If you think about the act of counting, it’s really aligning the number words (or symbols) with objects. This core insight is called one-to-one correspondence. And as simple as this concept is, this alignment is the beginning of many other numerical ideas. For example, understanding equality/greater-than/less-than begins by judging whether items in two sets can be matched up or if there is a group with leftover items.
What’s truly difficult about one-to-one correspondence is what we consider “abstract” correspondence. Sets of two can look radically different from one another and still embody “two-ness” perfectly! Even when you instruct children to identify sets that have the same number of items, a set of two flowers just seems more similar to an object match (i.e., set of three flowers) than a number match (set of two turtles). This cross-mapping task (see below) is so difficult because children have to ignore all the blatant commonalities and focus simply on numerosity.
Interestingly, there are certain contexts that naturally support abstract one-to-one correspondence! For instance, if a child has two dolls and wants to give each one a cup, that situation supports abstract correspondence. Or when a kid helps set the table and has to put a spoon next to each bowl, that’s also abstract one-to-one correspondence. Kelly Mix conducted an interesting diary study of her son Spencer’s one-to-one correspondence activities and noted that he frequently engaged in spontaneous one-to-one correspondence such as distributing toys to people or placing objects in slots such as flowers in vases (Mix, 2002, 2009). But do these activities eventually help improve children’s performance on other more difficult numerical tasks?
So in 2011, Mix, Moore, and Holcomb decided to test this hypothesis. They sent 3-year-old kids home with either objects that could be snugly placed in slots (e.g., little balls in muffin tins) or not (little balls and an equal number of little frogs). Children played with these types of sets for a total of 6 weeks at home. The children who were given the alignable object-in-slots toys ended up being better at the very difficult cross-mapping task!
What’s interesting about this experiment is that they showed that this object-in-slots play actually leads to more abstract understanding of number. It wasn’t that the kids who knew more about number did more object-in-slot play… but just having toys around that would facilitate such play caused better understanding of number! So you could start with kids (like mine) who have virtually no understanding of one-to-one correspondence (see video below, haha) and give’em some experience with the right kinds of play situations and produce a kid who understands number. Woohoo!
A little translation is in order… Mo is counting in Korean but he keeps saying 9 (ah-hop) again and again at the end while pointing at different cars on Nathan’s outfit. What’s up with that Mo?!
And not to be outdone by his big brother, here is Nathan rolling over at 2.5 months (it’s mostly because he’s on a cushy little mat that helps him out a bit).