4 ms·

Jean Piaget and the Child’s Spontaneous Geometry

49 points by jhshah 9y ago

Singletoned 9y ago
> Piaget’s theory formulates a peculiarly inverted version of Ernst Haeckel’s biogenetic law that unites historical phylogeny and mental ontogeny in a recursive Möbius-band-like figure. I've Googled quite a few words from that sentence and still can't wrap my head round it. Can anyone ELI6?
- zxcb1 9y ago
  I found this helpful: https://en.m.wikipedia.org/wiki/Recapitulation_theory#Cognitive_development https://en.m.wikipedia.org/wiki/Recapitulation_theory#Cognit...
  - Singletoned 9y ago
    Yeah, it was. So it's like how the order in which we learn philosophical ideas roughly mirrors the order in which they were discovered?
    - gumby 9y ago
      That was Herbert Spencer’s Belief, yes, as he had a rather reductio “Gadgrind” view of knowledge and worth (he is also the originator of the phrase “social darwinism” and, amusingly, is buried across from his rival Karl Marx. This simplistic view is pretty much dead these days.
      - zxcb1 9y ago
        I am still a bit confused, am I interpreting this correctly? From an individual perspective, embodied tacit knowledge precedes conceptualized knowledge. In this example the process of drawing refines the spatial skills / cognition required to grasp Euclidean geometry. And the process of cultural knowledge progression does not necessarily follow this developmental order?
        gumby 9y ago
        Up to “and the process” yes, this is what Piaget taught. And that learning is a process of comtinuous rewriting of what you think you know, based on your experiences. Separately: some people, like Spencer, who believe that “progress” has a direction, that “more advanced” societies have more universal knowledge that accumulates like stacking paper on a table, (and this was the challenge of Darwin) that humans are closest to god and all other creatures are inferior (you can see how this extends to a belief that there are different races (=breeds) of humans, both in genetics/god’s engineering and in culture). Then tying the two together: you can look at the development of an individual human as an iterative, never ending and somewhat meandering process or you can say that you just have to transfer those stacks of paper, bottom to top, and then you’re done. The connection between the two may sound absurdly tenuous but sad to say it is highly politicized and to this very day affects how schools are organized and funded, culture, politics, beliefs about right and wrong and how people should behave.
        zxcb1 9y ago
        Ok, thanks! It seems to me that these aren’t mutually exclusive, rather complementary. The embodied approach, reminds me of the Montessori attitude of exploration / discovery and the metaphor of stacked paper, the industrial age, man as machine. How about seeing it as the difference between cultivating (complex, holistic, iterative, like ANNs) vs constructing (simple, compositional) or the principles of intuition and logic? Also, I suppose one may move in the other direction, from higher level conceptual to embodied understanding via iterative refinement.
- tremens 9y ago
  > Piaget’s theory formulates a peculiarly inverted version of Ernst Haeckel’s biogenetic law that unites historical phylogeny and mental ontogeny in a recursive Möbius-band-like figure. Individual development (ontogeny) restates historical evolution (phylogeny). Haeckel’s biogenetic law says that as an embryo develops it will pass through its past historical states as a species. It's a long discredited 19th century scientific hypothesis. Inverting the relationship would state that historical evolution is restating individual development OR in the other sense of inverting, they move in the opposite order to one another (Mathematicians: Euclid -> Topology, Kids: Topology -> Euclid). Basically, kids build up knowledge of topology from everyday interaction with the world and then move onto Euclidean shapes with the knowledge of topology. Mathematicians discovered it all in the opposite order, starting with Euclidean geometry and only later documenting topology.
  - Singletoned 9y ago
    Thanks. That seems a lot more understandable.
- gumby 9y ago
  Tremens answered about Häckel; the Möbius strip part is Piaget’s model of learning which says that knowledge undergoes continuous rewriting rather than being simply accretive, a view which I would think should be unremarkable today. Häckel came from a 19th century conception of “advancement” or “progres” — think of that absurd 19th century picture of various apes followed by a human, as if a human is somehow the “most evolved” of the animals. The idea of adaptation to the environment was alien (and apparently frightening) to most people in the West.
baldfat 9y ago
I work with 3 to 5 year old children, all bellow the poverty line, working with STEM and early literacy learning. This was a great article just due to the frustration I see of my students literacy programs we spend thousands of dollars on. They think all children can just see and learn letters without going to the foundations of shapes and distinguish sounds. I can't tell you how many children have difficulty with straight lines vs curved lines. Now bring that to learning letter shapes of A and H or S. It is believed that children learn straight line letters that cross quicker than curved, but I have not seen this with the hundreds of children I see every week. I now struggle on the now what in my work to get down to the shapes sooner rather than later with that work and how to convince these horrible developmentally inappropriate children applications that I use to work more in these foundational steps. If anyone wants to back me to take a 2 year sabbatical to develop some children tools it would be greatly appreciated :)
- goldenkey 9y ago
  I'm sure if you had some way to app-ize your ideas or generate a return on investment, many people here would back you. (Shouldn't need to be said, but I do feel expedient education of our youth is endlessly valuable despite where it might sit in the capitalistic cabal)
  - baldfat 9y ago
    > generate a return on investment Right now there are two models A) Web based with ads (Most children activities and games online) B) Subscription Model (ABC Mouse, iStation) I would love to figure out another model
- mkempe 9y ago
  Have you looked at Maria Montessori's pedagogy? my daughters both learned to write cursive, starting at age 2 with tracing activities (geometrical inset/outset, sandpaper letters, etc.). Having watched them interact with apps on the iPad, I think the sensorial and perceptual presence of the learning materials is very important -- apps are not a sufficient substitute.
xrd 9y ago
My favorite introduction to Piaget was the book Mindstorms, about Seymour Papert and the development of logo at MIT. I'm interested in anyone on this thread contributing more to my reading list. Some of the references in that article are very esoteric to me.

49 points by jhshah 9y ago

> Piaget’s theory formulates a peculiarly inverted version of Ernst Haeckel’s biogenetic law that unites historical phylogeny and mental ontogeny in a recursive Möbius-band-like figure. I've Googled quite a few words from that sentence and still can't wrap my head round it. Can anyone ELI6?

zxcb1 9y ago
I found this helpful: https://en.m.wikipedia.org/wiki/Recapitulation_theory#Cognitive_development https://en.m.wikipedia.org/wiki/Recapitulation_theory#Cognit...
- Singletoned 9y ago
  Yeah, it was. So it's like how the order in which we learn philosophical ideas roughly mirrors the order in which they were discovered?
  - gumby 9y ago
    That was Herbert Spencer’s Belief, yes, as he had a rather reductio “Gadgrind” view of knowledge and worth (he is also the originator of the phrase “social darwinism” and, amusingly, is buried across from his rival Karl Marx. This simplistic view is pretty much dead these days.
    - zxcb1 9y ago
      I am still a bit confused, am I interpreting this correctly? From an individual perspective, embodied tacit knowledge precedes conceptualized knowledge. In this example the process of drawing refines the spatial skills / cognition required to grasp Euclidean geometry. And the process of cultural knowledge progression does not necessarily follow this developmental order?
      - gumby 9y ago
        Up to “and the process” yes, this is what Piaget taught. And that learning is a process of comtinuous rewriting of what you think you know, based on your experiences. Separately: some people, like Spencer, who believe that “progress” has a direction, that “more advanced” societies have more universal knowledge that accumulates like stacking paper on a table, (and this was the challenge of Darwin) that humans are closest to god and all other creatures are inferior (you can see how this extends to a belief that there are different races (=breeds) of humans, both in genetics/god’s engineering and in culture). Then tying the two together: you can look at the development of an individual human as an iterative, never ending and somewhat meandering process or you can say that you just have to transfer those stacks of paper, bottom to top, and then you’re done. The connection between the two may sound absurdly tenuous but sad to say it is highly politicized and to this very day affects how schools are organized and funded, culture, politics, beliefs about right and wrong and how people should behave.
        zxcb1 9y ago
        Ok, thanks! It seems to me that these aren’t mutually exclusive, rather complementary. The embodied approach, reminds me of the Montessori attitude of exploration / discovery and the metaphor of stacked paper, the industrial age, man as machine. How about seeing it as the difference between cultivating (complex, holistic, iterative, like ANNs) vs constructing (simple, compositional) or the principles of intuition and logic? Also, I suppose one may move in the other direction, from higher level conceptual to embodied understanding via iterative refinement.
tremens 9y ago
> Piaget’s theory formulates a peculiarly inverted version of Ernst Haeckel’s biogenetic law that unites historical phylogeny and mental ontogeny in a recursive Möbius-band-like figure. Individual development (ontogeny) restates historical evolution (phylogeny). Haeckel’s biogenetic law says that as an embryo develops it will pass through its past historical states as a species. It's a long discredited 19th century scientific hypothesis. Inverting the relationship would state that historical evolution is restating individual development OR in the other sense of inverting, they move in the opposite order to one another (Mathematicians: Euclid -> Topology, Kids: Topology -> Euclid). Basically, kids build up knowledge of topology from everyday interaction with the world and then move onto Euclidean shapes with the knowledge of topology. Mathematicians discovered it all in the opposite order, starting with Euclidean geometry and only later documenting topology.
- Singletoned 9y ago
  Thanks. That seems a lot more understandable.
gumby 9y ago
Tremens answered about Häckel; the Möbius strip part is Piaget’s model of learning which says that knowledge undergoes continuous rewriting rather than being simply accretive, a view which I would think should be unremarkable today. Häckel came from a 19th century conception of “advancement” or “progres” — think of that absurd 19th century picture of various apes followed by a human, as if a human is somehow the “most evolved” of the animals. The idea of adaptation to the environment was alien (and apparently frightening) to most people in the West.

baldfat 9y ago

I work with 3 to 5 year old children, all bellow the poverty line, working with STEM and early literacy learning. This was a great article just due to the frustration I see of my students literacy programs we spend thousands of dollars on. They think all children can just see and learn letters without going to the foundations of shapes and distinguish sounds. I can't tell you how many children have difficulty with straight lines vs curved lines. Now bring that to learning letter shapes of A and H or S. It is believed that children learn straight line letters that cross quicker than curved, but I have not seen this with the hundreds of children I see every week. I now struggle on the now what in my work to get down to the shapes sooner rather than later with that work and how to convince these horrible developmentally inappropriate children applications that I use to work more in these foundational steps. If anyone wants to back me to take a 2 year sabbatical to develop some children tools it would be greatly appreciated :)

goldenkey 9y ago
I'm sure if you had some way to app-ize your ideas or generate a return on investment, many people here would back you. (Shouldn't need to be said, but I do feel expedient education of our youth is endlessly valuable despite where it might sit in the capitalistic cabal)
- baldfat 9y ago
  > generate a return on investment Right now there are two models A) Web based with ads (Most children activities and games online) B) Subscription Model (ABC Mouse, iStation) I would love to figure out another model
mkempe 9y ago
Have you looked at Maria Montessori's pedagogy? my daughters both learned to write cursive, starting at age 2 with tracing activities (geometrical inset/outset, sandpaper letters, etc.). Having watched them interact with apps on the iPad, I think the sensorial and perceptual presence of the learning materials is very important -- apps are not a sufficient substitute.

xrd 9y ago

My favorite introduction to Piaget was the book Mindstorms, about Seymour Papert and the development of logo at MIT. I'm interested in anyone on this thread contributing more to my reading list. Some of the references in that article are very esoteric to me.