# The Principles of Counting

## Sequence, Quantity, Cardinality and More

A child's first teacher is their parent. Children are often exposed to their earliest math skills by their parents. When children are young, parents use food and toys as a vehicle to get their children to count or recite numbers. However, the focus tends to be on rote counting, always starting at number one rather than the understanding the concepts of counting. As parents feed their children, they will refer to one, two, and three as they give their child another spoonful or another piece of food or when they refer to building blocks and other toys. All of this is fine, but counting requires more than a simple rote approach whereby children memorize numbers in a chant-like fashion. Most of us forget how we learned the many concepts or principles of counting.

### Principles Behind Learning to Count

Although we've given names to the concepts behind counting, we don't actually use these names when teaching young learners. Rather, we make observations and focus on the concept.

Sequence: Children need to understand that regardless of which number they use for a starting point, the counting system has a sequence.

Quantity or Conservation: The number also represents the group of objects regardless of size or distribution. Nine blocks spread all over the table are the same as nine blocks stacked on top of each other. Regardless of the placement of the objects or how they're counted (order irrelevance), there are still nine objects. When developing this concept with young learners, it's important to begin with pointing to or touching each object as the number is being said. The child needs to understand that the last number is the symbol used to represent the number of objects. They also need to practice counting the objects from bottom to top or left to right to discover that order is irrelevant--regardless of how the items are counted, the number will remain constant.

Counting Can Be Abstract: This may raise an eyebrow but have you ever asked a child to count the number of times you've thought about getting a task done? Some things that can be counted aren't tangible. It's like counting dreams, thoughts or ideas--they can be counted but it's a mental ​and not tangible process.

Cardinality: When a child is counting a collection, the last item in the collection is the amount of the collection. For instance, if a child counts 1,2,3,4,5,6, 7 marbles, knowing that the last number represents the number of marbles in the collection is cardinality. When a child is prompted to recount the marbles how many marbles there are, the child doesn't yet have cardinality. To support this concept, children need to be encouraged to count sets of objects and then probed for how many are in the set. The child needs to remember the last number represents the quantity of the set. Cardinality and quantity are related in counting concepts.

Unitizing: Our number system groups objects into 10 once 9 is reached. We use a base 10 system whereby a 1 will represent ten, one hundred, one thousand etc. Of the counting principles, this one tends to cause the greatest amount of difficulty for children.

We’re sure you'll never look at counting quite the same way when working with your children. More importantly, always keep blocks, counters, coins or buttons to ensure that you are teaching the counting principles concretely. The symbols won't mean anything without the concrete items to back them up.