Children are using early math skills throughout their daily routines and activities. This is good news as these skills are important for being ready for school. But early math doesn’t mean taking out the calculator during playtime. Even before they start school, most children develop an understanding of addition and subtraction through everyday interactions. For example, Thomas has two cars; Joseph wants one. After Thomas shares one, he sees that he has one car left (Bowman B. T. et al., 2001, p. 201). Other math skills are introduced through daily routines you share with your child—counting steps as you go up or down, for example. Informal activities like this one give children a jumpstart on the formal math instruction that starts in school.
What math knowledge will your child need later on in elementary school? Early mathematical concepts and skills that first-grade mathematics curriculum builds on include: (Bowman, B. T., Donovan, M. S., & Burns, M. S., (Eds.), 2001, 76).
Click below to skip to the topic of your choice:
Key Math Skills for School
How Math Skills Link to Other Areas of Development
What You Can Do
Key Math Skills for School
More advanced mathematical skills are based on an early math “foundation”—just like a house is built on a strong foundation. In the toddler years, you can help your child begin to develop early math skills by introducing ideas like: (From Diezmann & Yelland, 2000, and Fromboluti & Rinck, 1999.)
Number Sense: This is the ability to count accurately—first forward. Then, later in school, children will learn to count backwards. A more complex skill related to number sense is the ability to see relationships between numbers—like adding and subtracting.
Ben (age 2) saw the cupcakes on the plate. He counted with his dad: “One, two, three, four, five,
Representation: Making mathematical ideas “real” by using words, pictures, symbols and objects (like blocks).
Casey (aged 3) was setting out a pretend picnic. He carefully laid out four plastic plates and four plastic cups: “So our whole family can come to the picnic!” There were four members in his family; he was able to apply this information to the number of plates and cups he chose.
Spatial sense: Later in school, children will call this “geometry”. But for toddlers it is introducing the ideas of shape, size, space, position, direction and movement.
Aziz (28 months) was giggling at the bottom of the slide. “What’s so funny?” his Auntie wondered. “I comed up,” said Aziz, “Then I comed down!”
Measurement: Technically, this is finding the length, height, and weight of an object using units like inches, feet or pounds. Measurement of time (in minutes, for example) also falls under this skill area.
Gabriella (36 months) asked her Abuela again and again: “Make cookies? Me do it!” Her Abuela showed her how to fill the measuring cup with sugar. “We need two cups, Gabi. Fill it up once and put it in the bowl, then fill it up again.”
Estimation: This is the ability to make a good guess about the amount of size of something. This is very difficult for young children to do. You can help them by showing them the meaning of words like more, less, bigger, smaller, more than, less than.
Nolan (30 months) looked at the two bagels: one was a regular bagel, one was a mini-bagel. His dad asked: “Which one would you like?” Nolan pointed to the regular bagel. His dad said, “You must be hungry! That bagel is bigger. That bagel is smaller. Okay, I’ll give you the bigger one. Breakfast is coming up!”
Patterns: Patterns are things—numbers, shapes, images—that repeat in a logical way. Patterns help children learn to make predictions, to understand what comes next, to make logical connections, and to use reasoning skills.
Ava (27 months) pointed to the moon: “Moon. Sun go night-night.” Her grandfather picked her up, “Yes, little Ava. In the morning, the sun comes out and the moon goes away. At night, the sun goes to sleep and the moon comes out to play. But it’s time for Ava to go to sleep now, just like the sun.”
Problem-solving: The ability to think through a problem, to recognize there is more than one path to the answer. It means using past knowledge and logical thinking skills to find an answer.
Carl (aged 15 months) looked at the shape-sorter—a plastic drum with 3 holes in the top. The holes were in the shape of a triangle, a circle and a square. Carl looked at the chunky shapes on the floor. He picked up a triangle. He put it in his month, then banged it on the floor. He touched the edges with his fingers. Then he tried to stuff it in each of the holes of the new toy. Surprise! It fell inside the triangle hole! Carl reached for another block, a circular one this time…
Math: One Part of the Whole
Math skills are just one part of a larger web of skills that children are developing in the early years—including language skills, physical skills, and social skills. Each of these skill areas is dependent on and influences the others.
Trina (aged 18 months) was stacking blocks. She had put two square blocks on top of one another, then a triangle block on top of that. She discovered that no more blocks would balance on top of the triangle-shaped block. She looked up at her dad and showed him the block she couldn’t get to stay on top, essentially telling him with her gesture, “Dad, I need help figuring this out.” Her father showed her that if she took the triangle block off and used a square one instead, she could stack more on top. She then added two more blocks to her tower before proudly showing her creation to her dad: “Dada, Ook! Ook!”
You can see in this ordinary interaction how all areas of Trina’s development are working together. Her physical ability allows her to manipulate the blocks and use her thinking skills to execute her plan to make a tower. She uses her language and social skills as she asks her father for help. Her effective communication allows Dad to respond and provide the helps she needs (further enhancing her social skills as she sees herself as important and a good communicator). This then further builds her thinking skills as she learns how to solve the problem of making the tower taller.
What You Can Do
The tips below highlight ways that you can help your child learn early math skills by building on their natural curiosity and having fun together. (Note: Most of these tips are designed for older children—ages 2-3. Younger children can be exposed to stories and songs using repetition, rhymes and numbers.)
Bowman, B. T., Donovan, M. S., & Burns, M. S., (Eds.). (2001). Eager to learn: Educating our preschoolers. Washington, DC: National Academy of Sciences.
Diezmann, C., & Yelland, N. J. (2000). Developing mathematical literacy in the early childhood years. In Yelland, N. J. (Ed.), Promoting meaningful learning: Innovations in educating early childhood professionals. (pp.47-58). Washington, DC: National Association for the Education of Young Children.
Fromboluti, C. S., & Rinck, N. (1999 June). Early childhood: Where learning begins.
U.S. Department of Education, Office of Educational Research and Improvement,
National Institute on Early Childhood Development and Education. Retrieved on September 22, 2008 from http://www.kidsource.com/education/math/whatis.html