
Jean Piaget and the Child’s Spontaneous Geometry - jhshah
https://www.mpiwg-berlin.mpg.de/news/features/features-feature11
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baldfat
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 :)

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mkempe
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.

~~~
jerf
"I think the sensorial and perceptual presence of the learning materials is
very important -- apps are not a sufficient substitute."

I have wondered if a custom touchscreen setup could be designed to make this
easier. The problem seems to me not to be something intrinsically "wrong" with
screens, but that the touchscreens are too smooth if you use them with some
sort of stylus, and to have too much difference between static and dynamic
friction if you use your finger directly on the screen. As an adult, my
handwriting gets noticeably worse on a touchscreen with a stylus, and only
marginally better than my third-grader's writing when using my finger. It
seems like if someone put their mind to it, a touchscreen+stylus combo could
be created that would be very similar to pencil-on-paper in feel. It's even
possible this could be done with a stylus and a generic overlay that could be
put on any existing touchscreen (albeit possibly limited to higher quality
capacitive screens).

The disadvantage is that this overlay will probably render the underlying
touch screen no longer pleasant to use with a finger, and you probably want a
semi-permanent adhesion so it's not going to be a thing you can easily take on
and put off. (It could be experimented with but I bet it doesn't work out very
well.) But still, an off-the-shelf tablet + $20 (at scale) in stylus + overlay
might be able to mitigate and/or eliminate the sensory issues, while retaining
the advantages that an app can bring, instant feedback primarily.

(In my opinion, the biggest thing that computers can bring to education is
instant feedback, which can be mathematically shown to improve the maximum
possible learning rate, and any attempt to bring computers into education that
don't involve harnessing this are starting at a severe disadvantage.)

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xrd
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.

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Singletoned
> 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?

~~~
tremens
> 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
Thanks. That seems a lot more understandable.

