The History of Algebra

   

     In trying to find my next topic I started looking though the Common Core Standards.  I wanted to see the progression of ideas taught in elementary mathematics and find out what I am comfortable with, and identify what I need to explore a little more.  I noticed for each grade level in the standards there is a section titled, Operations & Algebraic Thinking.  That got me thinking about last weeks asynchronous work and the story about ancient Greece and the Pythagorean Theorem.  So, I asked myself, what is Algebra?
   
     This week I want to discover the history of algebra so I have a better understanding of why this type of mathematics is so important to the elementary mathematics curriculum.  Stories help us make connections and I want to be able to tell the story to my students.    Maybe if my students understand the history of algebra it will help them understand the mathematics they need to learn and why they are learning it.

Definition of Algebra¹  

The branch of mathematics that deals with general statements of relations, 
utilizing letters and other symbols to represent specific sets of numbers, 
values, vectors, etc., in the description of such relations.

The History of Algebra

    

     Last year I taught 6th grade social studies for the first two months of the school year.  The students begin learning about early man and the stone ages.  As things improve for man, the students learn about the early civilizations built in the great river deltas and the discoveries made by man.  Our first stop is in Mesopotamia and ancient Babylon.  Here we learn about how man no longer needs to be a hunter/gather to survive.  They build homes and live together in one area and construct a set of laws to live by.  They have domesticated animals and plants to survive.  There is art and trade and commerce.  A counting system based on stones evolves into tablets of clay and further still to our first written language.  I learned that algebra was used here too.    

     Khan Academy has a brief video explaining the history of algebra and the region it came from.  It begins in Baghdad, Iraq, in 820 A.D. with the publication of the book, Compendious Book on Calculation by Completion and Balancing, by Al-Khwarizmi.  Al-Khwarizmi is considered to be one of the fathers of algebra because he is the first to write down the ideas of algebra in a book.  Sal Khan explains there are earlier men who use the concepts of algebra, but Al-Khwarizmi is the first to write them down and the name algebra comes from the title of his book.  Al-gabr is Arabic for restoration or completion.         

https://www.khanacademy.org/math/algebra/introduction-to-algebra/overview-hist-alg/v/origins-of-algebra  (7:17)

     The video, Science in a Golden Age,  explains more about Al-Khwarizmi and his book, "Hisab Al-jabr w’al-muqabala."  The book does not have any algebraic equations in it; it contains only words.  The mathematical ideas are applied to problems of the times; the division of land, the payment of workers and the distribution of inheritance.  There is an example of a common problem and how algebra would solve it.  A man dies owning only one camel.  The camel is worth 80 dirhams, a monetary unit in the United Arab Emirates. He has decided to leave one quarter of the camel to his friend, one eighth to his wife and the rest will be split between his three sons.  How much would each son receive?  To solve this they would use an algebraic equation.

80 = 80 + 80 + 3x 
          4      8                                                         

80 = 20 + 10 + 3X

50 = 3X

50 = X            Each son would receive 16.7 dirhams.
 3

The explanation of the problem begins at 06:43 and ends at 08:10.
https://www.aljazeera.com/programmes/science-in-a-golden-age/2015/10/al-khwarizmi-father-algebra-151019144853758.html  (25:02)

     The video goes on to explain how algebraic equations are used in math and science. Quadratic equations are necessary in determining how planes fly and preform the functions that they do.  Cubic equations, discovered in medieval times, help scientists build machines that are capable of breaking the sound barrier. 

Conclusion

     I enjoyed finding out more about algebra and its importance in the world of mathematics and science.  I love the idea of connecting something my students learn about in social studies to mathematics.  I would show them the Khan Academy video and explain the early roots of algebra.  They will already know about Babylon and some of the advances made in the Fertile Crescent.  I think they will be interested in knowing that they can add algebra to the list.     



Sources:

1.  https://www.dictionary.com/browse/algebra