Most of the criticism regarding Piaget’s work is aimed at this methodology, since it fails to meet many criteria of good scientific research: repeatability, for instance.
I agree that classifying things that kindergarteners says into categories like “conveys information to others” or “just comments loudly on what he sees, ignoring the audience” is going to be very subjective. Piaget already admits it in his book, and says something like… the exact categories do not matter, you just have to make some and evaluate them consistently for different age groups, and then you will observe a change of frequency in the categories between age groups. (Not an exact quote.) That sounds kinda doable.
But a more precise part is where he started. He worked for Alfred Binet—the guy who made one of the first IQ test—and while Binet was interested in counting the number of correct answers and calculating the IQ, Piaget noticed a different thing in the same tests:
Naively, if the test has four answers A, B, C, D, we should expect small children to start with a random distribution, like 25% chance of choosing each answer… and ending with smart adults choosing the right answer all the time (assuming reasonable adults, and a reasonably simple test)… and in the meanwhile, if we make a graph with a age on one axis and the frequency of choosing a specific answer on the other axis, we would expect the correct answer to go up, and the incorrect answers to go down (albeit at a different rate, if one of them is more obviously wrong than another). But what we often see instead is that some wrong answer gets more popular as the kids grow up, until some moment where the trend reverses and the kids finally start to converge on the correct answer.
This is what led him to the conclusion that kids tend to have certain wrong models (in LW lingo: cognitive biases) specific for certain age, such as magic thinking etc. so those answers go up before they go down. And this part should be relatively easy to replicate; actually all you need is the raw results of many IQ tests plus the age.
I agree that classifying things that kindergarteners says into categories like “conveys information to others” or “just comments loudly on what he sees, ignoring the audience” is going to be very subjective. Piaget already admits it in his book, and says something like… the exact categories do not matter, you just have to make some and evaluate them consistently for different age groups, and then you will observe a change of frequency in the categories between age groups. (Not an exact quote.) That sounds kinda doable.
But a more precise part is where he started. He worked for Alfred Binet—the guy who made one of the first IQ test—and while Binet was interested in counting the number of correct answers and calculating the IQ, Piaget noticed a different thing in the same tests:
Naively, if the test has four answers A, B, C, D, we should expect small children to start with a random distribution, like 25% chance of choosing each answer… and ending with smart adults choosing the right answer all the time (assuming reasonable adults, and a reasonably simple test)… and in the meanwhile, if we make a graph with a age on one axis and the frequency of choosing a specific answer on the other axis, we would expect the correct answer to go up, and the incorrect answers to go down (albeit at a different rate, if one of them is more obviously wrong than another). But what we often see instead is that some wrong answer gets more popular as the kids grow up, until some moment where the trend reverses and the kids finally start to converge on the correct answer.
This is what led him to the conclusion that kids tend to have certain wrong models (in LW lingo: cognitive biases) specific for certain age, such as magic thinking etc. so those answers go up before they go down. And this part should be relatively easy to replicate; actually all you need is the raw results of many IQ tests plus the age.