CTK Exchange
Front Page
Movie shortcuts
Personal info
Awards
Reciprocal links
Privacy Policy

Interactive Activities

Cut The Knot!
MSET99 Talk
Games & Puzzles
Arithmetic/Algebra
Geometry
Probability
Eye Opener
Analog Gadgets
Inventor's Paradox
Did you know?...
Proofs
Math as Language
Things Impossible
My Logo
Math Poll
Other Math sit's
Guest book
News sit's

Manifesto: what CTK is about |Store| Search CTK Buying a book is a commitment to learning Table of content Things you can find on CTK Chronology of updates Email to Cut The Knot

CTK Exchange

Subject: "Pestallozzi on number words"     Previous Topic | Next Topic
Printer-friendly copy     Email this topic to a friend    
Conferences The CTK Exchange Early math Topic #15
Reading Topic #15
alexb
Charter Member
672 posts
Nov-13-00, 10:44 PM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
"Pestallozzi on number words"
 
   Following is a copy of my post to the Numeracy listserv:
========================================================

What do you know? I have just purchased a 3 volume set of selected works of J. H. Pestalozzi - in Russian. The first volume starts with a diary he kept of his son's education. Following is my attempt at a literal translation of a couple of paragraphs on the 3rd page of the diary:

"Explaining to him the true significance of the first numbers I tried to confer some definiteness on those words that he learned by heart without understanding their real meaning. From this example, the least capable person might verify how big an obstacle for grasping the truth is the habit of learning words not related to valid properties of things. The habit of not thinking of how in essense the numbers are different that are assigned number words was evident and hindered his understanding.
7, 8, 9, and 1 were for him much the same as 3, 5, and 17, and I could not remove the consequences of that habit of not thinking.

"Why have I done such a stupid thing, teaching him ahead of time the words so important for grasping the truth without simultaneously taking care of making more precise the underlying notions while uttering the first number words? How natural would have it been not to teach him to say _three_ until he recognized correctly 2 in all things shown to him. How naturally would have he learned to count, and how much have I swayed in my haste from the nature's ways! Oh, you, the truths, so important for the wisdom and virtue, please teach me being cautious!"

(Written in 1774.)

All the best,
Alexander Bogomolny


  Alert | IP Printer-friendly page | Edit | Reply | Reply With Quote | Top
Ed Wall (Guest)
guest
Nov-13-00, 10:49 PM (EST)
 
1. "RE: Pestallozzi on number words"
In response to message #0
 
   Fantastic, Please post more of these gems for our reflection.

Ed Wall

At 12:56 AM -0500 11/12/00, Alexander Bogomolny wrote:

>What do you know? I have just purchased a 3
>volume set of selected works of J. H. Pestalozzi - in Russian. >The first volume starts with a diary he kept of his son's >education. Following is my attempt at a literal translation of
>a couple of paragraphs on the 3rd page of the
>diary:
>
>"Explaining to him the true significance of the first numbers
>I tried to confer some definiteness on those words that
>he learned by heart without understanding their real meaning.
>From this example, the least capable person might verify how
>big an obstacle for grasping the truth is the habit of learning
>words not related to valid properties of things. The habit of
>not thinking of how in essense the numbers are different that >are assigned number words was evident and hindered his >understanding. 7, 8, 9, and 1 were for him much the same as 3, >5, and 17, and I could not remove the consequences of that habit >of not thinking.
>
>"Why have I done such a stupid thing, teaching him ahead of time
>the words so important for grasping the truth without >simultaneously taking care of making more precise the underlying >notions while uttering the first number words? How natural would >have it been not to teach him to say _three_ until he recognized >correctly 2 in all things shown to him. How naturally would have >he learned to count, and how much have I swayed in my haste from >the nature's ways! Oh, you, the truths, so important for the >wisdom and virtue, please teach me being cautious!"
>
>(Written in 1774.)
>
>All the best,
>Alexander Bogomolny


  Alert | IP Printer-friendly page | Edit | Reply | Reply With Quote | Top

Conferences | Forums | Topics | Previous Topic | Next Topic

You may be curious to visit the old CTK Exchange archive.

|Front page| |Contents|

Copyright © 1996-2018 Alexander Bogomolny

[an error occurred while processing this directive]
 Advertise

New Books
Second editions of J. Conway's classic On Numbers And Games and the inimitable Winning Ways for Your Mathematical Plays