The youngest children choose whatever looks like the biggest amount of juice. They seem to believe that the juice becomes "more" when it is poured from one glass to another.
from watching video of these studies, i reached a different interpretation. specifically, i believe that group 1 is best modeled as playing a language game with the facilitator.
the facilitator places the lumps of identical clay, and asks which is more. the child indicates that they are the same. one piece of clay is flattened, and the facilitator asks again which is more. the child now indicates the flattened clay.
what's interesting to me, here, is that the child's focus is on the facilitator, and not on the clay.
my best understanding is that the child is uncertain about the meaning of the word 'more' in the context. it's a bit of an odd question the facilitator is asking, right? and perhaps the child is thinking "well, maybe 'more' means 'bigger'?" or some unverbal equivalent. (note that, if the facilitator did ask "now, which one is bigger?", then the flattened clay would be a natural choice, even for an adult.)
(i think this is actually in accordance with the overall essay, which essay i found very interesting!)
Glad you liked it. And yes, I would agree that this is in accordance with what I tried to point out.
Being asked a question two times incentivises children (and adults, I might add) to favour a different answer. This makes interpretations blurry and the categorisation notoriously unreliable. The child in the video you describe could well be regarded as in second or even third phase, yet not engaged in the intended task (but focussed on the "language game") -- or simply unclassifiable. Criticism will often point out these weak data points but fail to check how that affects Piaget's deduction of constructivism as a description of how concepts are acquired (not at all, as long as there is also some compelling evidence for phase 2).
Maybe some day we will have more objective measurements of people's reasoning. Evolutionary biology started out with spotty data and took a long time to fill the gaps it couldn't explain in detail, the human eye being the most prominent example,* but nothing in biology makes sense except in the light of evolution. For me, it's the same with constructivism and learning theory. And it's exciting, if scary, to see how we might learn more about our own minds in the near future.
*) I think it's 300-odd evolutionary steps, and every single one brings a gradual fitness advantage.
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 want to break a lance for Jean Piaget. When I come across his name, it's mostly in the context of criticism, much of which misses the point, IMO. Beware, though: I am no developmental psychologist -- just a teacher -- and I will not try to defend or even explain everything Piaget has thought up, but focus on one central point that, as I see it, ...
Piaget's constructivism and its applications to teaching have been discussed on LW before, but I'm a bit late for an actual response.
The man ...
Piaget is best known for his contributions to pedagogy and developmental psychology, but he started out as a biologist. Young Jean was a massive nerd -- introvert, anxious, physically fragile, with no interest in sports but an incredible creative power in science. By the time he finished school, he had published 20 papers about molluscs. It took him only three years to study biology and finish with a PhD. He then went on to become a professor of psychology before turning 30.
... and his work
The big arc of Piaget's life was a project to take epistemology into natural sciences, a theory he called genetic epistemology. He would have loved LessWrong! Regrettably, the theory itself had little impact, but its empirical foundation was special in many ways: it consisted mainly of clinical interviews in which he (and his collaborators, Bärbel Inhelder and Alina Szeminska) basically just talked to children of different ages, showing them little experiments to find out how the kids thought about them. 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. Whatever findings these interviews produced need to be evaluated with careful reflection, and indeed some of Piaget's interpretations have proven wrong. He wasn't just being sloppy though -- it's just not possible to produce the same kind of insights in a controlled, double-blind clinical trial.
Let's see what we can take from the results. The most famous example, by far, is the first chapter of the first monograph that Piaget et al. published on the topic: the one where sirop is poured from one glass to another (Piaget & Szeminska, 1941). The glasses had different shapes, so the same amount of juice might look more or less depending on which glass contains it. By asking the children which glass they thought contained more liquid, Piaget et al. found different types of responses, which they classified into three groups that differed by age. Groups 1 and 3 are not surprising at all.
Group 1: The youngest children choose whatever looks like the biggest amount of juice. They seem to believe that the juice becomes "more" when it is poured from one glass to another.
Group 3: The oldest children argue that the quantity of the juice doesn't change when it is poured from one glass to another, even if it may appear so. They have acquired the concept of conservation of quantity.
So far, so trivial. Considering that most adults know about the conservation of quantity and newborns never do, it follows that the learning must happen somewhere in childhood. But there is another stage in between:
Group 2: The intermediary children reason about what glass might contain more juice than the other. In some cases they might deduce that the amount of juice stays the same, but not by referring to the conservation of quantity, but rather by "calculating" and comparing quantity in something that almost resembles a primitive algebra. It's complex reasoning, in a place where it doesn't seem necessary.
Now, this is remarkable. One would think that a kid who is capable of considering the diameter and filling height of a glass would also have understood that the juice isn't created or destroyed in the process of pouring, but that is not the case. Piaget found similar behaviour for other little experiments (deforming clay, stacking coins, ...).
Note how this doesn't hinge on the specific age boundaries. Something interesting and surprising happens at some point -- even if this occurs only occasionally, it conveys meaning. Indeed, repetitions of Piaget's studies have shown that the results depend a lot on how the task is framed by the interviewers, but only quantitatively; children can show an understanding of conservation of quantity much earlier than the original study determined. But the findings stand qualitatively, and that turns out to be enough.
These experiments shed light on how concepts are built within a mind: not in an instant realisation, but in a costly process. If you try to transfer a concept directly, e.g. by telling a toddler something like "Don't you see, it's the same amount of juice?", the child won't understand what you're saying. They don't know what "amount" means, and they can't until they have figured out a concept of its conservation. Changing the phrasing won't help, words alone won't take them there. So how do they figure it out? That's a complex cognitive task, real dirty work, and much harder than just applying the concept, once it is learned. We may not remember it, but each one of us has followed that stony path at some point -- by ourselves. That is what constructivism means for Piaget. It is a theory that describes how humans acquire concepts, not an ideology for teaching.
What can teachers learn from this?
What does not follow from constructivism?
Grokking ~ Piaget-phase 2?
When I first saw time diagrams of transformer overfitting like the one in Power et al., (2022), I was immediately reminded of Piaget's children and their long struggle to learn a seemingly simple concept. For transformers, just as for children, generalisation arrives with a delay:
Gemini sketch loosely after Power et al., (2022)
If intelligence ~ compression and generalised concepts enable the compression of out-of-sample data, the similarity might indeed carry some meaning, although I'm not sure what exactly. Nanda et al. (2023) studied grokking phases and explained them as memorization, circuit formation and cleanup, respectively. Children, however, behave differently from undergrokked LLMs mostly in that they don't know how to use language in a way that fakes understanding ("guessing the teacher's passwords"), or, more generally: human brains can't store as much isolated information as a naive LLM. Our ability to absorb information increases gradually during childhood, which might actually be an advantage, as it constantly forces us into the "grokking" phase, rather than filling the memory prematurely. (Pure speculation on my part.)
Viliam mentions this in his post as an example of excessive "constructivism" in teaching. It's clearly exaggerated, but I have seen examples of this concept in action.