One of the oldest branches of mathematics is number systems.  When we analyze when and where exactly the number system came from we end up working our way all the way back to the development of mathematics in general.  Some say that the first discovery of a placement of any number is the highest achievement of ancient elementary arithmetic and the foundation of mathematics in general.  Relating this to my capstone class now, where we do a lot of mathematics that people would use in ancient times, I cannot imagine trying to think about any form of mathematics without having a scale to relate it back to.  It makes me curious as to what mathematics actually took place prior to this discovery of number placement.  The discovery of this positional principle was made during the Babylonian mathematics around 2000 BC.  After the discovery of the positional principle of a number representation, came the decimal number system at around the 8th century.

A few mathematicians that we know of today were some of the original supporters of this “unusual” numerical organization.  A couple of examples of these people is the famous French mathematicians Laplas and Leonardo Pisano, better known as, Fibonacci.  After doing some research, I came to a quote of his that I really liked where he said,

“The nine Hindi numerals are the following: 9, 8, 7, 6, 5, 4, 3, 2, 1. Using these numerals and the numeral of 0 called “zephirum” in Arabian, one may write some number”.

This quote allows me to put myself into other peoples’ shoes and realize what a drastic change, and upgrade this must have been.  To simplify what I mean, if you look at the number 5,555,555, even though this one number consists of all of the same number, 5, each one of these 5’s means something different to the whole number.  The reason why is the placement of it.  This is a very complex and confusing problem to someone who has been doing mathematics in a completely different way before discovering this new way.

A great link that I found had a interesting visual on how to talk about the number system and why we use it.  I liked getting the chance to explore other’s thoughts and ideas on this matter.  The link is written below:


The “So what?” for my students?  That’s simple.  The reason we must know about the number system is to have something to relate to.  For every math problem we do, there is a way to show it through this system.  The number line is a good example of that.  Whether dealing with measurement, fractions, addition, multiplication, etc.  Showing it on the number line provides a clear precise way of what we are doing when be asked to solve a problem.