by ParentPowered contributing author Curran Mahowald, M.A. Cognitive Science in Education
When I was in kindergarten, the 100th day of school was special. Each child was asked to bring in one hundred of something. I first looked at some of my favorite objects — beanie babies and roly polies—but soon realized I didn’t have (or couldn’t wrangle, in the case of the live bugs) one hundred of those. I settled on one hundred pieces of my favorite cereal, and my parents helped me pack the right amount into a plastic bag. The next day I was proudly counting each item one by one along with my classmates and their collections of paper clips, pennies, and popsicle sticks.
Most of what I remember from that day, which feels like it happened a century ago, is eating cereal (in addition to my one hundred pieces, there was an activity for the whole class in which we strung one hundred fruit loops onto a necklace). But I was also learning important mathematical concepts and numerical abilities through the counting, estimating, and number talk that was going on that day. From an educational perspective, that day was about early numeracy skills.
Early numeracy development has become better appreciated in education because developmental psychology research is revealing that preschool-aged children’s numerical skills in the early years actually lay the foundation for learning math concepts once they get to school. Children’s early experiences with caregivers and early childhood educators play a big role in building this foundational mathematical knowledge.
This means there’s a lot parents can do to invest in their child’s future mathematical abilities—if only they knew what and how! Parents often have questions about when their children should begin learning math, how they can support their children’s math learning at home, and what they can do to help a child struggling in math.
In this article, we’ll answer some of these common questions from families. We’ll explain what early numeracy skills are, why they matter, how they can be developed, and how early childhood teachers and families can partner to improve learning outcomes for all children through family math activities.
Answering common parent questions about early math
Educators play a key role in supporting parents in their efforts to promote early numeracy. Having answers ready to some common parent questions is a great way to foster understanding and equity around math readiness and achievement. Being a trusted source of helpful information about their child’s learning process can also go a long way in building meaningful relationships with families.
When should my child start learning math?
Although students don’t typically multiply or divide before third grade, they do learn important mathematical skills and concepts well before kindergarten. Also known as number sense, early numeracy skills are the foundations of mathematical reasoning that children acquire in early childhood. For example, by about four years of age, children can recognize and complete simple patterns, identify the number of objects in a small set, and compare physical attributes such as height. These are all examples of early numeracy skills! You can check out the “Cognition” domain of the Head Start Early Learning Outcomes Framework to see more specific math-related skills and concepts that children should learn before kindergarten.
Just as early reading skills and literacy development refers to the basic building blocks of language and reading (the alphabet, the sounds letters make, phonological awareness, common word meanings, and an understanding of how stories work), early numeracy refers to the basic building blocks of mathematics ability—counting with numerals, comparing size, matching and sorting, combining and separating quantities, parts of a whole, and recognizing the use of numbers in everyday life (e.g. prices, addresses, shoe sizes).
Early numeracy skills are the ways of thinking that support future mathematical skills, and they can be organized into three main categories:
Numbers and operations
The basic understanding and manipulation of numbers. This category of mathematical skills includes several numerical abilities such as:
- Number recognition: The ability to identify and name numbers when they are seen or heard.
- Counting: The numerical ability to recite numbers in the correct order and understand that each number represents a quantity.
- One-to-one correspondence: The understanding that each object in a set can be counted once and only once.
- Quantity comparisons: The ability to understand the concepts of more, less, greater than, and less than.
- Basic arithmetic: The understanding of addition, subtraction, multiplication, and division, initially with small numbers.
Geometry and spatial awareness
Identifying shapes, reasoning about spatial relationships, and mentally manipulating objects in space. Key components of this category include:
- Shapes: Children learn to identify and name different shapes, such as circles, squares, triangles, and rectangles. They also understand the characteristics and properties of these shapes.
- Spatial Relationships: This skill involves understanding and describing the relative positions of objects in space, such as above, below, next to, behind, and in front of.
- Directional Concepts: Children develop an understanding of directional terms like left, right, up, and down. They learn to follow and give directions based on this conceptual knowledge.
- Visualization: Spatial awareness includes the ability to mentally manipulate objects or visualize shapes and patterns in different orientations.
Patterns and measurement
Recognizing and understanding patterns, as well as developing the mathematical concept of measurement. Key skills include:
- Pattern Recognition: Children learn to recognize and create patterns using various attributes, such as color, shape, size, or number sequences.
- Pattern Extension: This skill involves continuing or completing a given pattern by identifying the missing elements based on the pattern’s rules.
- Measurement: Early measurement skills include understanding and comparing attributes like length, height, weight, capacity, and time. Children learn to use non-standard units (e.g., using blocks to measure length) before progressing to standard units (e.g., inches, pounds).
- Estimation: Children develop the ability to estimate or make educated guesses about quantities and measurements based on their understanding of number and measurement concepts.
By developing proficiency in these three categories, children build a strong foundation in early numeracy skills, which is crucial for their mathematical development as they progress through school.
Why are early numeracy skills important?
1. Early numeracy skills help children make sense of their world.
The same conceptual knowledge that prepares children for developing formal math skills also helps children process what they perceive in their environment by observing and organizing it in meaningful ways. Numeracy development involves thinking logically, reasoning about the physical and imagined world, and connecting related ideas. Even outside the realm of mathematical performance per se, mathematical learning also supports science, social studies, art, and music.
2. A focus on the early years can improve mathematics outcomes later.
The research is in—math success begins before school. This is because formal math skills rely on basic conceptual knowledge that children develop early in life. For example, before children can learn to manipulate fractions, they must understand the concept of parts of a whole.
Longitudinal studies that have followed children from early childhood to adolescence have shown a strong association between early numeracy skills and mathematics ability later on. For example, Siegler et al., 2012 found that children’s ability with fractions and division in elementary school predicts their knowledge in algebra and overall academic achievement in high school.
3. Formal math skills have prerequisites.
Like many domains of academic achievement, math builds on itself, even beginning with very fundamental concepts. Some of these concepts are so basic that adults forget we ever had to develop or learn them. But as babies, we did not come pre-programmed with the knowledge that numbers represent quantity or even that quantity is conserved despite changing shape. We had to learn it through interacting with the world. We all had to develop the ability to perceive multiple dimensions, like width and height, and take them into account when estimating volume.
Children also have to learn that the last number used to count a group of objects represents how many are in the group (the cardinality principle). This is why a child may count to 10 while touching each item once, but when asked how many are in the set, he has to start from 1 again.
This important cognitive development happens over the course of children’s early experiences in the physical world. It’s important that children have opportunities to actively play and explore with adult support and enrichment so they can develop these concepts. It’s also important for children to acquire the mathematical language for these concepts, which they pick up from adults using words in context.
How do children develop early numeracy skills?
Children develop early numeracy skills through a combination of innate abilities, environmental variables, intergenerational variables, and intentional instruction. Here are some key factors that contribute to the development of these skills:
Natural curiosity and exploration
Young children have an innate curiosity about their environment, including numbers and quantities. They naturally engage in activities that involve counting, sorting objects, and making comparisons. Early childhood teachers and caregivers can help by encouraging this exploration, which provides a foundation for developing early numeracy skills.
Everyday experiences
Daily experiences offer numerous opportunities for children to encounter and engage with numbers and math concepts. For example, they may count toys, identify numbers on street signs, measure ingredients while cooking, or compare the sizes of objects during play. These real-life experiences help children form a strong association between the concepts of math and the real world.
Language and communication
Language abilities play a crucial role in developing early numeracy skills. Through conversations, songs, and stories, children learn number words, counting rhymes, and mathematical vocabulary. Adults and caregivers can facilitate math abilities by engaging children in math-related conversations and providing mathematical language to describe their experiences.
Play-based learning
Play is an essential vehicle for the development of mathematical abilities. Playful activities, such as building with blocks, puzzles, board games, and pretend play with numbers and shapes, allow children to explore mathematical concepts in a hands-on and meaningful way. These activities promote problem-solving, reasoning, and spatial awareness.
Explicit instruction
While natural exploration and play are important, deliberate instruction also plays a role in laying the foundations for mathematical achievement. Teachers and caregivers can provide intentional instruction by introducing concepts like counting, number recognition, basic operations, and shape identification. They can use concrete materials, visual aids, and manipulatives to make learning more tangible and engaging.
Progression and building on concepts
Early numeracy skills develop in a sequential manner. Children start with basic concepts like counting and number recognition and gradually build upon them. Teachers and caregivers should scaffold instruction, providing support and gradually increasing the complexity of tasks to help children progress in their understanding of numbers, operations, patterns, and measurement.
Individual differences and readiness
It’s important to recognize that children develop at their own pace and have different strengths, interests, and needs. Some children may grasp certain concepts quickly, while others may require more time and practice. Creating a supportive and inclusive learning environment that accommodates individual differences is essential for promoting mathematical achievement.
What strategies can I use to support my child’s early numeracy and math at home?
Many adults hesitate before getting involved in their child’s math learning because of the anxiety they feel about their own math abilities. But it turns out that promoting math skills in preschool children as well as older children isn’t as difficult as many parents fear. Here are some insights to help families feel more confident about supporting their children’s mathematical development.
Good questions help more than right answers.
To help a child with math, you don’t need to have good answers—you just need to have good questions. In a previous blog post, we shared some examples of the types of questions that help children overcome difficulties in mathematics.
Growth mindset improves mathematical achievement.
“I’m not a numbers person.”
Many people think that math skills are something you either have or you don’t. And adults who think this way can inadvertently pass along a misguided belief to their children. Because the truth is, anyone can learn and excel at math with the right instruction, practice, and persistence. Math is not a talent that some people are born with and others aren’t. This is a much more positive disposition that encourages sustained effort, which is known to play a major role in mathematical achievement. Parents and early childhood teachers can model this effort-based philosophy for their children.
In an earlier blog post, we shared ways to reframe common statements about math using a positive disposition and growth mindset. It’s amazing how the way we talk about mathematical development affects academic achievement.
Mistakes help your brain grow.
When most people think of math, they think of a world of right and wrong. And it never feels good to be wrong. Except when you realize that making a mistake is one of the best things that can happen to your brain for learning!
When you make mistakes, it signals your brain that there is something new to figure out. Your brain gets challenged to find different ways to solve problems or correct the errors. As you work through these mistakes, your brain forms new connections and pathways, strengthening your understanding of math concepts.
We don’t need to be afraid of mistakes in math—they’re a natural part of learning and growing!
Mistakes provide valuable learning opportunities, and they promote resilience, a deeper understanding of mathematical concepts, and problem-solving skills in preschool children.
Math is all around us!
Everyday activities are full of opportunities to gain mathematical knowledge. For example, molding clay, cutting and folding paper to make different shapes, and playing with blocks can help young children build conceptual knowledge related to spatial reasoning and geometry. For older children, sorting laundry by color or pattern, guessing how much time something will take, and pointing out numbers throughout daily routines around the house or while running errands are all ways to support math abilities in the realm of numbers and operations.
Education equity and early numeracy skills
As we discussed above, children pick up some foundational knowledge about numbers and math even before they enter kindergarten. This is important because what they know about math when they start school can affect their learning for many years to come, all the way from elementary school to high school.
But there are disparities in mathematics achievement based on race and income. Children from low-income and minority backgrounds are at risk for poor math performance (Hanushek & Rivkin, 2006). Preschool-aged children from low-income families are more likely to start school with less advanced mathematics ability than kids from middle-income families.
And as they go through school, this gap in math abilities between low-income and middle-income kids keeps getting bigger, ultimately leading to disparities in mathematical learning in high school and beyond.
The good news is that children’s early mathematical development can be promoted through education in school and parental support at home. Well-informed early childhood teachers can partner with families to increase all children’s school readiness and help close the achievement gap.
Shareable math messages for families
Here are some ideas for supporting early numeracy that early childhood educators can share with families. These are sets of text messages that are part of ParentPowered’s family engagement program.
Infant
FACT: Using words like more/less and bigger/smaller with your baby is a great way to introduce early math concepts. Math words help your baby’s growing brain.
TIP: As you feed your baby, try using math words. Say, “Look, the spoon is full. Now it’s empty. That was a big bite! You’re a hungry baby! Do you want more?”
GROWTH: Keep using math words. You’re building your baby’s brain. Now count items as you hand them to your baby during playtime: “One. Two. Three. Three bears!”
Toddler
FACT: When we count things with kids, they have fun learning the names of numbers. It’s also key for helping kids learn that numbers have meaning.
TIP: Count in the tub! Scrub your child’s fingers and count each finger as you do: “1, 2, 3, 4, 5, 6, 7, 8, 9, 10. You have 10 fingers!” Try toes, too!
GROWTH: Keep counting. Now count your fingers and their fingers all together: 1, 2, 3…18, 19, 20! Gently wiggle each finger as you count it.
PK3
FACT: When you match colors, you help your toddler learn to make observations and classify things. These key early math skills will pay off down the road.
TIP: After a snack, name a color on your child’s shirt. Now hunt around the house for other things that are the same color: The pillow is blue like your shirt!
GROWTH: Keep matching colors. You’re helping your toddler grow! As you sort laundry, invite your toddler to make a pile of all the clothes that are white.
PK4
FACT: Patterns are hiding here, there, and everywhere! When children discover and talk about patterns, they are learning key math concepts.
TIP: When getting dressed, describe a pattern you see. Say, “I spy a pattern that goes red stripe, blue stripe, red stripe, blue stripe. Can you find it?”
GROWTH: Keep finding patterns for success in math. Now, as your child gets dressed, challenge them to share a pattern that they see around them.
Kindergarten
FACT: As kids learn to count higher and higher, they get stronger in math! You can build this skill with fun counting challenges throughout the day.
TIP: As you do dishes ask, “Do you think I can wash the plates before you count to 20? Ready, set, go!” Jump in and offer help if your child gets stuck.
GROWTH: Keep counting to build math skills! Now count to 30 as your child puts on their socks and shoes. When you get to 29 ask, “What number comes next”?
1st Grade
FACT: When you ask questions that involve addition and subtraction, your child gets better at solving word problems. Word problems are key to math.
TIP: Have fun asking addition questions at the table. Try questions like, “I have 3 beans and you have 2. How many beans do we have all together?”
GROWTH: Keep solving word problems! Now ask a subtraction question at the table. Say, “I have 5 carrots but I’m about to eat 1. How many will be left?”
About the author
Curran Mahowald is a former high school language teacher turned education research advocate. In addition to having worked at ParentPowered, she has also designed parent-facing informational materials at Oakland Unified School District and currently works on improving national research-to-practice infrastructure at the Annenberg Institute for School Reform at Brown University. Curran holds an M.A. in Cognitive Science in Education from Teachers College, Columbia University and B.A.s in Linguistics and French from the University of Southern California.
