To Accumulate a Rate — Integrate!

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History Included part 2 (Origins-Chapter 1)

I’m reading, “A History of Mathematics,” by Carl Boyer. I’m blogging about things that I think are interesting, things that I think we should teach, or areas where learning might increase by including interesting history surrounding the topic.
History Included part 1

Chapter 1 – Origins

I was most intrigued in the first chapter by a quote on the 4th page. “From the mathematical point of view it is somewhat inconvenient that Cro-Magnon man and his descendants did not have either four or six fingers on a hand.”

It made me wonder why base 4 or 6, or are they thinking 8 or 12, would be better than base 10. I couldn’t stop thinking about it because at church this morning I took the tithe envelope and started doing calculations in bases 2 and 4 and comparing to the same quantities in base 10. I concluded that the process we use for adding, subtracting, multiplying, and dividing would not change except that each number system would have a different multiplication table… and I guess addition as well. Once you have the multiplication table for the digits everything else is basically the same. It’s so strange to look at a number like 222 base 4 and it really means a quantity of 42. It feels so weird.

There are currently multiple people groups out there that have bases other than 10 as their number systems. Check out 12 Mind Blowing Number Systems from other Languages at the Mental Floss Website.

So, does learning about number systems and how to compute and convert between bases fit into the mathematics curriculum? If so, It would pique most students interests to find out that there are people that still use other number systems. I liked what I read on the mathematics exchange about this: Teaching Children to Convert Between Number Bases. There was a great comment about the process of doing conversion between, and in my opinion computation with other base systems helping students understand how our base 10 system works if they made it through elementary school by only memorizing facts. I think learning about different bases is historically relevant and beneficial to understanding our base ten system. It’s the kind of thing that gets left out because we skip all the best kids at elementary school math into pre-algebra when they get to middle school in the race to get to Calculus by Junior year. Number systems were created to deal with a problematic situation. Making a large number of tick marks to record numbers would be ridiculous. So, what did humans do? They created systems to deal with it. Different people in different places created different systems and the one we now use, for better or worse, is the base 10 system. This is what mathematics is all about and people should learn about it.

History Included part 1