Mathematicians often say that they find math beautiful—a sentiment that used to leave me scratching my head. My perspective changed while working on the July issue of Young Children, which describes math learning experiences that are meaningful and enjoyable for children and teachers.*
Since research shows that math is a topic some teachers find stressful, I hope readers will agree after reading these articles that there is beauty in early childhood math. Most beautiful is the spark in a child’s eye when a foundational concept clicks in her mind—it’s beautiful in the moment and in the promise it holds for the future. As a couple of these cluster articles explain, mathematical understanding in the early years is a strong predictor of later academic success across subject areas.
Another source of beauty in early childhood math emerges from how it can be taught: playfully. From board games to scavenger hunts for shapes, teachers can create math activities that are playful. Teachers can also highlight features of children’s play that are mathematical.
This cluster begins with carefully crafted math activities that feel like games. “Playful Math Instruction in the Context of Standards and Accountability” by Deborah Stipek provides several examples of engaging activities that show how to use standards, curricula, and assessments to support—not stifle—math learning through play. As Stipek writes, “Abundant research has demonstrated that young children enjoy learning math and can learn far more than was previously assumed—without a single flash card or worksheet.”
The article “Not All Preschool Math Games Are Created Equal” by Sally Moomaw combines rigorous research and teachers’ expertise to offer guidance for using four different types of board games to foster children’s mathematical development. From simple games that give children concrete ways to represent number to more challenging games that support a mental number line, teachers will learn how to effectively use board games with 3-, 4-, and 5-year-olds.
“More than Counting: Learning to Label Quantities in Preschool” by Hoa Nha Nguyen, Elida V. Laski, Dana L. Thomson, Martha B. Bronson, and Beth M. Casey takes us a little deeper into how preschoolers develop an understanding of labeling quantities and counting. The authors explain that “When children learn that specific number words can be used to describe certain amounts, they begin to understand that numerosity is a unique ... attribute of the world.” The article also discusses the errors young children often make—giving their teachers a new lens on the beautiful moments in this developmental trajectory.
“‘Making Change’ in Second Grade: Exploring Money through Project-Based Learning” by Karen Capraro reveals yet another way that math in the early years is beautiful: it delights children to acquire a new and powerful way to understand their environment. After discovering that her second graders have forgotten all they learned in first grade about coins, Capraro—their teacher—decides to embark on a series of student-driven projects based on a large jar of coins. Offering readers a compelling example of meeting standards through playful instruction, this class engages in counting, graphing, mapping, and grasping the values of coins—and more!
To complete the cluster, “Mathematical Structure and Error in Kindergarten” by E. Paul Goldenberg, Sharon J. Miller, Cynthia J. Carter, and Kristen E. Reed helps teachers see children’s errors as clues not only to their misconceptions but also to their current and growing understandings. Through detailed examples with two students, the authors demonstrate that “in general, the most useful place to intervene—adding challenge, correcting errors, or calling for reflection—is where the child’s intellectual growth is currently most rapid.” Errors provide important clues as to which concepts children are beginning to understand.
Although the cluster does not directly address the math anxiety that many teachers of young children report feeling, my hope is that the examples of playful math in this issue will inspire teachers to try some of these ideas stress free. As teachers engage in the enjoyable mathematics instruction discussed here, they will see children’s understanding grow. And when children make mistakes, teachers will be able to use those errors as signals for the types of new learning opportunities to provide. Even better, by creating mathematically playful classrooms, teachers will be sharing with children a new way to explore, understand, and discuss their world.
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Will feeds Maya, his 8-month-old daughter. He pauses for a moment and Maya signs “more.” Will laughs. “You want more? Okay, here it comes!” When the bowl is empty, Will says and signs, “All gone. Maya ate her food. All gone.” Maya looks at him and smiles.
Children develop math concepts and skills very early in life. From the moment they are born, babies begin to form ideas about math through everyday experiences and, most important, through interactions with trusted adults. Language—how we talk with infants and toddlers about math ideas like more, empty, and full—matters.
Math is everywhere!
We use basic math language all the time, without realizing it. For example, when we separate clothes by color, we’re using the math concepts of sorting and classifying. When we keep score during a game and determine how much our team is ahead or behind (number and operations), or give someone directions to get from one place to another (spatial relationships)—that’s math. We constantly use comparison words (measurement) such as big and little and use patterns to explain the order of daily routines and activities (“We brush our teeth after breakfast”). With our children, we play games and sing songs that use numbers and counting (such as ”One, Two, Buckle My Shoe”).
Even without our support, infants and toddlers use math concepts to make sense of their world. For example, infants like Maya signal when they want more food. More is one of the first math concepts understood by children. Babies tell us—often dramatically—that they know the difference between familiar and unfamiliar adults (sorting and classifying). Toddlers try to climb into boxes of various sizes (spatial relationships) and say words and phrases from familiar stories or songs that use repetition (patterns).
We can make the math that occurs in daily life visible to children through math talk. Each day offers us countless opportunities to help children deepen their understanding of math concepts. The more we talk math, the better chance infants and toddlers have to build a positive attitude toward math learning and learning in general.
Basic math concepts
When we are aware of early math concepts, we can be more thoughtful in our everyday interactions with infants and toddlers. Here are five basic math concepts that can be woven into our everyday conversations with infants and toddlers.
1. Number and operations—understanding the concept of number, quantity, order, ways of representing numbers, one-to-one correspondence (that one object corresponds to one number), and counting.
- “You have two eyes, and so does your bear. Let’s count:--1, 2.”
- “I have more crackers than you do. See, I have 1, 2, 3, and you have 1, 2. I’m going to eat one of mine. Now I have the same as you!”
- “That’s the third time I’ve heard you say mama. You’ve said mama three times!”
2. Shapes and spatial relationships (geometry)—recognizing and naming shapes, understanding the physical relationship between yourself and other objects and the relationships between objects.
- “Look, Jason went under the climber and Aliyah is on top!”
- “You’re sitting next to your brother.”
- “Some of the crackers we have today are square, and some are round.”
3. Measurement—size, weight, quantity, volume, and time.
- “Moving that chair is hard. It’s heavy.”
- “Your nap lasted a long time today!”
- “Let’s count how many steps it takes to reach the mailbox.”
4. Patterns, relationships, and change—recognizing (seeing the relationships that make up a pattern) and/or creating repetitions of objects, events, colors, lines, textures, and sounds; understanding that things change over time and that change can be described with math words. These are the basic building blocks of algebra!
- “Daddy has stripes on his shirt—white, blue, white, blue, white, blue.”
- ”Let’s clap to the beat of this song.”
- “I put the blocks in the bucket; you dump them out. I put the blocks back in the bucket; you dump them out!”
- “Our plant looks taller today. I think it grew overnight.”
5. Collecting and organizing information—gathering, sorting, classifying, and analyzing information (data) to help make sense of what is happening in the environment.
- “Let’s put the big lid on the big bowl and the small lid on the small bowl.”
- “You always smile when Mommy sings to you!”
- “Let’s put the dolls in the basket and the balls in the box.”
- Talk math with your child as a matter of routine. For example, diapering, meal and bath times, neighborhood walks, and shopping trips are ideal times to count, point out shapes and sizes, talk about patterns, and describe how things are the same and different.
- Make a list of math talk words and phrases. Post it on the refrigerator or somewhere else handy to remind you to take advantage of math talk opportunities.
Math talk enriches everyday learning experiences for infants and toddlers. You’ll be surprised at how much they know and can learn. Your math talk today can help your children be successful in math as they get older.
Source: Adapted from a Rocking and Rolling column written by Jan Greenberg and published in the May 2012 issue of Young Children. The full article is available at www.naeyc.org/yc/files/yc/file/201205/RockingAndRolling_YC0512.pdf.
For more information on early math learning, see the joint position statement of NAEYC and NCTM (National Council of Teachers of Mathematics): “Early Childhood Mathematics: Promoting Good Beginnings” (2002, updated 2010) at www.naeyc.org/positionstatements/ mathematics.