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After discussing Piaget's stages, this demonstration may suggest college students still use pre-operational thinking. A short class discussion leads students to consider factors like working memory and task specifics, providing a bridge to another class on information processing theories of development. Here are PowerPoint slides for this Piagetian Thinking or Information Processing Task Analysis activity.
When we teach about Piaget's theory, we typically include the famous Piagetian conservation tasks to show the transition from pre-operational thinking to concrete operational thinking. You might show video clips or demonstrate it in class. First I'll review the standard way to conservation tasks work and review the key Piagetian concepts used to explain pre-operational thinking. Second, we'll go through a new demonstration that college students, graduate students, and professors routinely fail (including me). Third, we'll use students failing the task to introduce ideas that bridge to a coming class about informatin processing theory.
Start, for example, with two short fat glass jars. Put the same amount of water (or colored liquid) in both and ask the child, "Does this one have more, does this one have more, or do they have the same amount?" Often children get very precise and say one has more. If so, pour a few drops from the one with less into the one with more. Keep repeating until the child agrees that both have the same amount.
Now say, "Watch what I do." Take, for example, a tall thin glass jar and pour everything in one of the short fat glass jars into the tall thin glass jar. Exagerate out getting every last drop. Put the empty jar asside and repeat the questions about the two jars with water. "Does this one have more, does this one have more, or do they have the same amount?"
Prior to using concrete operational thinking, children will say (typically) that the tall thin glass has more because it looks like it does. But children who use concrete operations will say that both jars have the same amount. "Why?" Some children answer by overcoming centration (over-emphasis on one dimension to the exclusion of others), "This one looks like it has more because it's taller, but it's also fatter." Others explicit mention the operation (a transformation mental transformation that can be undone, like pouring one way and pouring back), "You didn't put any in and you didn't task any away, so it has to be the same.?
At the end of class, having seen several conservation tasks and discussed Piaget's stages, I close class with one last demonstration of a conservation task. I demonstrate it using as simiilar language and gestures as I can to the earlier demonstrations. Bring to class two small bins with 25 trinkets (e.g., marbles) in each of two colors.
Ask, "does this bin have more red trinkets, does this bin have more blue trinkets, or do both bins have the same number of trinkets." Time permitting you can have a volunteer count, but I usually brush over this step and have students trust me that there really are 25 in each.
"Now watch what I do. I am going to take 5 from the red bin and 5 from the blue bin." Exagerate 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 them up.
"Now I am not going to look and I am going to pull 5 at random from the mostly red bin. And 5 at random from the mostly blue bin. Now I'll put them in the opposite bins. 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. "This leads us to a question and you should vote for one of these choices:"
Which bin has more of the other color?
Every time i have done this, the vote has been overwhelmingly that you can not tell. But count it out and you will see it's exactly the same. Tell students it has to be the same. Many won't belive you, so do it again (faster) and you will have the same number again. Still not convinced? Let students tell you how many of each odd color to pull from each bin. No matter what they choose, it's the same." Have a discussion about why. The easiest answer is that you did not put any in and you did not take any away. So for every blue in the mostly red bin, you mist have moved a red into the mostly blue bin. It's much harder to explain the multiple dimensions (how many of the odd color that's pulled from each bin). But you can suggest students set it up for themselves with 9 nickels and 9 pennies, and testing each possibility from 0 to 3 randonly chosen on the second switch.
The most important discussion to have is easy to raise, with a simple provocative question, "So does this mean all of you are stuck in pre-operational thinking?" They'll say "no." They might mention the chance element makes it confusing. But retort, "so you got confused by focusing on chance. Doesn't that mean you were centrating on the probability instead of considering all the elements? So you are thinking pre-operationally!" But they'll still put out the task has more steps and not seeing everything means you have to keep more in mind. Incidentally point out that this is called "working memory." Lead the conversation so students note that it's not about a kind of thinking but about qualities of the task. Sometime in the conversation, I reveal the caveat that the trinket game is actually a Piagetian formal operations task because we're taking the physically-apparent concrete operations and making them abstract (formal). But keep this point minimal. End class with a teaser for the next class about information processing theories by saying something like, "In our next class will see a theory that focuses in on all the particulars of tasks, called task analysis, to examines how children work with very particular processes, like working memory, in order to trace developmenta without overarching broad stages."
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