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Topic: Common Core snippet a little distressing
Replies: 73   Last Post: Jul 26, 2013 6:27 PM

 Messages: [ Previous | Next ]
 kirby urner Posts: 3,690 Registered: 11/29/05
Re: Common Core snippet a little distressing
Posted: Jul 17, 2013 12:37 PM
 att1.html (2.9 K)

On Wed, Jul 17, 2013 at 9:22 AM, Robert Hansen <bob@rsccore.com> wrote:

>
> On Jul 17, 2013, at 12:21 PM, kirby urner <kirby.urner@gmail.com> wrote:
>
> Does Euclidean geometry make more sense than non-Euclidean?
>
>
>
> Bob Hansen
>

They've never seen any such thing as an infinitely flat infinitely thin
plane. Might we have geometry that goes away from those?

Karl Menger suggested a "geometry of lumps" where we didn't go with the
standard ideas of 0, 1, 2, 3 dimensions -- he was a dimension theorist,
originally Vienna Circle, later worked at Illinois Institute of Technology.

Everything is a lump. Everything has an interior.

Makes about as much sense as saying a cube is made of 0D points stacked

http://coffeeshopsnet.blogspot.com/2009/03/res-extensa.html

Anyway, it's a spiral. The field is wide open to lesson planning so I'm
not going to nail down exactly when to say what to whom at what age
level. There's a natural shake-out that occurs when many people try many
things.

Pouring water or dry grain from a unit tetrahedron to other shapes,
appropriately sized, is something I've done successfully with Montessori
kids (pre-K).

I've also presented this Lesson in different countries, e.g. Lesotho and
Bhutan.

The whole number volumes are easy to grasp.

Tetrahedron: 1
Cube: 3
Octahedron: 4
Rhombic Dodecahedron: 6
Cuboctahedron: 20

Computing volume relative to a unit cube is scarier, algebraically, which
is probably why, in the older curricula, polyhedrons are at the back of the
book and rarely discussed in much detail, beyond the obligatory topics of
sphere, cone and cylinder.

Kirby

Message was edited by: kirby urner (fixed Menger affiliation)

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