Children's Play and Early Number Knowledge

When preschool-aged children learn about number, they learn not only to count sets of objects. They learn to compare sets (mathematicians call this correspondence of sets), and to figure out exactly what happens when sets get bigger or smaller (precise addition and subtraction). None of this is easy, but kids figure it out, often without any coaching. How do they do this?

Recent research at U. C. Berkeley’s Institute of Human Development (IHD) suggests that children’s early number knowledge comes about because as children play with objects, they spontaneously set up correspondences between sets and they track what happens as set sizes change. They seem to understand correspondence and simple arithmetic quite well when they actually play with objects. However, they find it quite difficult to look at object sets and try to judge whether sets are of the same size or not.  

The IHD research has used a variety of methods to study this in children as young as 21 months old, and more frequently in children aged about 2-1/2 years to 3 years. Generally, the research compared two methods in which the experimenter asks children to solve simple number problems. In an “active” method, children moved objects from one location to another, and in so doing they created object sets. The children then showed what they know about how many objects there were by moving them (again) to another location, one by one. In another, “passive” method, experimenters showed children a set of objects and asked them to point to a set whose quantity was exactly the same, from a choice of two sets. With both methods, children attempted to solve correspondences, addition and subtraction problems whose solution set sizes ranged up to three objects.

When children solved number problems in the active method, they succeeded up to three times more frequently than they did when they solved the same problems in the passive method. In the active method tasks, their responses to the correspondence problems were nearly perfect, whereas in the passive method correspondences the children responded correctly only about half of the time. When children solved addition and subtraction problems, they were similarly more successful in the active method than in the passive method.

One explanation for these differences is that the active method more closely mimics the sort of “number play” that young children do when they sort objects, when they set up tea parties, when they arrange for each of their friends to have a toy, and so on. These are examples of naturally occurring correspondences. And importantly, these all involve the children’s actions upon the objects. 

It is also interesting to note that these early number abilities do not associate directly with children’s ability to count sets of objects. The children in these studies were younger than three years. They sometimes knew some number words, and perhaps could recite the counting sequence up to five or so, but they were not particularly good at saying how many objects were in front of them. And yet they could solve problems that look remarkably like object based arithmetic when they could act upon the set materials. 

The punchline: early number knowledge has a lot to do with children’s activity. Children get distracted or confused when they try to figure out what number has to do with sets of objects when they just look at the sets, but they seem to have a pretty good idea of how to think about number when they play with the objects making up the sets. They do this without tutoring, without coaching. So get out the tea set and the teddy bears. Number knowledge is just around the corner.