I want to break a lance forJean 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, ...
stands unencumbered by the methodological criticisms,
sheds light on how concepts are learned,
comes with real-world use for teaching and learning,
and even bears some parallels to recent AI research.
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 loton 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?
Respect the perspective of the learner and try to empathise with it.
The language that teachers use needs to be precise and reliable, but this isn't always the most effective way to communicate new concepts to learners. The core advantage of cooperative methods like peer instruction is that learners get to teach each other in their own language.
What does not follow from constructivism?
You should not leave any learner alone with any task.[1] Who came up with this?! Constructivism means that each learner has to construct the concepts for themselves anyway -- no matter how much you help them! Leaving them alone to pronounce that fact doesn't "leverage constructivist learning theory" or whatever, and it's a less-than-ideal learning environment for almost everyone.
Introducing abstraction early in teaching goes against constructivism. The abstract model is coded in a language that the learners don't speak yet. There is no easy way around the construction and integration of concepts by every learner.
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:
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.
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.