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Topic: Real Numbers in the Primary Grades
Replies: 39   Last Post: Jan 2, 2010 11:36 PM

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 kirby urner Posts: 3,690 Registered: 11/29/05
Re: Real Numbers in the Primary Grades
Posted: Dec 26, 2009 8:00 PM
 att1.html (4.3 K)

On Thu, Dec 24, 2009 at 1:15 PM, Anna Roys <roys.anna@gmail.com> wrote:

> RE: On Thu, Dec 24, 2009 at 10:29 AM, Hecman Gun <sirgodel@live.com>wrote:
>

>> For students of all ages, definitions of basic
>> mathematical concepts have to be framed with care: not too formal, not too
>> informal...
>>
>>
>> ...What should be argued for a class (learning) the real numbers,
>> fractions, etc., is to learn by intuition.
>>

>
>

Hi Anna --

Let me try with the topic of real numbers again. How might we spark the
intuition in some curriculum?

REALS AS EDGE LENGTHS:

First, I agree with Bill and Dr. Wu that the number line is important, but
why exactly? Because it's graphical, not lexical, is part of the answer,
and because it relates number to length, a distance. The relation of
numbers to length is primal and should drive many of our early lesson plans.

However, instead of starting with just any old lengths, it'd make sense to
look at some specific distances in a geometric context. We'll want to build
some specific objects, will need specific lengths to do so.

FRACTIONS AS VOLUMES:

What's a common context for fractions, one with practical applications and
associations? Cooking skills, following recipes, in terms of whatever
units. Half cups, three quarter teaspoons etc. Nothing new here (so far).

But what might our measuring bowls actually look like? Here's one version:

http://www.wikieducator.org/Image:Still_life_sm.jpg ("mixing bowls", world
class).

http://www.wikieducator.org/Image:Syn_volumes_sm.jpg

http://worldgame.blogspot.com/2009/12/district-standard.html

COMBINING EDGES AND VOLUMES:

There's much to recommend this bevy of inter-connecting concepts, in that
we've got spatial geometry going in tandem with both fractional and real
number relationships. In addition to lengths, we have angles. We could add
rotation matrices, spherical coordinates.... looking down the road, yet

SUMMARY:

We have some specific fractions relating to volumes, measuring discrete
amounts, motivating computations and detection of equivalancies.

We have irrationals relating to lengths, motivating a discussion of Real
Number, their appearance in the history of ideas. Bill's use of intervals
might feature here.

MEETING A STANDARD

With polyhedra in view, we've got a state standard to hit: understand how
area and volume change as a 2nd and 3rd power of changes to linear scale.
Double edges, four fold area, eight fold volume. Have edges, reduce area
4x, volume 8x.

SOURCES

Published sources for using polyhedra in this way include a 1965 paper in
Math Teacher by MIT crystallographer Arthur Loeb. Robert Williams in his
The Geometrical Foundation of Natural Structure (Dover), and of course Bucky
Fuller himself (the dome guy). Lotsa street cred here, websites, books,
teaching supplies... everything one might need (including free computer
source code if you're taking a more digital approach -- on tap at my site,
with expository video).

I go into more biblographic detail here. Bill, this post mentions our

http://worldgame.blogspot.com/2009/12/real-and-rational-numbers.html

Kirby

PS: I didn't learn all this in ed school, which should be a point in my
favor with Haim.

Date Subject Author
12/23/09 Bill Marsh
12/24/09 Robert Hansen
12/24/09 Kirby Urner
12/24/09 Hecman Gun
12/24/09 Anna Roys
12/25/09 Bishop, Wayne
12/26/09 kirby urner
12/24/09 Robert Hansen
12/24/09 Bill Marsh
12/25/09 Robert Hansen
12/25/09 Robert Hansen
12/25/09 Hecman Gun
12/26/09 Robert Hansen
12/26/09 Robert Hansen
12/27/09 Haim
12/27/09 kirby urner
12/28/09 Bill Marsh
12/28/09 Haim
12/29/09 Bill Marsh
12/29/09 Robert Hansen
12/29/09 Michael Paul Goldenberg
12/29/09 Bill Marsh
12/29/09 Bill Marsh
12/30/09 GS Chandy
12/30/09 Michael Paul Goldenberg
12/30/09 Robert Hansen
12/30/09 Michael Paul Goldenberg
12/30/09 Robert Hansen
12/30/09 Michael Paul Goldenberg
12/30/09 Dave L. Renfro
12/30/09 Michael Paul Goldenberg
12/30/09 Bill Marsh
12/30/09 Louis Talman
12/30/09 Robert Hansen
12/30/09 Robert Hansen
12/31/09 Michael Paul Goldenberg
12/30/09 Dave L. Renfro
12/30/09 Bill Marsh
12/31/09 Robert Hansen
1/2/10 Bill Marsh