Rocking and Rolling. Nurturing Early Math Play and Discovery
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In the nursery, Isa, 6 months, adjusts her reach in order to grab the rattle on the floor. At snack time, Demaris, 9 months, runs his fingers around the square lid to the crackers. He then touches the point at the corner of the cracker box and runs his fingers down its straight edge.
Ben, 11 months, crawls over to the wooden barn and tries to fit his body inside while Ashanti, 12 months, fills a bucket with plastic blocks, then dumps them out.
In the toddler room next door, Kyra, 28 months, notices her friend at the snack table has two crackers while she has one. She points to her friend’s crackers with a questioning look on her face. Across the room, Josiah takes his teacher’s hand and walks her over to the tower he built with blocks: “Hey, look! Mine is so big!”
Outside, Marley, 30 months, sits at the water table and starts filling a jar using a small spoon. It takes a long time, so she switches to a ladle instead. Nearby, the teacher is telling Chase where the balls are: “In the basket, next to the shed.”
It may not seem possible that infants and toddlers take in and develop a foundation of math knowledge as very young children. But in the examples above, children are developing and displaying their understanding of math concepts like calculations, measurement, comparison, and spatial relationships as they explore and move through the world around them. Research shows that children are born with some math knowledge (Nuwer 2013) and that math concepts continue to develop and deepen across the early years.
Experience with math matters. During the toddler years, more frequent exposure to math vocabulary and math play at home is associated with the development of early math knowledge. A longitudinal study (focusing on children 14 to 30 months of age) found that the frequency of math words spoken by their family predicted a child’s understanding of number concepts at 46 months. That is, children who heard more math words during those 16 months tended to have a stronger understanding of cardinality over a year later when compared with children who heard fewer number words (Eason & Levine 2017). Similarly, exposure to spatial language positively predicted children’s skills in that area.
Early learning environments are important too. Children who have access to playful math activities in their early education settings thrive as they discover math concepts through age-appropriate learning experiences like sorting toys and exploring objects with different sizes and shapes. Furthermore, children can develop early math concepts through play-based activities when teachers engage in rich math language. Consider the block area, where teachers might use measurement terms (tall, short, wide, narrow) or spatial language (on top of, next to, behind, underneath). They also might model language to describe quantity and comparisons: “I think you have more blocks in your pile than I have in mine. You really have a lot of blocks” (Cohrssen et al. 2013).
Early math experiences help to build a strong foundation that prepares children for both preschool and kindergarten entry. This early knowledge positions children for success in kindergarten and beyond: research has found that preschool math skills (like counting, patterning, and nonsymbolic quantity—or a child’s ability to understand the size of relative sets without using number names) predict fifth-grade mathematics achievement (Rittle-Johnson et al. 2016).
Introducing math in the early years may also help to address inequities in learning and achievement once children enter school. Data on the early math skills present at kindergarten entry show a disparity between children from affluent families and those experiencing economic insecurities (Lombardi & Dearing 2020). These differences do not reflect ability; rather, they likely reflect different access to rich early math experiences. Providing engaging math activities in infant and toddler classrooms may be one way to address this disparity and to support the development of a strong foundation in numeracy skills.
Focusing on Math’s “Big Ideas”
Preschool educators know that math matters: a 2014 survey found that almost 90 percent believed children have the cognitive abilities to learn math, and 76.5 percent believed children were interested in learning math (Chen et al. 2014). However, when preschool educators are asked about math instruction, they report their confidence varies based on the area of math they are tasked with teaching (Chen et al. 2014). Professionals express a range of concerns, including a lack of familiarity with teaching methods and a lack of mathematical content knowledge (Bates, Latham, & Kim 2013).
In order to introduce meaningful, age-appropriate math activities into the infant-toddler classroom, teachers can turn to the “big ideas” of early math and focus on simple ways for making math a part of daily routines. This includes creating a variety of engaging experiences that will pique children’s curiosity and support their math exploration.
The Erikson Early Math Collaborative has identified a set of “big ideas” (O’Nan Brownell, Chen, & Ginet 2014) for early mathematics instruction that can be applied to an infant and toddler setting. These (and ideas for some corresponding activities) include
- sets and sorting: Creating sets is all about noticing the attributes (or features) of items. Teachers can provide opportunities for babies to explore by providing a basket of fabric swatches with soft and rough textures. They can describe the textures’ attributes as infants explore and even group items into piles of “soft” and “rough.” Even though these concepts will not be meaningful to infants yet, ongoing discussions and experiences with sorting and noticing the features of objects in their world build children’s conceptual knowledge.
- number sense and counting: To help toddlers grasp these concepts, teachers can set up activities like a dinosaur egg hunt. After hiding “eggs” (plastic replicas or cut-outs) around the classroom, the teacher can offer children a basket or bag and ask them to collect one, two, or three eggs, depending on their current counting skills.
- number operations: To introduce the concept of addition, teachers can plan a “one more” activity for their young toddlers. For instance, as children start to build a tower and place down two blocks, the teacher may pause and ask, “Should we add one more?”
- shapes: Giving children the opportunity to explore both two- and three-dimensional shapes by touching them, manipulating them, and combining them to make designs or structures is a great way to foster age-appropriate learning.
- spatial relationships: On top, under, in, and out are spatial relationships that infants and toddlers can grasp. Teachers might offer chunky blocks and a bucket so older babies can explore in and out by playing fill-and-dump. For older toddlers, playing “Teddy Bear and the Chair” is engaging. Ask children, “Can you put Teddy on the chair? Under the chair? Next to the chair?”
- 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 (like “The Itsy Bitsy Spider”) or stories (like The Napping House, by Audrey Wood) with strong, clear patterns throughout.
- measurement: Measurement is a diverse domain. It includes temperature (Is it hot or cold outside?), distance (Did the ball roll far away?), volume and capacity (Is it full or empty?), and more. The water table encourages toddlers to begin understanding capacity. Teachers can offer toddlers the chance to engage in water play using a variety of cups while modeling language like full, empty, almost full (or almost empty), and overflowing.
By reviewing the areas above, teachers can decide what topic(s) of early math they would like to focus on each day. Choosing a specific topic makes planning easier and ensures that, over time, children are receiving broad and repeated exposure to the various subdomains of early math learning.
Five Guiding Principles for Early Math Learning Experiences
As educators begin planning to incorporate more math into children’s days, the following principles can inform their development of early math activities.
Focus on Curiosity
For very young children, the goal is to provide repeated opportunities to explore math concepts and foster learning through play (Reikerås 2020). This age-appropriate and low-pressure approach sparks children’s curiosity and natural desire to learn. Teachers can help children develop new understandings by encouraging them to be curious, explore, and try again (rather than focusing exclusively on securing the right answer).
Research shows that children are born with some math knowledge and that math concepts continue to develop and deepen across the early years.
This approach also encourages a mindset in which mistakes are seen as part of the learning process. For example, when a teacher sees a 2-year-old lining up cars, she might say: “Wow, what a long line of cars! I wonder how many you have?” The toddler may begin to count but quickly lose their place and come up with an incorrect answer. The teacher might suggest they count again together, then model one-to-one correspondence by pointing to each car as they do so. Later, the teacher may see the same child pointing to each cracker on their plate as they count their snack.
Use Math Language Across the Day
In addition to numerals, educators can use math language that describes calculations (add to, take away), quantities (more, less, the same), and measurement (big, bigger, biggest). They can also describe the attributes of items (color, shape, and size) and point out patterns in the children’s world (“The floor tiles go blue, white, blue, white, blue, white”). Deciding what math language they might introduce in various activities should be an intentional part of educators’ curriculum planning.
It is important to keep in mind that children may not master these early math skills during their first three years. However, repeated exposure introduces key concepts and gives children opportunities to practice age-appropriate skills. Using descriptive math language is one of the most important ways early childhood educators can create a math-rich environment. Exposing very young children to math language is positively associated with their later math skills (Eason & Levine 2017).
Think About Ways to Mathematize Everyday Interactions
Mathematizing means using mathematical thinking and talk during play or routine activities (Swartz 2017). When feeding the classroom fish, count how many fish are in the bowl or notice whether they eat a lot or a little. During diaper changes, count baby toes or sing a song like “SOOO Big.” When playing with people and animal figures, ask children if they would like to sort them into two piles: figures with two legs and figures with four legs, or big animals and small animals.
Build Connections to Home
Share information with families about everyday ways to include math language or play into routines. Offer resources like the free Math4Littles activity set for toddlers (ZTT & AIR, n.d.), which provides suggestions for at-home early math play. This type of everyday play is important because children’s early math skills are associated with the frequency of home numeracy activities (Bernabini et al. 2020).
Pair Early Math Experiences with Children’s Literature
A wide range of outstanding children’s titles introduce early math concepts in joyful and playful ways (Hintz & Smith 2013). Sharing these texts with very young children invites play-based activity extensions that help children practice and explore the concepts raised in the books.
For example, teachers may share the book Ten Black Dots, by Donald Crews, then take out a roll of black dot stickers. They can ask each toddler, “How many black dots would you like?” If needed, they can prompt, “One, two, three, or four?” Children can place the stickers on the page and create a picture or design around them (as in the book) with crayons. (See “Braiding Early Literacy and Early Math Experiences” for resources that can assist you in locating great children’s books that include math themes.)
Braiding Early Literacy and Early Math Experiences
The following resources offer math-themed books and activities appropriate for infants and toddlers.
- Development and Research in Early Math Education (DREME) lists 40 children’s books that foster a love of math. It also outlines ways that educators can point out math concepts when sharing books: dreme.stanford.edu/sites/g/files/sbiybj9961/f/dreme_at-home_early_math_learning_kit_for_families.pdf
- Erikson Institute’s Early Math Collaborative offers a wide range of children’s titles organized by the various areas of math learning.
- The Story Time STEM Project provides tips for developing math and literacy skills through shared reading experiences.
- ZERO TO THREE’s Problem Solvers Program is a free, downloadable early math curriculum supplement that provides play-based early math activities, suggested children’s books and extension activities, and parent resources for educators of children ages 30 to 48 months.
Adding It Up
Educators can create a math-rich environment for babies and toddlers by using math language and play as joyful ways to connect and discover. Mathematizing everyday routines is another way to infuse everyday moments with numbers and numeracy concepts. While we do not expect very young children to master math skills by age 3, these early experiences can build a strong foundation for later learning and spark a love of math that children take with them into formal schooling.
Think About It
- What were your experiences with math instruction as a child or adolescent? What did you enjoy or not enjoy about these early math experiences?
- How do you see the very young children in your setting exploring math concepts like counting, comparing, measuring, identifying patterns, and more?
- What early math experiences have you offered to the children in your setting? What is challenging about planning for early math instruction? What do you enjoy about planning for these experiences?
- What resources would support your ability to plan and implement early math experiences?
- Think about some of the daily routines you share with children. What math language might you introduce into these everyday interactions?
- Observe children as they play. How do you see them already using early math knowledge? For example, you may see children counting food as they pretend to grocery shop or comparing quantities in the block area (“I have more in my tower”). Children may use measurement terms while playing with trains (“Mine is longer!”) or create sets or patterns while playing with large building bricks.
- Choose an area of early math learning. How might you introduce this concept through an age-appropriate play experience? What materials will you need? What math language will you plan to use?
Rocking and Rolling is written by infant and toddler specialists and contributed by ZERO TO THREE, a nonprofit organization working to promote the health and development of infants and toddlers by translating research and knowledge into a range of practical tools and resources for use by the adults who influence the lives of young children.
Photographs: © Getty Images
Copyright © 2022 by the National Association for the Education of Young Children. See Permissions and Reprints online at NAEYC.org/resources/permissions.
Bates, A.B., N.I. Latham, & J. Kim. 2013. “Do I Have to Teach Math? Early Childhood Preservice Teachers’ Fears of Teaching Mathematics.” Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal 5. Retrieved from https://files.eric.ed.gov/fulltext/EJ1061105.pdf.
Bernabini, L., V. Tobia, A. Guarini, & P. Bonifacci. 2020. “Predictors of Children’s Early Numeracy: Environmental Variables, Intergenerational Pathways, and Children’s Cognitive, Linguistic, and Non-Symbolic Number Skills.” Frontiers in Psychology 11. Retrieved from https://www.frontiersin.org/articles/10.3389/fpsyg.2020.505065/full.
Chen, J-Q., J. McCray, M. Adams, & C. Leow. 2014. “A Survey Study of Early Childhood Teachers’ Beliefs and Confidence About Teaching Early Math.” Early Childhood Education Journal 42 (6): 367–377.
Cohrssen, C., A. Church, K. Ishimine, & C. Tayler. 2013. “Playing with Maths: Facilitating the Learning in Play-Based Learning.” Australasian Journal of Early Childhood 38 (1): 95–99.
Eason, S.H., & S.C. Levine. 2017. “Math Learning Begins at Home.” ZERO TO THREE 37 (5): 35-\–44.
Hintz, A., & A.T. Smith. 2013. “Mathematizing Read-Alouds in Three Easy Steps.” The Reading Teacher 67 (2): 103–108.
Lombardi, C.M., & E. Dearing. 2020. “Maternal Support of Children’s Math Learning in Associations Between Family Income and Math School Readiness.” Child Development 92 (1): e39–e55.
Nuwer, R. 2013. “Babies Are Born with Some Math Skills: Number Sense of 6-Month-Olds Translates into Math Ability in Preschool.” Science (web site). https://www.science.org/content/article/babies-are-born-some-math-skills
O’Nan Brownell, J., J-Q. Chen, & L. Ginet. 2014. Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know. The Early Math Collaborative Erikson Institute. Saddle River, NJ: Pearson Education.
Reikerås, E. 2020. “Relations Between Play Skills and Mathematical Skills in Toddlers.” Mathematics Education 52 (4): 703–716.
Rittle-Johnson, B., E.R. Fyfe, K.G. Hofer, & D.C. Farran. 2016. “Early Math Trajectories: Low-Income Children’s Mathematics Knowledge from Ages 4 to 11.” Child Development 88 (5): 1727–-1742.
Swartz, R. 2017. “Mathematize!” Illinois Early Learning Project. https://illinoisearlylearning.org/blogs/growing/mathematize/.
ZERO TO THREE, & American Institutes of Research. n.d. “Math4Littles: Early Math Activities for Two- and Three-Year-Olds. www.zerotothree.org/resources/3117-math4littles-early-math-activities-for-two-and-three-year-olds
Rebecca Parlakian is the senior director of programs at ZERO TO THREE. She has developed a video series on early STEM and coauthored a recently released early math curriculum supplement. Rebecca has also coauthored five parenting and professional curricula and published articles on topics ranging from dual language development to the impact of screens on very young children. Rebecca holds a master’s degree in education and human development, with a concentration in infant-toddler special education, from the George Washington University, where she currently serves as adjunct faculty. Her most important work in child development, however, is her two children, Ella and Bennett.