Mathematics Knowledge & Skills Framework icon

Mathematics Knowledge & Skills refers to the conceptual understanding of numbers, their relationships, combinations, and operations. Mathematics also includes shapes and their structure; reasoning; measurement; classification; and patterns. Because math is also about generalizations and abstractions, math skills during the early years help children to connect ideas, develop logical and abstract thinking, and to question, analyze, and understand the world around them. Math knowledge, interest, and skills are basic to children's success in school and later life. Early math skills are highly predictive of later academic achievement in multiple subject areas. In the domain of Mathematics Knowledge & Skills, programs need to ensure that children who are dual language learners can demonstrate their abilities, skills, and knowledge in any language, including their home language.

Strategies to Advance Children's Understanding of Number Concepts & Quantities

  • Encourage children to count all sorts of objects and events and to think about quantity and number.
  • Arrange materials and use games and verbal encouragement to involve children in — matching and sorting objects by color, shape, size, and other features; and using one-to-one correspondence (one napkin at each person's place at the table, for instance).
  • Draw children's attention to numbers around them and what they are used for, such as finding addresses, prices of objects, and shoe sizes.
  • Use strategies to help children learn to count accurately and efficiently, such as conveying to children that counting lets us know how many things there are in a group; pointing to each object in turn as the person counting (be it the child or the teacher) calls out each number name; and making use of fingers to count and encouraging children to do so.
  • Explore number concepts from the perspective of various cultures and languages. Perhaps children have an interest in counting and knowing how different cultures or languages represent numerals and quantities.

Domain Element: Number Concepts & Quantities

Title of Resource Type of Resource Notes
Where's the Math (Webcast #1) Hoop Game Lesson

En Español
Video and Lesson Ways for teachers and home visitors to support children in building their understanding of numbers, using "five" as an example.
Putting It All Together (Webcast #6) Bag Grab Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this game to help children improve counting skills and better understand the concept of "zero".
Putting It All Together (Webcast #6) Snake Game Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this activity to help children count and reinforce the concept of "zero".
Putting It All Together (Webcast #6) Watering Hole Lesson

En Español
Video and Lesson Adults can use this exercise to help children learn estimation.
Putting It All Together (Webcast #6) Baby and Block Building Lesson

En Español
Video and Lesson Teaching teams and parents can use this video to watch the child explore new materials.
Learning with Leaves Lesson Teaching teams and parents can use this activity with leaves as a tool for practicing basic math skills and introducing some plant science concepts.

Strategies to Advance Children's Understanding of Number Relationships & Operations

  • Teachers can use everyday experiences to promote concepts of number, counting, and one-to-one correspondence by posing questions such as, "Do we have enough chairs for everyone? How can we figure that out?" "Shall we count how many steps to the playground?" and "Who is third in line?"
  • Highlight the relationships critical to developing number concepts and operations, such as the parts that make up a whole (a concept that underlies addition and subtraction). A teacher might say, "Brian is showing us how old his brother is by holding up five [fingers] and one. Can anyone think of another way to show six with their fingers?"
  • Help children to become familiar with the skills and vocabulary of estimating, such as using words regularly including more than, less/fewer than, about, near, approximately, and in between; asking children to estimate how much, how long, or how many ("How many shovelfuls do you think it will take to fill that bucket?"). During snack, sand or water play, art activities, and other opportune times, teachers can then encourage children to test for the actual answer; and making it a point to return to a problem type to allow children to try again. As children begin to make judgments closer and closer to the real count, they hone their estimation skills. Teachers should stress that it is not important for children to get the "right" answer, but to see how close they can come.

Domain Element: Number Relationships & Operations

Title of Resource Type of Resource Notes
Where's the Math (Webcast #1) Number Assessment Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this activity to develop children's addition and subtraction skills.
Number & Operations (Webcast #2) Counting Assessment Lesson

En Español
Video and Lesson Teaching teams and parents/families can use these opportunities to improve and assess children's counting skills and development.
Number & Operations (Webcast #2) Number Stations Lesson

En Español
Video and Lesson Teaching teams and parents/families can use these activities to enhance children's counting abilities and improve their understanding of related math concepts.
Number & Operations (Webcast #2) Penny Activity Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this activity to help children compare quantities and determine which one has more.
Number & Operations (Webcast #2) How Many Are Hiding Lesson?

En Español
Video and Lesson Teaching teams and parents/families can use this activity to allow children to solve problems by talking, drawing, and acting out problems and to use creative thinking, teamwork, and mathematical reasoning.
Number & Operations (Webcast #2) Five Creatures Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this activity to help children relate and compare quantities and heights.
Hallie and Hassan: How Many Are There? [PDF, 46.99KB] Guided Practice Teaching teams may review this example of children's use of pattern blocks and consider how it offers evidence of progress in number and operations, understanding patterns, language development, and fine motor skills.

Strategies to Help Understand Geometry & Build Spatial Sense

  • Encourage children to identify different shapes (not just circle, square, and triangle but others as well) and three-dimensional figures as they draw, look at books, work with geometric puzzles, build structures in the block center, or take a neighborhood walk.
  • Give children many opportunities to handle objects, such as blocks, boxes or containers, shape sorters, and puzzles.
  • Let them climb in and out of boxes or large block structures; on or around outdoor equipment; and under, over, around, through, into, on top of, and out of different things to experience themselves in space.
  • Encourage them to make new shapes by putting materials together and taking them apart in different arrangements. They can do this when cutting or folding paper, molding clay, or building structures.
  • Introduce spatial vocabulary, including location and position words (such as on/off, over/under, in/out, above/below, in front of/in back of); movement words (such as up/down, forward/backward, toward/away from, straight/curved path); and distance words (such as near/far, close to/far from, shortest/longest).

Domain Element: Geometry & Spatial Sense

Title of Resource Type of Resource Notes
Where's the Math (Webcast #1) Block Towers Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this learn-by-doing activity to encourage inquiry, observation, and construction.
Geometry and Spatial Sense (Webcast #3) Baby and Ball Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this activity to expose children to many early math concepts, including active exploration of a ball's roundness.
Geometry and Spatial Sense (Webcast #3) Block Play Lesson

En Español
Video and Lesson Teaching teams and parents/families can learn how to assist children with exploration of blocks, which enhances children's observation skills, spatial concepts, teamwork, and language development.
Geometry and Spatial Sense (Webcast #3) Transformation Lesson

En Español
Video and Lesson Teaching teams and parents/families can use these experiences to enhance children's understanding of geometric shapes and vocabulary.
Geometry and Spatial Sense (Webcast #3) Finding Rectangles and Circles Lesson

En Español
Video and Lesson Teaching teams and parents/families can use these activities to assist children with identifying, tracing, and labeling the shapes.
Geometry and Spatial Sense (Webcast #3) Rectangular Quilt Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this activity to enhance children's inquiry and comprehension skills and the ability to follow directions.
Geometry and Spatial Sense (Webcast #3) Where's the Teddy Bear Lesson?

En Español
Video and Lesson Teaching teams and parents/families can use this activity that involves the use of ordinal and positional words.
Geometry and Spatial Sense (Webcast #3) Look, Make, and Fix Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this activity to allow children to demonstrate spatial memory. It assesses children's visual memory and their ability to follow directions.
Geometry and Spatial Sense (Webcast #3) Puppy Search Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this exercise to allow children to demonstrate reading comprehension and identify clues and geometric shapes.

Strategies to Promote Children's Knowledge of Patterns

  • Increase awareness of patterns around the classroom and throughout the day. For instance, teachers help children find patterns in designs and pictures, as well as in movement and in recurring events such as the daily classroom schedule, the days of the week, or the seasons of the year; engage children in creating and noticing patterns as they string beads; place shapes or blocks into arrays; and arrange other materials.
  • Talk to children about patterns created or noticed in constructing with unit blocks, legos, and other construction materials.
  • Over time children can reproduce and create more complex patterns. Movement, dance, and playing musical instruments offer opportunities for children to extend and repeat patterns in a variety of ways.
  • Explore artifacts from various cultures, including artworks, weavings, music, and songs. Identify patterns that may have special meaning or reflect cultural icons.

Domain Element: Patterns

Title of Resource Type of Resource Notes
Where's the Math (Webcast #1) Pattern Counting Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this strategy to help children develop basic counting skills and improve their ability to follow directions.
Patterns (Webcast #5) Pattern Songs Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this method to improve children's auditory memory skills, their ability to follow directions, and their modeling skills.
Patterns (Webcast #5) Repeating Patterns Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this strategy to help children learn to recognize and create repeating patterns.
Patterns (Webcast #5) Growing Patterns Lesson

En Español
Video and Lesson Teaching teams can use stories, such as The Bear Snores On, to help children identify missing elements of growing patterns.
Patterns (Webcast #5) Number Patterns Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this activity to encourage children's comprehension of numerical concepts from one to ten.
Patterns (Webcast #5) Mrs. McTats and Her Houseful of Cats Lesson

En Español
Video and Lesson Teaching teams and parents/families can use this activity to enhance children's ability to recognize and create unique growing patterns.
'Ideas to Help Children Learn Math When At the Park' [in] A Family Note on Finding the Math Article- Excerpt Teaching teams and parents/families can learn about how noticing patterns in nature and playing on playground equipment can help children count, recognize patterns and shapes, and use one-to-one correspondence.
'Ideas To Help Children Learn Math During Everyday Home Routines' [in] A Family Note on Finding the Math Article- Excerpt Teaching teams and parents/families can learn about how to use daily activities to enhance children's mathematic skills. These every day routines can help children count, use one-to-one correspondence, repeat patterns, solve problems, compare sizes, recognize positions of objects, and understand quantities.
Hallie and Hassan: How Many Are There? [PDF, 46.99KB] Guided Practice Teaching teams may review this example of children's use of pattern blocks and consider how it offers evidence of progress in number and operations, understanding patterns, language development, and fine motor skills.

Strategies to Promote Children's Knowledge of Measurement & Comparison

  • Let children figure out their own units for measurement ("Carlos is five cereal boxes tall"). Using standard units like inches, feet, and yards is only one way to measure. Children better understand these units when they have lots of experiences working with their own ways of comparing and measuring.
  • Use many daily activities such as construction, cooking, woodworking, science, and other experiences that involve measurement. In any of these activities, teachers look for opportunities for children to make comparisons and measurements of volume, weight, length, and temperature.
  • Capitalize on children's interest in comparing all sorts of things about themselves. In charts and graphs, they can see quantities displayed, which contributes to their understanding of numbers and their ability to make comparisons. You can create a chart recording children's favorite desserts and pose questions such as, "Do more children like ice cream or cookies best?" Chart-making can be a very simple process. For example, placing one color form or sticker in a column to indicate each child's preference creates a basic bar graph that makes sense to children.

Domain Element: Measurement & Comparison

Title of Resource Type of Resource Notes
Measurement (Webcast #4) Conversion Tasks Lesson

En Español
Video and Lesson Teaching teams and parents can use this activity to assess children's abilities to compare volumes.
Measurement (Webcast #4) Balloon Rocket Lesson

En Español
Video and Lesson Teaching teams and parents can use this activity to assist children with measuring and comparing distances.
Measurement (Webcast #4) Elephant Feet Lesson

En Español
Video and Lesson Teaching teams and parents can use this activity to teach children comparison and measurement skills.
Measurement (Webcast #4) Car Racing Lesson

En Español
Video and Lesson Adults can use this activity to enhance children's measuring skills and assess their ability to repeat the task.
Measurement (Webcast #4) Walking the Circle Lesson

En Español
Video and Lesson Teaching teams and parents can use this strategy to teach children how to relate vocabulary with physical movements.
Measurement (Webcast #4) Measuring the Fruit Lesson

En Español
Video and Lesson Teaching teams and parents can use this exercise to teach children experimentation and measuring skills.
Measurement (Webcast #4) Sand Babies I Lesson

En Español
Video and Lesson Teaching teams and parents can use this activity to assess children's ability to make measurement comparisons of height and weight.
Measurement (Webcast #4) Sand Babies II Lesson

En Español
Video and Lesson Teaching teams and parents can use this exercise to review children's early writing and measurement skills.
"Big Bill and Little Larry (Length)" [in] Measuring Experiences for Young Children Excerpt-Article Excerpt from longer article on measurement. Teaching teams and parents can learn from this example how to enhance children's measuring skills and abilities.
" 'Buildings and the Runaway Gerbil (Length, Height, and Area)' [in] Measuring Experiences for Young Children" Excerpt-Article Excerpt from longer article on measurement. Teaching teams and parents can learn from this example how to support and develop children's measuring skills.
" 'Car Races (Distance)' [in] Measuring Experiences for Young Children" Excerpt-Article Excerpt from longer article on measurement. Teaching teams and parents can learn from this example how to enhance children's counting and measuring skills.

Domain Element: General

Title of Resource Type of Resource Notes
Math Webcasts Series

En Español

Viewing Guide for Math Leaders – Math Webcast #2: Number and Operations [PDF, 47.46KB]

En Español [PDF, 62.02KB]

Viewing Guide for Math Leaders – Math Webcast #3: Geometry and Spatial Sense [PDF, 104.62KB]

Viewing Guide for Math Leaders – Math Webcast #4: Measurement [PDF, 67.44KB]

Viewing Guide for Math Leaders – Math Webcast #5: Patterns [PDF, 68.56KB]

Viewing Guide for Math Leaders – Math Webcast #6: Putting it All Together! [PDF, 99.93KB]
OHS Webcasts and Related Resources Six webcasts address the domain elements within Mathematics and include training resources for use by personnel who support Head Start teaching teams, supervisors, directors, curriculum specialists, mentor-coaches, and T/TA staff.
Introduction to 'Helping Your Child Learn Math' Article- Excerpt Teaching teams and parents can use these everyday activities to encourage children's interest in math.
Activities: Math in the Home Article- Excerpt Teaching teams and parents can use these ideas to encourage children to enjoy math and science.
'Ideas To Help Children Learn Math When at the Grocery Store' [in] A Family Note on Finding the Math Article- Excerpt Teaching teams and parents can learn how trips to the grocery store can develop children's mathematics skills, including practicing counting and recognizing shapes, numerals, and repeating patterns.
A Family Note on Finding the Math Tool Teaching teams and families can learn how to use everyday experiences to help children learn math.
Finding the Math in Books: Ideas for Teaching Staff [PDF, 780.67KB]

Glossary [PDF, 33.73KB]
Article, Lesson Teaching teams can use the ideas in this article to learn strategies for "mathematizing" children's book-reading experiences and highlighting math learning through reading.
Training Activity. Practice Finding the Math

The Math in Books: Ideas for Teaching Staff. Highlighting Number and Operations

PowerPoint Presentation. Practice Finding the Math
Training (Professional Development) Trainers, education managers, mentor coaches, center directors, and others involved in staff development can use this 2-hour training activity in conjunction with the PowerPoint presentation to increase and reinforce the skills of the teaching staff in identifying and expanding opportunities for everyday mathematical learning. Patterns, spatial sense, geometry, measurement, and number and operations are all addressed.
Playing Games in Classroom Helping Pupils (Children) Grasp Math Article Parents may find information and ideas from this article useful to help strengthen their children's math skills at home.
What's Going on at the Math Center? PowerPoint [PDF, 140.72KB]

What's Going on at the Math Center – Handout [PDF, 12.46KB]

What's Going On At The Math Center [PDF, 34.91KB]
Training (Professional Development) Professional Development providers can use this material with teaching teams to highlight the application of ongoing assessment techniques to the area of mathematics.
Mathematics on the Go Lesson Parents and teachers can use this resource to take advantage of the real world of travel to explore math concepts including distance, time, maps, and numbers.
Curriculum Web Planning Tool: Extending Early Mathematics Knowledge Through Planned Learning Experiences Around Books [PDF, 751.16KB] Lesson Teaching teams and educators can use this curriculum planning tool packet for developing experiences and opportunities that extend the mathematical concepts introduced in books. Included in this packet are four curriculum web examples, a description of each of the books used in the examples, and a blank curriculum web.
Hallie and Hassan: How Many Are There? [PDF, 46.99KB] Guided Practice Teaching teams may review this example of children's use of pattern blocks and consider how it offers evidence of progress in number and operations, understanding patterns, language development, and fine motor skills.
Mathematics and Scientific Inquiry [PDF, 171.45KB] Article Teaching teams can learn about connecting children's everyday interests to intentional math and science experiences that enhance learning.
Mathematics at the Grocery Store: Activities

En Español
Lesson Parents and teachers can use this resource to help children explore sizes, shapes, sorting, counting, and money in the real world of the grocery store. It offers many math activities that can be done using the grocery store as a learning lab.
Mathematics for the Fun of It

En Español
Lesson Parents and teachers can use this resource to explore math concepts with children using everyday surroundings.
Teaching About Numbers and Counting Article Teachers and child care providers can enhance children's mathematical knowledge by supporting children's natural curiosity and interest in numbers. This resource offers strategies for integrating the understanding of math concepts, like similarities and geometric shapes, into daily routines.
 

References for Evidence-Based Practice for the Mathematics Knowledge & Skills
Domain of the 2010 Early Learning Framework

The body of research that focuses on early education intervention as a key contributor to children's school readiness and successful achievement has grown significantly since the creation of Head Start in 1965. In order to highlight the significance of this research across the outcome domains of the Early Learning Framework, we include a variety of references that describe various levels of evidence in the research base. Specifically we include levels of evidence that support the scientific believability of approaches, strategies, instructional practices, and outcomes. These levels of evidence include results of large scale research studies, documentation of evidence-informed practices, and/or replicable practices that effect children's progress toward outcomes, or have the potential to influence future research.

Mathematics Knowledge & Skills

Copley, N. (2009). Math in the Early Years 2nd ed. Washington, DC: National Association for the Education of Young Children.

Epstein, Ann S. (2008). Mathematics and scientific inquiry. In The Intentional Teacher: Choosing the Best Strategies for Young Children's Learning (41-66). Washington, DC: National Association for the Education of Young Children.

National Council of Teachers of Math (2007). Curriculum Focal Points. Reston VA: National Council of Teachers of Math.

National Research Council. (2005). Mathematical and scientific development in early childhood. Summary of a 2005 National Academy of Sciences workshop. Washington, DC: National Academy Press. Duschl et al. (2006).

National Research Council. (2009) Mathematics Learning in Early Childhood: Paths toward Excellence and Equity. Washington, DC: National Academies Press.

Nemeth, K. (2009, Fall). Math and science for dual language learners in preschool: The right place to start. National Clearinghouse for English Language Acquisition, 2 (1), 13.

Preschool California (2011). Early Learning and Latino Children: The Foundation for California's Future.

Sarama, Julie; Clements, Douglas H. (2008) Mathematics in early childhood. In O. Saracho & B. Spodek (Eds.), Contemporary Perspectives on Mathematics in Early Childhood Education (67-94). Charlotte, NC: Information Age Publishing.

Starkey, Prentice; Klein, Alice. (2008) Sociocultural influences on young children's mathematical knowledge. In O. Saracho & B. Spodek (Eds.), Contemporary Perspectives on Mathematics in Early Childhood Education (253-276). Charlotte, NC: Information Age Publishing.

Number Concepts & Quantities

Arnold, D. H., Dobbs, J., Doctoroff, G. L. & Fisher, P. H. (2003). Accelerating math development in Head Start classrooms. Journal of Educational Psychology 94 (4), 762-770.

Baroody, A. J., Eiland, M. & Thompson, B. (2009). Fostering at-risk preschoolers' number sense. Early Education and Development 20 (1), 80-128.

Curtis, R., Okamoto, Y. & Weckbacher, L. M. (2009). Preschoolers' use of count information to judge relative quantity. Early Childhood Research Quarterly, 24 (3), 325-336.

Kersh, J. E., Casey, B., & Young, J. M. (2008). Research on spatial skills and block building in girls and boys. In O. Saracho & B. Spodek (Eds.), Contemporary Perspectives on Mathematics in Early Childhood Education (233-251). Charlotte, NC: Information Age Publishing.

Pagani, L., Girard, A. & Jalbert, J. (2006). Does preschool enrichment of precursors to arithmetic influence intuitive knowledge of number in low income children? Early Childhood Education Journal 34 (2), 133-146.

Siegler, R. & Ramani, G.B. (2009). Playing linear number board games--but not circular ones--improves low-income preschoolers' numerical understanding. Journal of Educational Psychology, 101(3), 545-560.

Zur, O. & Gelman, R. (2004). Young children can add and subtract by predicting and checking. Early Childhood Research Quarterly 19 (1), 121-137.

Number Relationships & Operations

Arnold, D. H., Dobbs, J., Doctoroff, G. L. & Fisher, P. H. (2003). Accelerating math development in Head Start classrooms. Journal of Educational Psychology, 94 (4), 762-770.

Rogers, J. P. (2008). Cardinal Number and Its Representation: Skills, Concepts and Contexts. Early Child Development and Care, 178 (2), 211-225.

Geometry & Spatial Sense

Fersakis, G., Sofroniou, C. & Mavroudi, E. (2011). Using the internet for communicative learning activities in kindergarten: The case of the "Shapes Planet." Early Childhood Education Journal, 38 (5), 385-392.

Reed, M. (2007). Sense of place in child care environments. Early Childhood Education Journal 34 (6), 387-392.

van Nes, F. & van Eerde, D. (2010). Spatial structuring and the development of number sense: A case study of young children working with blocks. The Journal of Mathematical Behavior, 29 (3), 145-159.

Patterns

Copley, J., Glass, K., Nix, L., Faseler, A., De Jesus, M. & Tanksley S. (2004). Quilt cover (area with emphasis on length measurement) in Measuring Experiences for Young Children. Teaching Children Mathematics. Reston, VA: National Council of Teachers of Mathematics.

Papic, M., Mulligan, J. T. & Mitchelmore, M. C. (2011). Assessing the development of preschoolers' mathematical patterning. Journal for Research in Mathematics Education, 42 (3), 237-268.

Taylor-Cox, J. (2003). Algebra in the Early Years? Yes! [PDF, 407.36KB] Young Children. Washington, DC: National Association for the Education of Young Children.

Measurement & Comparison

Bart, W., Yuzawa, M. & Yuzawa, M. (2008). Development of mathematical reasoning among young children: How do children understand area and length? In O. Saracho & B. Spodek (Eds.), Contemporary Perspectives on Mathematics in Early Childhood Education (157-185). Charlotte, NC: Information Age Publishing.

Copley, J., Glass, K., Nix, L., Faseler, A., De Jesus, M. & Tanksley S. (2004). Measuring Experiences for Young Children [PDF, 344.94KB]. Teaching Children Mathematics. Reston, VA: National Council of Teachers of Mathematics.

Fox, J. (July, 2005) Child-Initiated Mathematical Patterning in the Pre-Compulsory Years. International Group for the Psychology of Mathematics Education Paper presented at the Conference of the International Group for the Psychology of Mathematics Education.

Last Updated: May 28, 2014