"In a rough way we may summarize the conclusions of the writers to whom reference has chiefly been made, as follows: 1. Let the child learn to count things, thus getting the notion of number. These things are, for the purpose of counting, considered alike, and they may be single objects or groups. 2. Let him acquire the number series, exercising with it beyond the circle of actually counted things. 3. In the learning of symbols it does not seem to be a matter of moment as to whether these are given with the first presentation of number or not. They must, however, be acquired soon. 4. Unconsciously and gradually the child will acquire the idea (never expressed to him in words) of the one-to-one correspondence of number, name, symbol, and thereafter the pure concept of number will play a small part in his arithmetical calculations. 5. The ratio idea of number should be introduced early, and applied in the work with fractions."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
David Eugene Smith, The Teaching of Elementary Mathematics (1904) pp. 108-109.
https://en.wikiquote.org/wiki/Number
Revision History
No revisions have been submitted for this quote.
Categories
Number
40 quotes on TrueQuotesView all quotes by Number →
Related Quotes
"Pythagoras... assumed as first principles the numbers and symmetries existing among them, which he calls harmonies, a…"
"If the early Greeks were cognizant of Babylonian algebra, they made no attempt to develop or even to use it, and ther…"
"With the intrusion of irrational numbers to disrupt the integral harmonies of the Pythagorean cosmos, a controversy t…"
"[T]he invention of writing... occurred somewhere around 3000 B.C. This is attributed to the ians... Sarton mentions t…"
"By the ancients [Greeks], arithmetic was studied through geometry. If a number was regarded as simple, it was a line.…"
"For measurements of time he collected and weighed water flowing from a container at a constant rate of about three fl…"
"A critical step was made sometime before the ninth century AD, when a new partial script was invented, one that could…"
"The arithmetization of mathematics... which began with Weierstrass... had for its object the separation of purely mat…"
"In speaking of arithmetic (algebra, analysis) as a part of logic I mean to imply that I consider the number concept e…"
"Ten is the nature of number. All Greeks and all barbarians alike count up to ten, and having reached ten revert again…"