Building Abstract Thinking
In Young Kids Through Numbers

Article Published August 9, 2018

One of the gifts we always want to give our children is the joy of abstract thinking and a love of numbers. However, understanding the mechanics of how children learn about numbers is not well understood?

Here we explore the role numbers play in developing and building the thinking of young children.

The Importance Of Nurturing Abstract Thinking

Many parents and teachers have a strong desire for their children’s learning experiences to be tactile and interactive. Parents often contrast the forms of learning with more abstract pen and paper based activities.

However, large areas of the human brain are devoted to abstract thinking and its important to a child’s cognitive development for them to explore the abstract as well as the tangible.

From Tangible Objects To Abstract Generalisations

Children develop an ability to abstract ideas by having exposure to tangible objects. We often point to a book or a bear while we are teaching children the meaning of individual objects.

Similarly, you can point to three apples on a bench and say "three," or you can point to a picture of the numeral ‘3’ and say "three."

Children quickly learn to abstract the idea of what the number ‘3’ means by extrapolating from their exposure to numerous sources and learning experiences.

Thinking About Numbers

From their birth to the time they reach first grade, children have been developing increasingly abstract ideas about numbers and the process of counting.

Babies from 8 to 12 months of age can differentiate between two small collections of items and identify the larger collection.

Researchers speculate babies are possibly thinking about numbers, they are starting out on the long journey involving learning about the many complex concepts attached to numbers and the mechanics of counting.

5 Rules Governing Abstract Thinking About Numbers

1. Stable-Order Method

Counting words must be pronounced only once and always consistently in order. A child counts, "one, two, three, four, five..." in order each time he or she counts. The child may not always be correct, but they are usually consistent.

2. A 1-To-1 Rule

Each number being counted must be coupled with a single object only. Many 5-year-olds may make errors or skip an object, but they frequently catch out other children making similar mistakes.

3. Cardinal Rule

If you ask a child just learning to count how many items he or she just counted, they answer by starting their count from the very beginning! However, practice enables children to quickly learn to abstract this approach and they soon discover the last number they counted is not only an attribute of the last object they counted, but is also an attribute of the complete collection they counted.

4. Order-Irrelevance Principle

Objects may be counted in any order whatsoever. A child can attach different numbers to different objects but their final count will always remain unchanged.

5. Rule Of Abstraction

Any type of object can be counted in a collection. Children can count peaches, steps, the number of horse whinnies, or how many slices of cheese are missing from the pack. As the label indicates, counting is an abstract, rule based activity!

Final Observation

Finally it's important to remember all significant learning involves an element of abstract thinking. We want children to be able to make confident generalizations based on tangible experiences.

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