**EDIT: Blog post due Wed Sept 23: Did Mesopotamian scribes have algebra? (And how can we recognize 'rhetorical' and 'syncopated' algebra?)

Here is the link to an explanation of Babylonia algebra to help understand Babylonian word problems. (Note that this is the sheet we were using in class as a handout!)

https://drive.google.com/file/d/0B00n89L6TX5gZ01BQndwczRQaEE/view?usp=drivesdk&resourcekey=0-arSdOZ88pkPwDfajhNbQMg

You'll see that the form of the problem is different from the algebra we are used to -- and there is no use of compact alphanumeric symbols for variables. Instead, concrete words and images are used.

 

(**Note that algebraic relationships stated in words are known as 'rhetorical algebra'; algebraic relationships stated with some abbreviations but not a systematic symbolism are known as 'syncopated algebra'. It's interesting to think how this relates to our students' initial learning of algebra...!)

Questions to consider:

• How could one state a general mathematical principle in a time before the development of algebra and algebraic notation?

• Is mathematics all about generalization and abstraction?

•Thinking about various areas of mathematical knowledge -- number theory, geometries, calculus, graph theory, etc. etc. -- how could you imagine stating general or abstract relationships without algebra?

• Do our students go through similar stages of rhetorical and syncopated algebra as they move toward learning and doing  symbolic algebra?