[Maths-Education] [ATM-mail] RS/JMC Inquiry into Geometry

[Stuart K Rollands]

--Message-Boundary-14062
Content-type: text/plain; charset=US-ASCII
Content-transfer-encoding: 7BIT
Content-description: Mail message body

Dear colleagues,

The Royal Society / Joint Mathematical Council working committee on 
the teaching and learning of geometry in schools is apparently 
divided on the issue as to whether Euclidean geometry should be back 
on the menu. The attachment (RTF) is a 1200 word proposal to the 
RS/JMC on this issue.

Euclidean geometry, at one time the staple of secondary school 
mathemartics, was taught very badly: the Elements introduced as a 
textbook without the necessary prior development of spatial intuition 
or introduction to proof. Unfortunately, what we have today is 'shape 
and space' without proof and without any sense of our 
rational heritage as developed by the Greeks. The attachment is a 
proposal for the teaching of Greek geometry through its history and 
the aim is to provoke debate on this issue.

--Message-Boundary-14062
Content-type: text/plain; charset=US-ASCII
Content-disposition: inline
Content-description: Attachment information.

The following section of this message contains a file attachment
prepared for transmission using the Internet MIME message format.
If you are using Pegasus Mail, or any another MIME-compliant system,
you should be able to save it or view it from within your mailer.
If you cannot, please ask your system administrator for assistance.

   ---- File information -----------
     File:  geometry.rtf
     Date:  30 Jun 2000, 14:07
     Size:  10831 bytes.
     Type:  MS-Richtext

--Message-Boundary-14062
Content-type: Application/RTF; name="geometry.rtf"
Content-disposition: attachment; filename="geometry.rtf"
Content-transfer-encoding: BASE64
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--Message-Boundary-14062--