Are You Smarter than a 3rd Grader?

You may not be as logical as you think you are.

Posted Nov 01, 2011


Your ability to think logically and effectively evolves gradually over life. According to the theory of Jean Piaget, world-renowned Swiss psychologist, logician, and mathematician, everyone develops through a set of four stages from infancy through adulthood. We go through these stages, he proposed, in steady order, reaching the highest pinnacle by the time we're 15 years old or so. Piaget discovered that children don't just know less than adults, they think differently. Their knowledge of the world is shaped by their continuing efforts to understand and adapt. At times this means they impose a faulty set of rules onto the conclusions they draw about what's happening around them.

Piaget proposed his famous theory after watching the antics of his children in their cribs, playpens, and playgrounds. He was fascinated by the way they interacted with their toys, and he began to introduce little games to test their understanding of simple concepts such as size and number.  Even the game "peek-a-boo" became one of his favorite experiments. He noticed that until children reached the age of about 6 months, they didn't become upset when one of their favorite toys disappeared. After the age of 6 months or so, they would start to hunt for the missing object. Piaget called this discovery "object permanence," and it's also the reason that babies 6 months or older show distress when their mother or father leaves the room. They realize that their parent continues to exist, but is not there to be with them. So they cry!

Parents often wonder whether children are able to "think" before they can express themselves in language. Piaget's answer was a definite "yes." He believed that children think in terms of actions and things, not words. They have ideas about what's happening around them even though they can't put these ideas into words. Piaget called the years from birth through about 1-1/2 the "sensorimotor stage" (meaning sensory + motor, but no language).

By the time children can use language, they begin to enter the next phase of thought, which he called "preoperational." He didn't consider this a stage, but a phase, because it was a transitional period. Piaget derived this term from the concept of "operation"—the logical analysis that we perform when solving a problem. Young children are "pre" operational because they are not capable of formal logic. They make the common mistake, shown in the so-called "conservation problems." of assuming that because objects change shape or appearance, they also change quantity. A long thin sausage of clay, they reason, has more clay than a round ball of clay because the sausage is longer. In short, children are easily fooled into making the wrong judgments about quantity because their eyes deceive them.

Gradually, children develop

into the stage of "concrete operations," so that by the time they're about 7 years old, they aren't fooled by the conservation problems. Now they understand the principle of reversibility—meaning that an object can be changed into one shape and changed back into its original form without changing quantity. One by one, they can tackle the conservation tasks like those that Piaget presented to his children. They realize that a row of 5 pennies has the same number of pennies whether it's spread out in a long row or clumped together. This stage is called "concrete" operations because children can only solve these problems when they can manipulate the objects with their hands. They're not yet able to use abstract thought.

Finally, beginning at about age 11, children can use abstract reasoning. This is when they're capable of learning algebra because they can understand symbolic logic. Piaget called this ability "formal" operations meaning capable of formal logic. In the classic test he used to study formal operations, the child tries to determine which factors influence the swinging rate of a pendulum-not by moving the pendulum but by developing a set of logical steps to test hypotheses about such influences as weight of the pendulum and length of the string. After that, teens can do just about anything using abstract, symbolic reasoning, so the theory goes.

As it turns out, most adults rarely use formal operations, much less concrete. In a study designed to test consumer behavior, University of Kentucky researcher Maura Scott and her team asked college-age students to state how many calories were in each of 4 combinations of bags of M&M's: large or small plastic bag with large or small (mini) M&M's. In the key comparison, people said that the large bag with large M&M's had fewer calories than the 4 small bags filled with M&M mini's that had the exact same number of calories. Therefore, participants were more likely to eat more from the large candy-large bag combination, assuming it was lower in total calories. The same calorie content but with different size bags and different size M&M's led people with "formal operational" ability, much less concrete operations, to be completely confused. Scott was actually interested in factors related to consumer behavior and not Piaget's theory, but when I raised this possibility with her in an email communication, she agreed that lack of conservation ability could account for the findings. Our eyes are as easily fooled by the size and shape of a product as are those of a 7-year-old child.

We're also likely to use our sensori-motor thinking to solve problems in many real-life "adult thought" situations. For example, during the great Halloween storm of 2011, I was one of the millions of people affected by widespread power outages in the Northeast. During the storm, a large tree fell in the middle of the road exactly in front of (but not on, luckily!) my home. As my neighbors slowly crawled out on the morning after, we started to assess the damage and figure out what we could do to unblock the road. Another piece of good luck-my altruistic neighbor had a gas-powered chainsaw and was willing to take down the tree so cars could pass. As he methodically took the 30-foot tree apart, I could see him testing each branch with his hands to see what would happen when he chopped it away. Eventually, he got to the trunk, having established at each step that its removal would be safe. Now he could have calculated a formula comparing weight, length, and angle of each branch before making each cut, but through using the sensorimotor approach of gently shaking it back and forth, he accomplished the task successfully.

Thinking like less than a 3rd grader may not be all that bad, then. However, when you can get into trouble is when you are fooled by marketers who realize we often are fooled by conservation problems. That long, tall jar of perfume may contain the same if not less than the short, fat one, but marketers often bet that you'll pay a higher price for the long, tall jar.  Manufacturers of all sorts of packaged foods apply this principle every day. The cereal box gets taller and narrower, but costs the same as the package it replaces, and you don't realize it unless you check the package contents.  

Now you're ready to take the  3th Grader Test. Answer yes or no to each of these questions:

1. I occasionally count on my fingers when I want to be sure I'm adding correctly.

2.  When shopping for the best value in a liquid such as orange juice, I tend to go for the tallest bottle.

3. I get annoyed at logic problems and would much rather deal with concrete examples.

4.  It's easier for me to work with my hands to find a solution to a problem rather than to think it through mentally.

5.  When something goes wrong with my computer, I attempt to reason through what's wrong before I start to attempt to fix it.

6.  I would rather have a wallet full of dollar bills rather than one full of 10's even if it totaled to the same cash value.

7.  If something is broken, I'd rather try to fix it by trial and error than to reason out a solution.

8.  I agree with the expression "out of sight is out of mind."

9.  If someone gives me a math puzzle to solve, I can answer it fine as long as I can work it out on paper.

10. It's much more efficient for me to use a formula to figure out interest rates rather than calculate them individually.

Can you figure out which answer goes with which type of intelligence? Now promise not to cheat. You get one point for each "Yes" answer.

Sensorimotor= 1, 4, 7, and 8

Preoperational= 2 and 6

Concrete operational = 3 and 9

Formal operational = 5 and 10  (congrats, you're smarter than a 5th grader!)

I hope that this explanation of Piaget's theory and the little test give you some insight into how your ability to solve problems evolves over life. Take advantage of whichever approach works best for you, and you'll definitely end up with better solutions than the average 3rd grader!

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Copyright 2011 Susan Krauss Whitbourne, Ph.D.



Scott, M. L., Nowlis, S. M., Mandel, N., & Morales, A. C. (2008). The effects of reduced food size and package size on the consumption behavior of restrained and unrestrained eaters. Journal of Consumer Research, 35(3), 391-405. doi:10.1086/591103