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# Mathematics Development (page 6)

By Pearson Allyn Bacon Prentice Hall
Updated on Jul 20, 2010

### One-to-One Correspondence

As toddlers have experiences with authentic hands-on learning, and with counting and sharing, they begin to develop the concept of one-to-one correspondence. When distributing a snack, for example, toddlers can give each child one mini muffin or one orange section. In this way, they are learning to relate to the notion of one for each person: “One for you, one for you, one for you, and one for me.” Teachers can provide many opportunities to distribute “one” to “each child” and model this concept.

One-to-one correspondence extends as toddlers count a collection of items. Toddlers learn the counting sequence of numbers but are not always consistent in their ability to name the numbers in order. Toddlers seem to enjoy practice counting and know “how” to count although the actual sequence of naming numbers is not always followed. Teen numbers are often confused or left out. Teachers can model the stable order principle and keep track of counted items when counting a collection of things (e.g., 1, 2, 3, 4,...).

Learning to count is a similar process to learning the alphabet. Wanting to show what they know, children take great pride counting aloud. They seem to enjoy reciting the counting numbers and will attempt to count objects in their environment. They may not have one-to-one correspondence or stable order, but practicing these skills is important. We must recognize, however, that children’s verbal counting does not indicate real conceptual numeric understanding, only that they can sequence particular sounds. We may ask toddlers how many blocks they have, and they may give a number that seems to be selected at random. By about age 4 or 5 years, however, they are able to understand the logical concepts for numbers under 10.

As their skills develop, children relate the rote counting sequence to rational counting. They might have a stack of blocks in front of them and start pointing to particular blocks and, at the same time, start the counting sequence. However, close observation indicates that they might count at a different rate than that at which they point. It is also common for them to point to the same items more than once.

For children to be able to count rationally, they need to demonstrate one- to-one correspondence. This is demonstrated when a child actually relates the counting to specific individual items. Touching each item only one time as the child recites the counting sequence illustrates this concept. “This is car 1. This is car 2. This is car 3.” Children can confirm their one-to-one correspondence by keeping track of each item counted.

Relating the concept of one-to-one correspondence to rational counting is a complex skill. Young children must be able to keep track while reciting a stable order of numerals to their one-to-one counting. This skill often does not occur until the kindergarten years.

The mathematical concepts highlighted here are important components of rational and logical thinking. As children interact with their environment and with people in their world, they begin to see order in and make sense of their world.