By Daniel Willingham
December 17, 2013
Pop quiz: What’s the earliest age that children think abstractly?
- 2 years
- 4 years
- 7 years
- 9 years
In truth, it’s a bad question because the answer depends on the type of abstraction. If the subtext of the question is “what’s the earliest age at which children show understanding of an abstraction?” the best choice from those offered above is “2 years.” And very likely earlier.
Here’s one example.
Caren Walker and Alison Gopnik (2013) examined toddlers ability to understand a higher order relation, namely, causality triggered by the concept “same.”
The experimental paradigm worked like this. The toddler was shown a white box and told “some things make my toy play music and some things do not make my toy play music.” The child then observed three pairs of blocks that made the box play music, as shown below. On the fourth trial, the experimenter put one block on the box and asked the child to select another that would make the toy play music.
There were three choices: a block that looked the same as the one already on the toy, a block that had previously been part of a pair that made the toy play music, and a completely novel block.
Toddlers (21 to 24 months old) selected the identical block most often (61% of the time).
Further experiments showed that children as young as 18 months got the task right, and showed that children this age can use the concept “different” as well as they understand “same. “
What’s interesting about this finding?
It would be easy to believe that children so young would fix attention on features of an individual block, rather than relations among blocks (i.e., red blocks make it work). Importantly, the child is not just appreciating sameness—he or she is using that property by understanding its causal role.
And, the child ignores other properties (e.g., shape or color) that are more salient. Furthermore, children learn this property readily, after exposure to just three trials. This finding may speak to the importance to our species of understanding causality.
I want to use this experiment to illustrate a broader point.
A dominant theme within cognitive developmental psychology over the last thirty years has been that children look more clever in proportion to the cleverness of experimenters. That is, as experimenters develop more subtle ways to evaluate children, it becomes clear that children understand more at a younger age than we appreciated. They were capable of learning it all the time. The problem lay in how we were looking.
The same applies to the concept explored by Walker & Gopnik. Dedre Gentner (Christie & Gentner, 2010) has reported data showing that even preschoolers seem to have trouble with reasoning tasks that call for higher-order relations—they seem to need scaffolding in which the important relation is labelled. Walker and Gopnik point out that Gentner used a task requiring verbal labeling, whereas their task merely called for an action. Seemingly small differences in what look like conceptually similar tasks can make a big difference in whether the child seems to understand.
This is one (but not the only) reason that I think it’s important to be cautious in making claims about what children are and are not ready for. The extent to which they appear ready to understand an abstraction depends partly on how we measure knowledge.
It is the normal state of developmental affairs that a child’s initial understanding of a concept looks fragile, fragmented, and uncertain. The child shows understanding on one task but is stumped by a conceptually similar task with (seemingly) trivial differences in format. He seems to understand one day, but not the next (e.g., Flynn & Sielger, 2007).
In fact, I’d suggest that complete mastery of concept across materials, types of query, and times is a good indication that the concept was introduced at a developmentally inappropriate time. We waited too long--the child probably already knew the concept.
Christie, S., & Gentner, D. (2010). Where hypotheses come from: Learning new relations by structural alignment. Journal of Cognition and Development, 11, 356–373.
Flynn, E., & Siegler, R. (2007). Measuring change: Current trends and future directions in microgenetic research. Infant and Child Development, 16, 135-149.
Walker, C. M. & Gopnik, A. (2013). Toddlers infer higher-order relational principles in causal learning. Psychological Science, published online doi: 10.1177/0956797613502983