Preoperational College Students: A Piagetian Concrete Operations Stage Task College Students Fail

Among the trickiest parts of teaching Developmental Psychology is having our students put themselves in the place of children. Really feel their perspective. Until about 8 years of age, children preoperational thought is so magical and different than grownups, it's especially hard for us to imagine. I wonder if even Jean Piaget struggled to understand their perspective? Why? Notice how each of his stages is named for how children think, except preoperational, it's named for children being before "pre" a way of thinking, with operations. Jane Ewens Holbrook (1992) created a task closely resembling a Piagetian Conservation task, but somehow so challenging even advanced high school and college students fail! Discussing what's special about her task and why it's so hard for us, can help us really talk about children's development.

Hollbrook's task only provokes thought if students first learn Piaget's stages and some of his tasks, especially his Conservation Tasks. They need to recognize themselves as formal operational in their thinking since they're adults. They need to recognize failing conservation tasks suggest preoperational thought (about 2 to 7 years old), and they should have a clear idea of how experimenters ask questions during conservation tasks and the kinds of answers children give. Personally, I show short video clips of little kids completing the task and I highlight different elements to students with my commentary.

Prior to an operation, a reversible transformation, children need to agree there's the same amount in both identical glasses. In video 1, a little girl completes a Conservation of Liquid task. Though we don't see this girl doing so, it's very common for children to quibble having you ever so slight pour back and forth until they agree the two glasses are the same.

Recognizing the glass have the same amount, the experimenter does the operation (pouring). The experimenter draws attention to what she's doing and narrates, "Now watch what I do; I'm pouring all the water in this glass into this one." In this version of Conservation of Liquid, the experimenter pours into a taller thinner glass, but the task works just as well pouring to a shorter fatter glass. After pouring, the experimenter asks the exact same question as before. Being very precise, she asks, "Does this glass have more (gesture to a glass), does this glass have more (gesture to other glass), or do they have the same amount?"

In video 1, the girls fails the Conservation of Liquid task, so she has not achieved concrete operational thought yet. She is still preoperational in her thinking. Regardless of children's choice, the experimenter asks why. Children with preoperational thought answer with by describing an appearance along a single dimension just like this girl says, "it's taller."

Video 1 continues with a Conservation of Number task - two rows of trinkets (quarters) are laid with identical spacing and lines with each other. I like showing this task because it most closely resembles the college student version. The transformation in this video spreads the quarters of a row but the task works just as well with the operation of "crunching" being the operation rather than "spreading." Notice every operation is reversible; there's always an inverse like crunching undoes spreading, just like subtracting undoes adding. I love this video because the girls knows how to count, knows counting is how you find out, and knows five and five are the same. Yet when the experimenter spreads the quarters, she focuses entirely on the dimension of how long the line is.

The third task is a fun extra, not a standard Piaget task, but it makes the point again. Sometimes students are skeptical and believe the effect is purely about knowing definitions like "more." But real life versions like this one show it's not about the language. Preoperational children genuinely think differently.

A common misunderstanding of college students is what passing and failing mean. The task measures concrete operational thinking but we only use it at the beginning of the stage. We're trying to find when the previous stage ends. Failing means the child is still pre-operational.

Notice the girl fails all three tasks. That's consistent with Piaget's idea of a global shifting of stages. Children should respond to very different looking concrete operational tasks in the same way. Once children succeed at one task (often number), they experience horizontal décalage - passing the other tasks follows in the near future as the child grasps particulars. But right now, in all three tasks the girl does centration - focusing on a single dimension while ignoring any other dimensions. She focuses on height, length, and number respectively. But she misses width, spacing, and area respectively. But being able to think with concrete operations means being able to understand situations have many dimensions.

In video 2, a somewhat older girl completes the same Conservation of Liquid Task with the same experimenter. But she gives the correct answer. She isn't centrating. When asked "why," she states two dimensions matter. Yes, the new glass is taller, but it's also skinnier. As children proceed through concrete operations, becoming more capable of understanding operations, they explain what conservation means, "You didn't put any in and you didn't task any away, so it has to be the same."

I experimented with many variations of this conservation task and I'm describing the version I use, keeping the task simple but just hard enough college students routinely fail. In preparation you'll need to gather 50 trinkets, 25 in each of two contrasting colors. You shouldn't be able to tell the difference by touch, so they should have an identical texture, shape, and mass. They should be small enough you can hold 5 in your hand at once but big enough to be visible to your students around your classroom. You could choose trinkets like: marbles, play coins, checkers, jelly beans, poker chips, individually-wrapped chocolates, and buttons. You'll need two opaque containers each able to comfortably hold 25 trinkets while you mix them with your hand or by shaking. Before class, have 25 trinkets of a color in one container and 25 trinkets of the other color in the other container.

It sets the stage if you use child-directed speech ("motherese") to match your conservation videos. So ask something like:

"Does this bin have more red trinkets? Does this bin have more blue trinkets? Or do both bins have the same amount of trinkets?"

A volunteer can count, but to save time, students usually would just trust you when you say there are 25 in each. Since we're doing a Conservation Task, presumably illustrating concrete operations, be very explicit about every step you do. You might say:

"Now watch what I do. I am going to take 5 from the red bin and 5 from the blue bin."

Exaggerate reaching in and counting out 5 from each.

"Now I'll switch them so there are 5 blue in the mostly red bin and 5 red in the mostly blue bin."

Shake themup.

"Now I am not going to look and I am going pull 5 randomly from the mostly red bin. And 5 randomly from the mostly blue bin. Now I'll put them in the opposite bins."

I count in each hand separately and dramatically cross my arms at the wrist to show the switch.

From their seats, students can't see exactly how many you pulled of each color. Remember to do this slow and deliberately so students follow what is happening. We now have a question we can poll our students about. I put them on a slide and tell them they need to vote for one of our four choices:

Every time I play, students overwhelmingly vote "you can not know because of chance."

They're wrong.

And if you're like me, playing the first time, you're wrong too!

Count and you'll see you have the same number of blues in the mostly red bin as reds in the mostly blue bin. Tell students it has to be the same.

Many of your students still won't believe you. So play again really quickly, and you'll have the same number again.

After a few times playing, always getting the same. I bring up how it doesn't make sense because it's total chance how many of the minority color I picked up with each hand. Students will nod along in agreement. I like to give this explanation myself rather than having a student ask it, because when I make a little joke about it, I'm the person most embarrassed for being wrong.

By this point, I've actually had students get out of their seats and insist on doing it themselves! They really think I'm doing magic trick. But I'm not.

"It really was chance. I had no idea what I colors I picked. And we're really focused on the element of chance. Kinda' like centration is what we're all doing!!"

"So I guess we're all pre-operational?"

Now I'll say something like:

"Let's take chance out of it. You tell me. When I pull 5 from the mostly red bin, how many should be blue? Okay. Now while I pull 5 from the mostly blue bin, how many should be red?"

Do the switch. Count. And you'll see the answer is again the same. Even without chance.

How do we explain to college students the correct answer on a Concrete Operations Task they failed? Just like the correct answers children give.

We didn't add any new trinkets and we didn't take any trinkets away, so there has to be 25 red and 25 blue trinkets. If 7 of the trinkets in the mostly red bin are blue, where are the 7 red trinkets they replaced? In the other bin! It's literally conservation of number. Just like in Physics and Chemistry classes, when we learn in a closed system, energy can be neither created nor destroyed; it can only be transformed from one form to another. In our closed system of the game, trinkets are neither gained nor destroyed, they mere change location across bins.

Since we do transformations twice, it's pretty hard to say why with multiple dimensions. But I recommend students simplify the task. Task 9 nickels and 9 dimes. Play the game trying every combination of moving 0, 1, 2, or 3 to the other bin.

"Are all of us stuck in the preoperational stage of thinking?"

Quite clearly the answer is no because all of us can easily pass typical Piagetian Conservation Tasks. So we need a deeper explanation. This provocative question opens our discussion.

There are several big ideas we can guide our students through in a discussion.

We already noted to our students how they're centrating by focusing exclusively on the role of probability to the exclusion of anything else. But there's a difference between little children who centrate perceptually (like on the height water reaches) and adults who centrate conceptually (like on the idea of chance).

Being concrete operational means we're bound by our perceptions to what's there, what's concrete. But part of this Conservation Task involves the operation (movement of trinkets) outside our view. So this task isn't about a concrete operation but about an abstract operation. In math, we call logic that abstracts away from concrete premises, "formal logic," which is why Piaget calls his last stage, "formal operations." We can handle abstract operations. So, yes, this is a Conservation Task, but it's a Conservation Task measuring Formal Operations.

In a typical Piagetian Conservation Task, there is one transformation. But we did the "move trinkets" operation twice. Moreover, chance means we have 6 possible transformations for each bin to imagine. So this way too many operations to keep in mind while manipulating. This is a nice connection to covering Working Memory, either when covering Information Processing perspectives of development, or Cognitive Psychology in an introductory class.


I like playing this game with students because they can become quite animated about something very abstract. We're coming to have empathy we children, who also sense they're understanding isn't quite correct, but don't quite know how to, in Piaget's terms, decenter, to solve the problem. Hopefully we're inspiring students to learn and grow while they develop their critical thinking and empathy.

Holbrook, J. E. (1992). Bringing Piaget's preopertational thought to the minds of adults: A classroom demonstration. Teaching of Psychology, 19(3), 169-170.

Color Blindness: In case some students are color-blind, avoid choosing red and green as your contrasting trinket colors. Other hard pairs to contrast include: green-brown, blue-purple, green-blue, light green-yellow, blue-gray, green-gray, and green-black. But it's okay if you pair colors with different saturation and lightness. For example, a deep red and a pale green work.