Preschool children need to be able to go beyond the number 3 to grasp the true concept of counting and this happens when they are taught to understand the number value of groups of objects greater than three.

We think that seeing that there are three objects doesn’t have to involve counting. It’s only when children go beyond three that counting is necessary to determine how many objects there are. In other words, knowing how to recite one, two, three and so on, isn’t the same as grasping that those numbers are connected to actual numerical values.

The following study looked at how children develop an understanding of the connection between number words and their actual numerical value. That connection is known as the cardinal principle, which states that the size of a set of objects is determined by the last number reached when counting the set.

Researchers in Chicago studied 44 children and their parents whose interactions were videotaped in 90-minute sessions every four months when the children were ages 14 months to 30 months. When the children were 4 years old, their understanding of the cardinal principle was assessed by the researchers. The results were then compared to the records of their conversations about numbers with their parents.

It was found that children most likely to understand the cardinal principle were those whose parents talked to them about sets of four to 10 objects that the child could see. When parents used smaller numbers in conversation or referred to objects that children couldn’t see (such as saying ‘I’ll be there in two minutes’), the children were less likely to understand the cardinal principle.

The results show that children who are exposed to number words from four through 10, in addition to the number words from one through three, acquire an understanding of the cardinal principle before children who have little exposure to these higher number words. This finding has important policy implications, showing that specific aspects of parents’ engagement in numerically relevant behaviors in the home seem to have an impact on children’s early mathematical development, the researchers concluded.

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