I doubt I'm much different from other people in that I tend to think about intelligence, academic success, smarts, whatever you want to call it, as something achieved by adding good things, whereas the opposite indicates a lack of good things. Or, in other words, positive academic outcomes are—it occurs to me, before I self-censor—caused by turning on some internal and external power sources, whereas with poorer outcomes there are stuck valves, leaky pipes, broken or frayed wires, somewhere.
These quasi-unconscious metaphors about people's mental states show up in idioms like bright (positive luminescence) and dim, not playing with a full deck (lacking cards), on the ball (positive causal force), beyond him/her (not the causal force), made sense of (positive), lost the plot/lost the thread/miss the point (negative), and sharp or dull.
It is natural, then, that I often forget that education doesn't work in just that one way. Positive outcomes are not always (or solely) achieved by making things happen, but often by stopping things from happening.
Huge Mice and Tiny Elephants
This study, which you can read online for free (thank you!) demonstrates one way in which "stopping things from happening" is an important—in fact, possibly critical—factor in learning and excelling at mathematics.
Researchers gave 58 children between the ages of 3 and 6 a Stroop task using pictures of animals (such as mouse and elephant) presented together either with their correct relative sizes (mouse much smaller than elephant) or their incorrect relative sizes (both pictures the same size). The children were asked to choose the animal that was largest in real life.
In order to perform on Stroop tasks, participants must inhibit responses to more salient characteristics of stimuli. And this inhibition can be measured. In the classic Stroop task, participants are asked to name the color of text. Color names are printed so that the color of the text matches the word (e.g., red, green, blue) or doesn't match (e.g., red, green, blue). It has been found that the words themselves interfere significantly with performance; i.e., it takes less time to respond that the color of blue is blue than it takes to say that red is green. In the animal size Stroop task, children must inhibit responses to the pictured sizes of the animals in order to produce a correct response regarding the animals' relative sizes in real life.
What researchers discovered in this study is that performance on the animal size Stroop task was a significant predictor of mathematics achievement, as measured by the Test of Early Mathematics Achievement—a finding that simply adds to a large and growing evidence base:
Cognitive development in the domain of number representation may therefore mean learning to ignore competing task-irrelevant dimensions of the stimulus. Indeed, a study in 3- to 5-year-old children from low-income families found that performance on a magnitude comparison task related to math achievement, but that this relationship was driven by trials that required inhibiting an irrelevant stimulus dimension (surface area) to select the larger numerosity (Fuhs and McNeil, 2013). This suggests that the ability to ignore irrelevant perceptual information and focus on number may explain why inhibitory control relates to early numeracy.
It is not clear to me—certainly not from this study—that inhibition can be taught. I remember years ago being required to write math problems containing unnecessary information so that students would have to choose the information that they needed. But just making kids do something is not the same thing as teaching them something. It is, rather, a total cave to assessment obsession—we just found a way to call assessment "instruction".
If inhibition can be taught, then it seems to me that we should try to be more knowledgeable about its effects and importance and then explicit in our instruction about how to apply this skill—particularly in mathematics. (See this post for a related discussion.)
Our intuitions—and even our language, as I mentioned above—prime us to see the clip below as an example of brilliant connection-making (positive). But try the problem if you haven't seen it already, and watch the solution. How much of the difficulty of this problem is captured in the unnecessary salience of the concrete scenario?
How much closer to hand might mathematics be to the unbrilliant if we could teach them how to strategically ignore the buzzing confusion of the real world?
Merkley, R., Thompson, J., & Scerif, G. (2016). Of Huge Mice and Tiny Elephants: Exploring the Relationship Between Inhibitory Processes and Preschool Math Skills Frontiers in Psychology, 6 DOI: 10.3389/fpsyg.2015.01903