## Introducing Number Sense in Preschool

Anyone who has watched a toddler grow knows that children have an amazing ability to learn. This affinity for absorbing new skills is especially apparent in the realm of language, but math is often considered an exception to the rule or an uphill battle. When children are exposed to the appropriate learning activities, however, they can develop number sense as intuitively as they do their native language.

The most common learning activity used by parents and teachers to introduce number sense is counting, but this is not a developmentally appropriate first step for very young children. When counting is used as the initial introduction to numbers, children must simply memorize a seemingly arbitrary sequence of unfamiliar words. Only later do they make the connection that these words represent specific quantities of items they can see and touch. This acts in reverse of the respected Montessori method of “[allowing] the child to come to an abstract understanding of a concept by first encountering it in a concrete form.”

All people are born with the natural ability to recognise small groups of numbers without counting; it is called subitising, and you can read more about it here. Subitising is what allows people to instantly recognise numbers on dotted dice. If preschool math instruction is focused only on counting, the skill of subitising will remain unpracticed; yet if this skill is nurtured, it can flourish into a strong, intuitive number sense.

### Preschool Addition Example:

Let’s look at a math question that a young child might come across:

A child who has learned only through counting will simply start at “one” and count all five ladybugs. The child will have reached the correct answer, but only through the reciting of a memorized sequence—this does little to build intuitive number sense or to develop useful arithmetic strategies. On the other hand, a child who has practiced subitising will instantly recognize that the first group contains two ladybugs, and the second group contains three. This child can then be introduced to the important number-sense concept of part-part-whole relationships by learning that two and three are a pair that make five; to extend this learning further, the ladybugs can be rearranged to show that one and four also make five.

### Elementary Addition Example:

Now, let’s look at how these skills can be applied to a more complex addition problem:

A child who has learned only through counting will likely approach this problem by starting with eight, then using the fingers on one hand to keep track while counting, “nine, ten, eleven, twelve, thirteen.” As in the previous example, this will allow the child to reach the correct answer, but it will do nothing to develop strategies for double-digit addition, nor will it instill the intuitive number sense needed to build long-term mathematical confidence. How might this problem be approached by a child who has practiced part-part-whole relationships, and who understands the significance of the tens place value? First, the child will ask “how much must eight borrow to become ten?” With practice, the child will recall that eight’s partner-to-ten is two; then the child needs only borrow two from five, leaving three. It is then an easy matter to combine ten and three to make thirteen. With this method, numbers become material values to be manipulated, rather than just labels in a sequence.

### Introducing Number Sense

Counting is undoubtedly an important skill, but it is not the most effective way to introduce number sense to preschool children (or younger). Rather than teaching toddlers to memorize a sequence of unfamiliar words, teachers and parents can begin by linking number labels with small groups of items. The natural skill of subitising will allow children to recognize the quantities of groups smaller than five, thereby linking the number names to concrete items which they can easily visualize. When numbers are introduced in this way, the subject of math will feel more rooted in physical reality, making children more confident in their ability to compute. This effect is amplified further when these beginning skills are built upon by teaching part-part-whole relationships and the utility of add-to-ten pairs in double-digit addition.

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