When Did Numbers First Appear in History?

When Did Numbers First Appear in History?
W hat is a number?
Definitions:
Enumeration: Keeping track of objects in a collection or set by matching objects one to one, such as fingers, toes, pebbles, or
sticks, notches in rope)
Numeration: Keeping track of objects using words.
Number:
A word or symbol used in counting or which indicates how many in a series;
A member or a set of positive integers.
35,000 years ago-The Lebombo Bone
A baboon’s fibula with 29 distinct notches. Discovered in Swaziland. Number of notches suggest
that the bone was used to mark the lunar days.
30,000 years agoThe W olf Bone
Found in Czechoslovakia.
Marked with 55 tally marks grouped in 5’s.
20,000 years ago- The Ishango Bone
The fibula of a baboon. Has a series of tally marks carved in three columns running the length of the
tool. Suggested that it’s the oldest table of prime numbers. Might represent a lunar calendar. The
markings on the first 2 rows add up to 60.
Row A notches = 20+1, 20-1, 10+1, 10-1.
Row B notches contains prime numbers between 10 and 20.
Row C notches may illustrate a method of duplication (multiplication by 2).
*Recent research indicating that it was a lunar phase counter.
8000-3500
BC-Counting Tokens
Neolithic plain counting tokens of various geometric forms made from clay. Appeared when local
peoples changed from a life based on hunting and gathering to one based on agriculture. (“Agricultural
Revolution”) Diameter=1.0 cm. Were used for 5000 years prior to the use of abstract numbers. Example: Cone=small
measure of grain. Sphere=large measure of grain, Ovoid= jar of oil. (2 jars of oil=2 ovoids).
4000-3200 BC-Stone Counting Tokens
These tokens had added lines, dots and various designs to cover the more
advanced counting needs. Sometimes attached to strings. Were superseded in
3200 BC with the clay pictographic tablets.
3700-3200 BC-Bulla
Small clay tokens. Tokens took on different shapes to represent different resources.
From left to right, historians believe these tokens represented the following: 1 type of garment, 1 unit
of metal, 1 unit of a particular oil, 1 sheep, no one knows what this stood for, 1 measure of honey, 1
type of garmanet.
3500 B.C.- Clay
tokens
Clay tokens. The clay ball in the picture is hollow and the clay tokens were stored in side the clay ball. The clay
ball was sealed off with no way to see inside. The Sumerians imprinted clay tokens on the outside of the clay ball
before placing them inside. Eventually, the clay ball became pointless. People just looked at the outside to get the
information they needed.
3300 B.C.-Clay tablets
The Sumerians and Egyptians created symbols to represent numbers which they would inscribe on clay
tablets. Originally they drew “word pictures which developed into symbols. These symbols are now called
Hieroglyphics (Egyptian) and cuneiform
(Sumerian).
Connections to Middle School Math Curriculum & reason why I picked this question:
“Teaching so that student’s understand the “why’s,” teaching for meaning and
understanding, teaching so that children see and appreciate the nature, role and
fascination of mathematics, teaching so that students know that men are still
creating mathematics and that they too may have the thrill of discovery and
invention…” (National Council of Teachers of Mathematics, 1989)
References
National Council of Teacher of Mathematics (NCTM) (1989): History Topics for the Mathematics Classroom.
Library of Congress: Reston, VA
Thomas, C. (2009) Schaum's Outline of Mathematics for Liberal Arts. Majors. New York, NY; The McGrawHill Companies, Inc.
Seife, C. (2000) Zero: the biography of a dangerous idea, Volume 2000, Part 2. New York, NY: Penguin
Putnam, Inc.
Greer, B. (2009). Culturally Responsive Mathematics Education. New York, NY: Taylor and Francis
Clawson, C. (1994) The mathematical traveler: exploring the grand history of numbers. Cambridge, MA:
Perseus Publishing.
Oystein, O. (1988) Number theory and its history. Mineola, NY: The McGraw-Hill Companies, Inc.
Cajori, F. (1928). A History of Mathematical Notations - Vol. I. Chicago, Il: The Open Court Publishing
Company.
Berlinghoff, W.P., & Gouvea, F. Q. (2004) Math through the ages: a gentle history for teachers and others.
Library of Congress.
http://www-history.mcs.st-and.ac.uk/Indexes/Babylonians.html
http://www.schoyencollection.com/math.htm#5067_1_8