I’d like five sandwiches please,” said Kelly Twibell to her four-year-old waiter. Before the children arrived that day, teachers had stocked the kitchen area of the classroom with restaurant props: a cash register, play money, tally sheets for taking orders. “As we set up the areas, we try to figure out ways children can bump into numbers,” explains Twibell, preschool coordinator at UC Davis Child and Family Studies.

Programs like Twibell’s introduce preschoolers to math concepts through play, rather than formal instruction. At Concord’s Child Care Center, Master Teacher Desirée Lopez says math concepts such as “numbers, patterns, relationships, and measurement” can be fun, relevant, natural parts of young children’s play.

Create environments full of numbers

“In the math area,” says Lopez, “we have things for kids to measure, sequence, classify, weigh, and develop spatial awareness”—measuring cups in housekeeping, water, and sand areas; puzzles; chains with different color links to arrange in different patterns. “We have a working clock at the children’s level and a poster of the day’s schedule with a picture of the clock showing the time, pictures of the activity, and words describing what happens at that time.”

In several learning stations in Oakland’s Harriet Tubman Educational Center, teacher Da’Monica Robinson includes puzzles and games that emphasize shapes and patterns. There’s also a math station stocked with board games like Bingo, peg games, number beads and string, and ditto sheets with numbers to trace. She has also created a simple board game using dice to help children recognize and count numbers from 1 to 100.

Help kids recognize symbols

Robinson acknowledges that games like Bingo do not teach the deeper understanding of numbers—“it just gets them to recognize the symbols, but the kids love it because it gives them a chance to play with each other.”  Lopez agrees that some rote learning of numbers is fine.  For example, “during physical education we count during routines, so children get used to hearing numbers up to 20 or 40.  This is for the rote learning.” 

Encourage them to count real things

But to understand what the numbers mean, young children need repeated concrete experiences. On nature walks, Twibell encourages children to count the number of acorns they collect, tally the number of ducks they see, or arrange their bug collection from smallest to largest. 

Staci Maldonado, the owner of Play & Learn Preschool in Cupertino, recently observed three-year-old “Molly” counting fallen leaves as she put them in a pattern. Molly asked her friend “Ivy” to help her get more leaves.  “How many?” asked Ivy.  “I don’t know,” replied Molly, “but I’ll count as I pick them up.” Ivy began to count her own leaves. “You missed a number,” said Molly.  “No, I didn’t,” said Ivy.  Their teacher just observed, storing away what she learned about each girl’s grasp of numbers.

Robinson encourages children to count everything in the classroom, from the number of ethnic groups in wall displays to the number of children present. And here’s where she gets evidence that children grasp what numbers mean—when a child complains, “Mrs. Robinson, there are too many kids in there.  You said no more than four.” 

When pushing children on the swing, Lopez says “after 20 pushes, it’s somebody else’s turn—that helps give meaning to the numbers.”

Help them figure out addition and subtraction

Through finger plays and chants like Five Little Monkeys, Maldonado begins to introduce concepts like subtraction. Twibell plays “Bubblegum, bubblegum in a dish” during circle time. Then after a few turns, she challenges the children, asking, “If I want 10 and I have three pieces in the dish, how many more do I need?”  Similarly, she might show the kids 10 bears, hide some, then ask, “how many are hiding?”

Both Maldonado and Twibell stress the importance of not shaming a child for having a wrong answer. At these young ages, says Maldonado, “it’s OK that they are not quite accurate.”  Twibell advises teachers to ask, “How do you know?” to get information on what to teach next.  “For example, one little girl wanted to make a book out of construction paper.  She wanted it to have eight pages (and) she had six…we talked and she was able to figure out she needed two more.  I asked, ‘how do you know?’” A younger child may give you a blank stare. This little girl held up two fingers to show how many more pages she needed. So she knew. “That helps me tailor instruction. If I get a blank look, I may model how to figure (this) out in a large group.”

Math for the very active

Outside Lopez’s school, “we put hopscotch on the ground and use shapes or symbols like hearts as well as the number symbols, so instead of ‘5’ there will be five hearts in the hopscotch square.” Twibell tapes shapes such as triangles or circles on floor.  Then she puts on lively music and asks children to hop to a circle or triangle. They get to move those big muscles, says Twibell, and “they learn a triangle has three sides, that a circle can come in many sizes.”

Build “interest, persistence and ability”

When Twibell noticed her waiter at the restaurant didn’t seem to know how to write down her order, she asked, “Would you like to write that down?  Or would you like me to write it down?” Then she wrote the number lightly so the child could trace it. Build on the child’s interest, says Twibell. “If he seems interested, provide a stencil.  We want to build interest, persistence, and ability while making it natural and play-based.” 

For more ideas

• Math Building Blocks, Colorado Department of Education,  www.cde.state.co.us/artemis/ed14_16/ED14202M4120032
  INTERNET.pdf
• Articles from Early Childhood Research and Practice:
  -Learning to Guide Preschool Children’s Mathematical Understanding, http://ecrp.uiuc.edu/v4n1/kirova.html
  -Quarters Are What You Put into the Bubble Gum Machine, http://ecrp.uiuc.edu/v9n1/
  vandermaas.html
  -Learning Stories and Children’s Powerful Mathematics,       http://ecrp.uiuc.edu/v9n2/perry.html
• Math ideas from A Place of Our Own,
  www.aplaceofourown.org/topic.php?id=3, scroll down to “mathematics”
• Playing Numerical Board Games Boosts Number Skills of Low-Income Preschoolers, BrightSurf, www.brightsurf.com/news/headlines/36668/Playing_numerical
  boardgames_boosts_number_skills_of_low-income_preschoolers.html
• Improving Early Mathematics Education May Enhance Children’s Academic Success, Society for Research in Child Development, http://www.srcd.org/
• Math resources online, NAEYC, http://journal.naeyc.org/btj/200301/onlinemath.asp