Jeremy and his classmate, Stacey, were arguing about who had more dessert. "She has more!" declared Jeremy. "I do not!" said Stacey. "We have the same." "No. see, I have one, two, three, four, and you have one, two, three, four, five."

"Jeremy, one of my cookies broke in half. You can't count each half. If you're counting pieces, I could break all yours in half, then you would have way more than me. Put the two halves back together and count. One, two, three, four. Four! We have the same."

Math in the Making

Good early mathematics is broader and deeper than early practice in "school skills." High-quality mathematics is a joy-not a pressure. It emerges from children's play and their natural ability to think.

The mathematical thinking that Stacey aptly explained to Jeremy was not only engaging-it also involved a high level of thinking. Stacey had to argue about what the unit was-what it was they were counting-and how the two halves were equivalent to one whole unit. Jeremy also exhibited excellent mathematical thinking skills in knowing that counting was the best way to compare two amounts.

Identify Learning Areas

What mathematics can young children learn? It can be broken down into two main areas: (a) geometric and spatial ideas and (b) numeric and quantitative ideas. Young children possess intuitive and informal capabilities in these areas. Three other mathematical themes that should be woven through experiences in these two main areas are: (a) patterns, (b) sorting and sequencing, and (c) measurement and data.

Plug Math Into Routines

Encouraging mathematical development can become part of your everyday routine. Suggest that children count to 15 (slowly!) while they wash their hands before snack. Point out places in their world where numbers are used, and read books and sing songs with numbers in them. These are easy activities that don't take long. However, they build the foundation for the type of numerical reasoning that Stacey displayed.

Encourage Geometric Thinking

Children are also naturally interested in shapes and spatial ideas. To encourage geometric thinking and reasoning, play "I Spy" using shape descriptions. Ask children what shapes they see in the classroom.

Make the Connections

Ask children questions, such as, "What number do you think will be on the next page? How do you know?" This encourages children to see counting as a pattern, a pattern through which they have the ability to predict what comes next. It also connects patterning to numbers. Likewise, when children naturally talk about relative size ("You have the biggest shovel"), encouraging them to measure to "prove" their prediction connects numbers and geometry.

Mathematical thinking comes naturally to young children and can develop substantially during the early years.