They begin to develop the vocabulary, skills and concepts of counting, adding and taking away, measuring, describing, and expressing order and position. Using a child’s own mathematical ideas and understanding to guide curriculum development is essential to assisting children in developing relationships between concepts and skills toward forging a strong conceptual foundation.

Parents, early childhood teachers and caregivers who are flexible can capture the teachable moments during daily routines and exercises by using open-ended questions. Planning activities that build on young children’s experiences, curiosity and enthusiasm helps children develop foundational math concepts.

Oregon K-12 Standard: Mathematics uses numbers and symbols to define, communicate and solve problems.

Head Start Child Outcomes Framework: Mathematics

Early Childhood Foundations: Numbers and Operations

Children develop an awareness of numerals by:

• Counting, grouping and matching
• Number recognition
• Using language to describe a sequence of events in time

Indicators:Observable Behaviors

The Child

• Counts up to ten.
• Uses number concepts and vocabulary such as: first, last, next to, before, after, etc.
• Combines, separates and names “how many” concrete objects.
• Uses words such as more than and less than to express some number concepts.
• Recognizes numerals 1 – 20.
• Uses words such as yesterday, today and tomorrow in conversation.

The Adult

• Provides opportunities, materials and activities for counting (number puzzles, finger plays, books, songs, grouping objects) that allow children to play with and develop the language and concepts of mathematics.
• Uses descriptive words throughout the day such as yesterday and today in conversation.

Supportive Learning Environments Include

• Mathematics materials for sorting and counting, available and easily accessible to the children throughout the day.
• Numbers posted throughout the home or educational environment.
• Pictures, posters and signage that include numbers and number words (clocks, timers, measuring cups, scales, number lines, calendars, etc.).

Early Childhood Foundation: Geometry and Spatial Sense

Children develop knowledge of geometric principles and spatial sense by:

• Correctly using comparison words and words that describe the relative position of things
• Classifying shapes
• Using shapes to make representative patterns
• Grouping objects (all large, all yellow, some big and others small, etc.)
• Providing reasoning for groupings

Indicators: Observable Behaviors

The Child

• Recognizes simple shapes.
• Compares various sizes of items (longer, shorter, same).
• Describes, compares and names common shapes, their parts and attributes (circle, square, triangle, round, three sides, etc.).
• Uses descriptive words such as: up, down, over, under, top, bottom, inside, outside, in front of and behind.

The Adult

• Ensures there are numerous blocks of various shapes and sizes, and encourages children to identify shapes, sizes and to make comparisons.
• Provides materials and opportunities for children to play with and create designs with pattern blocks, to paint and cut shapes in their artwork, to arrange blocks on the storage shelves by sorting and encourages identifications of shapes in their indoor and outdoor environments.

Supportive Learning Environments Include

• Numerous and varied purchased and homemade materials that promote the discovery of mathematical principles and concepts such as cut out shapes, varied plastic containers and geometric blocks.

Early Childhood Foundation: Patterns and Measurement

Children develop knowledge of patterns and measurement by:

• Recognizing and creating patterns
• Duplicating and extending simple patterns
• Using non-standard and standard measurement tools
• Recognizing a variety of measurement types (weight, length, etc.)
• Developing awareness of elements of time

Indicators: Observable Behaviors

The Child

• Recognizes, duplicates and extends simple patterns using a variety of materials.
• Creates original patterns.
• Makes predictions about what might come next in a pattern.
• Explores, compares and describes length, weight or volume using items in the environment (strings, cubes, blocks, sticks, rulers, cartons etc.).
• Shows awareness of time concepts (shows interest in calendar, clock, today, next week, etc. ).

The Adult

• Talks with children about quantity, comparisons and time as they play and interact with materials throughout the day.
• Demonstrates and encourages children to explore a variety of ways to measure things. (“This shelf is four books tall.”).
• Encourages children to “guess” or “predict” what will come next in a pattern or sequence of events.

Supportive Learning Environments Include

• Numerous and varied materials that include size, texture, color and shapes that can be used for sorting, comparing and measuring.
• Standard measuring tools (rulers, measuring tapes and cups, scales, etc.).

Resources

Children’s Mathematical Thinking: A Developmental Framework for Preschool, Primary and Special Education Teachers; Arthur J. Baroody

The Block Book, 3rd Edition; Elisabeth S. Hirsch

Counting Caterpillars and Other Math Poems; Betsy Franco

Graphing Across the Curriculum; Valeriein Williams

Learning Through Play: Math a Practical Guide; Sandra Waite-Stupiansky

Math for the Very Young: A Handbook of Activities for Parents and Teachers; Lydia Polonsky, Dorothy Freedman, Susan Lesher and Kate Morrison

Math Games and Activities From Around the World; Claudia Zaslavsky

Mathematics in the Early Years; Jauanita V. Copley

Number in Preschool and Kindergarten: Educational Implications of Piaget’s Theory (NAEYC); Constance Kamii

Showcasing Mathematics for the Young Child: Activities for Three, Four, and Five-Year- Olds; Juanita V. Copley

Spotlight on Young Children and Math; Derry G, Koralek

Early Childhood: Where Learning Begins, Mathematics; Carol Sue Fromboluti

Books for Children

Anno’s Counting Book; Mitsumasa Anno

The Doorbell Rang; Pat Hutchins

Eating Fractions; Bruce McMillan

The Greedy Triangle; Marilyn Burns

Hide and Snake; Keith Baker

How Many, How Many, How Many; Rick Walton

Is a Blue Whale the Biggest Thing There Is?; Robert E. Wells

Moja Means One: Swahili Counting Book; Murial L. Feelings

Over in the Meadow; Ezra Jack Keats

Too Many Tamales; Gary Soto

This product is made possible in whole or in part with funds from the Oregon Department of Education and the Department of Employment, Child Care Division.