When Did Numbers First Appear in History?

What is a number?

Def in it ions : Enumerat ion : 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) Numerat ion : 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 ago-The Wolf 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 Were superseded in 3200 BC with the clay pictographic tablets.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 quest ion:

“Teaching so that student ’s understand the “why’s , ” teaching for meaning and

understanding, teaching so that chi ldren see and appreciate the nature, role and fascination of mathematics , teaching so that students know that men are st i l l creat ing mathematics and that they too may have the thri l l 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 McGraw-Hill 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