It was a nationally published math series, I believe it was Addison Wesley
publishing company, however, I could be mistaken about that.  I think the
same ideas were included in other published materials though at around that
time.  I stopped teaching math about 12 years ago--concentrated on reading
since then--now retired.

One thing I noticed this week watching my grandchildren draw--the 4 year old
draws a verbal translation in a sense--she draws a sheep (or dog) as a body
with 4 legs sticking out at odd angles, a head, and eyes.  The 8 year old
does more observing and has more of the spatial aspects correct. `I'm sure
this is all researched, however, it's interesting watching it.    Judy
----- Original Message ----- 
From: "[log in to unmask]" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Wednesday, July 27, 2005 5:43 AM
Subject: Re: Drawing as Mathematical Language.


Thanks Judy!

Is this curriculum taught in one state (and I wonder which one) or is it
widely used in the USA?

I am convinced that drawing can provide rich visual contexts for
mathematics. I wonder if you have come across Chris Athey's work on schemas
(1990)? We find that very young children have a natural proensity to
explore personal patterns of behaviour or schemas, and that these are
highly mathematical (such as rotation, connection and vertical
trajectories). They explore these through thought, actions - and drawing.

Maulfry

Original Message:
-----------------
From: Judy Warner [log in to unmask]
Date: Tue, 26 Jul 2005 20:33:21 -0400
To: [log in to unmask]
Subject: Re: Drawing as Language.


I haven't taught this for more than 10 years, but when I taught 3rd grade
there were a series of "strategies" we introduced for solving word problems.
They differentiated between "making a diagram",  making a "chart", and
drawing pictures or a picture that could help you think about the problem.
(There were others too--) Of course there would be a lot of overlap or
different ways of thinking about the problem that children might choose, and
the teaching was intended to expose the children to different ways they
might think about the information.  I know I was never taught these
strategies specifically myself (I'm 64) and I thought it was such a good
idea--word problems were often confusing for me!  I'm sure many people
discovered these strategies on their own, however, for those of us who
didn't, having them laid out was a step ahead.

 Judy
----- Original Message ----- 
From: "[log in to unmask]" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Tuesday, July 26, 2005 11:45 AM
Subject: Re: Drawing as Language.


Hi Judy!

I'm sure that there's huge value in children using drawings in math, though
it's likely that we are talking about different approaches.

The way in which we would approach it (I've done a lot of joint research,
with children from 3 - 8 years) is to suggest they 'put down something on
paper' to show their thinking, or to help them explore their understanding.
The great thing about these words is that they don't restrict children to
one ways of representation, but completely open it out - for early
(scribble-type) marks; pictures; iconic marks (one mark for one object);
pictures; writing (letters or words) and symbols such as numerals and '+'
or '='. We put the emphasis on the child making the decision about how they
might best represent their mathematical thinking. To see some examples, go
to 'gallery' in www.e-magine.org.uk.

Using graphical representations (we term them 'mathematical graphics') is a
great way of solving math problems and supports all areas of maths, helping
children understand the math at a deep level!

It would be interesting to hear more about 'draw a picture' in US math
curricula too!

Maulfry


Original Message:
-----------------
From: Judy Warner [log in to unmask]
Date: Mon, 25 Jul 2005 04:49:16 -0400
To: [log in to unmask]
Subject: Re: Drawing as Language.


Re: Drawing as Language."draw a picture" is one of the strategies taught in
math curricula here (US) now--to 3rd graders (8) and probably younger--I
never thought of this until I taught it--hence,  my difficulty with
confronted with word problems as a child and grownup.  I'm sure other
people came up with this strategy on their own, I never did, (but wish I
had.)  Make a diagram or chart is another strategy that's taught now
slightly different than draw a picture, but still graphic not verbal---

Judy Warner
  ----- Original Message ----- 
  From: Rachel Pearcey
  To: [log in to unmask]
  Sent: Monday, July 25, 2005 5:30 AM
  Subject: Re: Drawing as Language.





  On 25/7/05 7:42 am, "Mike Metcalfe" <[log in to unmask]> wrote:


    Latour emphasises the connection between visualisation and the
development of knowledge:  Latour, B. (1986). Visualization and Cognition.
Knowledge and Society 6: 1-40.


    Mike


  John Ruskin said more less the same thing in ELEMENTS OF DRAWING

  Rachel Pearcey
  (shortly to begin her third year BA hons in fine art at Exeter (just to
put you in the picture, ha))

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