Mathematics Knowledge & Skills

Mathematics Knowledge and Skills refers to the conceptual understanding of numbers and their relationships, combinations, and operations. It also includes reasoning, measurement, classification, patterns, and shapes and their structure. Math skills during the early years help children to connect ideas and develop logical and abstract thinking. Young children learn to question, analyze, and understand the world around them.

Toolkit for Professional Development

Use the toolkit's Know, See, Do, and Improve sections to learn about and try best practices in math teaching at the early childhood level. Find tools to review and improve math teaching practices.

The materials in this toolkit are designed as professional development activities and resources. Head Start programs use a research-based curriculum. Some programs choose to add a supplemental curriculum with a focus on math. This kit can be used to enhance a quality curriculum that offers clear content, well-designed learning activities, and a research-supported scope and sequence.

Know / Read About It

Learn about high-quality math teaching at the early childhood level and important concepts in young children's math learning.

Key Concepts

Looking for "big-picture" messages about teaching math to young children? These resources provide a quick overview.

Mathematics Knowledge & Skills
This video highlights the elements of the Head Start Child Development and Early Learning Framework's (HSCDELF) math domain. It gives examples of teachers and children engaged in math learning.

Select the link to watch the entire HSCDELF video.

See pages 16 and 17 of the HSCDELF [PDF, 2MB] for more about the math domain elements.

Math Matters: Recommendations and Research
This presentation focuses on the importance of children's early math learning and ways that teachers can effectively support it. Download the Math Matters PowerPoint Presentation [PPT, 4MB] and Presenter Notes [PDF, 299KB].

What We Know about Early Math Learning [PDF, 119KB]
This article describes effective ways for teaching staff to encourage young children's mathematical skills.

What We Know about Improving Math Teaching [PDF, 105KB]
Read about how to help teachers improve their practices in teaching math to young children.

Selected Resources

Explore these resources for more information about effective math teaching.

Office of Head Start Math Webcasts and Lessons
Watch these six webcasts on math domain elements. They include demonstrations of teaching strategies for early childhood math.

High Five Mathematize: An Early Head Start and Head Start Math Resource Guide
This comprehensive guide outlines ways to support teaching staff in helping children birth to 5 understand developmentally appropriate math concepts.

Front Porch Series Broadcast Calls
The National Center on Quality Teaching and Learning's Front Porch Series includes several presentations on math. Select from the broadcasts below to get started.

Math Teaching Practices: Helpful Resources [PDF, 73KB]
Find resources to encourage young children's math learning.

Math Domain Elements: Helpful Resources [PDF, 78KB]
Discover strategies for teaching children about individual math domain elements.

Math for Infants and Toddlers: Helpful Resources [PDF, 74KB]
The materials listed in this resource discuss ways to support infant and toddler math learning.

Curriculum Guides

These tools can help guide curriculum decisions.

How to Select an Early Mathematics Curriculum [PDF, 77KB]
Explore what questions to ask when evaluating a math curriculum.

Choosing a Preschool Curriculum [PDF, 298KB]
This resource can help programs choose a preschool curriculum and assure high-quality implementation of it.

Head Start Curriculum and Assessment Alignment Tool [PDF, 357KB]
Use this tool to determine how well an early childhood assessment or curriculum aligns with the domains and domain elements of the HSCDELF.

See / Take A Look

Watch these video clips of teachers interacting with young children. Trainers and teachers can use these examples to identify and describe key math teaching practices. This video guide [PDF, 86KB] gives suggestions for ways to use the video to improve math teaching skills or learn new ones. Select the math concepts below to get started.

Number Concepts & Quantities

Counting and Recognizing Quantities

Number Relationships & Operations

Comparing and Combining Quantities

Geometry & Spatial Sense

Exploring Shapes and Space

Measurement & Comparison

Measuring and Comparing


Extending and Creating Patterns

Do / Try It

Use these resources to help teachers practice math teaching skills and create plans to try new strategies in the classroom. Teachers also can get ideas for ways to extend math activities to engage families.

Let's Practice! Staff Learning Activities

These materials can help teachers practice effective math teaching.

Practice and Plan to Mathematize [PDF, 344KB]
Learn more about how to encourage children's math skills throughout the day. Brainstorm language and steps to take to include mathematizing in the classroom.

Let's Check! Are We Using the Curriculum Well? [PDF, 145KB]
These activities can help staff explore their math curriculum.

Math Materials Around the Room [PDF, 60KB]
Identify math materials to put in all areas of the classroom to help children develop math skills.

Math Talk Around the Room [PDF, 63KB]
Teachers can use this tool to brainstorm math language.

Practice Finding the Math [PDF, 644KB]
Learn how language can guide math learning with these photographs of young children doing activities in the classroom.

Snapshots of Math Learning [PPTX, 13.3MB]
Use these photos of children engaged in math learning to enrich professional development programs for teachers.

Planning Tools

Support teachers in planning math activities with these tools.

Mathematics Planning Form [PDF, 55KB]
Teaching teams can use this tool to plan math activities and language that support children's learning throughout the day.

Curriculum Web Planning Tool: Extending Early Mathematics Knowledge Through Planned Learning Experiences Around Books [PDF, 465KB]
These four examples of curriculum webs illustrate ways for teachers to extend math concepts in children’s books to other classroom activities.

Classroom Resources

Enrich math learning with these recommendations for classroom activities.

Math Vocabulary and Phrases [PDF, 76KB]
Teachers can use the math vocabulary and phrases in this resource to strengthen children's math learning.

Math Through Books [PDF, 112KB]
Learn more about how to draw out the math in books to help children learn math concepts.

Finding the Math in Books: Ideas for Teaching Staff[PDF, 743KB]
Find suggestions for how teaching staff can use children’s books to highlight math learning. It includes books with Spanish versions.

Materials to Support Math Learning [PDF, 64KB]
Here's a list of possible math materials to put throughout the classroom to engage children in all types of math learning—patterns, geometry, number concepts and relationships, and measurement.

Math Through Songs and Music [PDF, 105KB]
Check out what math concepts children can learn when they sing common preschool songs!

Math Through Games [PDF, 82KB]
See all the math concepts children can learn when they play a variety of games.

Families Too!

Share these ideas for math learning with families.

A Family Note on Finding the Math [PDF, 349KB]
Offer these tips to families to encourage them to use everyday experiences to help young children learn math.

Improve / Improving Your Practice

Strengthen math teaching by helping teachers review and refresh teaching practices with a peer, a coach, or a teaching team.

Tips in 10

Engage teachers in math learning and reflection during staff meetings with these 10-minute professional development activities. The complete versions of these activities, plus many more, are available in High Five Mathematize. The activities include:

  • Triangle Challenge
    Use sticky notes to make triangles and other shapes (page 111).
  • Picture Posters
    Look at photographs to brainstorm vocabulary and concepts to "mathematize" children’s activities (page 55).
  • Playing with Patterns
    Play with small objects to sort, match, and make patterns (page 153).
  • Finding the Measurement in The Three Bears
    Write down measurement concepts you hear in a children’s story (page 208).
  • Songs and Sums
    Think of ways to use songs to highlight math concepts (page 59).

Taking it to the Classroom

These resources provide ideas for collaborating with teachers as they implement effective practices.

Practice-Based Coaching
Find an overview, research, tips, and ideas for coaching teachers in using effective teaching practices.

Last Reviewed: July 2015

Last Updated: January 6, 2017