The History of Mathematics
The Fifth Great Lesson
Teacher Preparation
I have purchased several books to help with this, but have never yet really used them. Maybe if I was an upper elementary teacher with students who could really understand mathematical concepts, I would. I have made it most of the way through The Story of Mathematics by Lloyd Motz and Jefferson Hane Weaver. Mathematics From the Birth of Number by Jan Gullberg goes through an amazing display of the uses of numbers and tells the history of each. This is where I got my information on the different notations of writing numbers. This would provide a wonderful way for upper elementary students who were talented mathematicians to study. They could take one chapter at a time and work their way through an understanding of history. The Universal History of Numbers by Georges Ifrah has wonderful illustrations that could easily be copied.
There are many different ways I have seen this lesson presented.
Don Jennings' album pages tells the lesson as a story very similar to the story of the History of Writing. Http://www.moteaco.com
I have also seen the lesson done with cards of famous mathematicians and what they developed. This is difficult material for Lower Elementary students who do not really understand exactly what it is they invented. I have taken the Mathematicians are People, Too available from Michael Olaf and cut it up into colored, laminated sections divided by time periods. The students can than read very accessible stories about mathematicians for research if they like.
Knowing that the students really like to do something with the lessons, I talk about how the use of numbers came from the same need as language or trade and then go on to something totally different.
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The Story of the History of Mathematics
You need to have laminated cards of Sumerian, Egyptian, Chinese, Roman and Mayan Numbers.
Early cultures counted to 1, 2 and maybe three. They counted higher by combining these numbers.
| 1 = one |
2 = two |
3 = two one |
4 = two tow |
5 = two two one |
They would just say a lot or many if the numbers got too high. Today we still use words like many when a number is too high. Forest, swarm or school (as in fish) are words that mean too many to count.
The Egyptians used additive notation to write their numbers. Every symbol was repeated to write a number. If there were no hundreds, then they wrote nothing. So 3,124 would be 1,000 1,000 1,000 100 10 10 1 1 1 1.
The Romans also used the additive notation to write numbers, but they used a zero to show nothing. The zero had been invented by the Hindus.
The Chinese used a multiplicative notation. 3,124 would be 1,000 x 3 100 x 1 10 x 2 1 x 4
The Mayans used a vertical place value system in base 20. If you haven't learned bases in math, then go ahead and just pretend they used base 10. If you have learned bases this will be a challenge for you. Their unit was at the bottom and their highest digit was at the top. In place value systems like ours you have to use a zero or the number is incorrect.
The unit is 1 - 19, the ten begins at 20, the 100 begins at 400 and the thousand at 8,000.
So 3,124 would be 7 100's = 2,800 16 10's and 4 1's
The 4 would be at the bottom, the 16 next and the 7 on top.
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Journal Suggestions
The people of Mesopotamia developed numbers to keep track of their business negotiation. There are some words that take the place of numbers. We use them when the amount is too big to count. Can you think of some of these numbers?
Three systems of counting developed in different cultures. The additive notation was the earliest, system of numbers and was even used by the Romans. The Chinese developed the multiplicative notation. The Mayans and modern cultures use a system based on place value. Write some numbers for us to figure out.
We owe our calendar to the Romans who added the last four months. Many months are named after gods and goddesses. Our calendar is called the Gregorian calendar. Can you find out why one month is named what it is?
Every January begins a new year. What century are we in?
Our calendar has twelve months, but this is not true of every culture. Different cultures keep track of time in different ways. A Chinese child is one year at birth while a western child has to wait a whole year to be one.
The AD time of our calendar begins with the birth of Christ. Christ is an important figure to Christians. People who do not believe in Christ's importance use other important cultural events.
Time zones help us keep track of time. If we did not have time zones, some people would have light at 8 PM and some would have night. Time zones are marked by the line of longitude running north to south.
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Follow Up
Now we just write numbers in different number systems with different notations. It's great practice for multiplication and the understanding of multiplication, bases and place value.
Calendars
Time Zones
Maps
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Resources
The Story of Numbers and Counting
Anita Ganeri
Oxford University Press ISBN 0 19 52158 4
Number Art
Calendar Art
Leonard Everett Fisher
Four Winds Press ISBN 0 02 735240 4
Mathematicians are People, too
Michael Olaf catalogue
Lucetta and Wilbert Reimer
Dale Seymour Publications ISBN 0 86651 823 1
The Story of Clocks and Calendars
By Betty Maestro
Lothrop, Lee & Shepard Books ISBN 0 688 14549
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Upper Elementary Ideas
I would do a time line of famous people in Upper elementary. Students could then research how mathematicians struggled with calculating the circumference of Earth, the wonders of buoyancy, the patterns and their mathematical nature in geometry and on into computers. It is a wonderful pronouncement on human nature that we wondered and solved so many of these huge, mathematical problems so early in our history without a solid mathematical understanding. Again Michael Olaf's books on mathematician's would be a good place to find stories, but they would then have to look further to extend the stories. This is an area that would be fun for the students to make their own time line.
Where to go From Here
The students return after their break and the Great Lesson are done, but the need to research and to know the history of things is ingrained. Animal research will continue, of course.
Vertical and Horizontal History
This leads to investigations of time periods in history and history of events through time periods. I had a group make a fun timeline on the history of fashion this year, another did a report on the history of video games. A parent had an old Atari that they brought in. We all played Space Invader.
The Work of Air and Water
Wonderful lesson that allow us to go outside and play with water and dirt. Get a stream tray and build different kinds of streams. Their are also many experiments to go along with this.
Botany
Growing plants and learning about the shapes of leaves is fun. Simple botany experiments let us learn about those critical needs of plants.
Interconnectedness
In Print put out a wonderful work that lets us investigate the interconnectedness of al life. After the traditional lesson about the sun, soil, water and supra nature, we all turn to our favorite thing - animals. I have laminated the cards so that the numbers of what they eat are on each card. I take different colored yarn and string a given animal to those it eats. Then I choose one of these animals and we see what was in its stomach with a different color. But shat was in the stomach of one of the animals it ate? Another color is used. This makes an intricate web of life. I have also strung the web across the hallway outside my room using the little copies of pictures In Print provides. It turns into an arbor that all the classrooms have to walk under to get outside.
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If you have any advice, experiences to share, or items you might like to post on this page please contact me via e-mail at:
bdubinsky@flxent.com
Copyright © 2007 Barbara Dubinsky