I found this book, by Denise Schmandt-Besserat, on the shelf in the library. I was having one of those moments where I just randomly browse a section and it looked interesting. I was particularly interested because of the learning that the Arithmeum inspired. Can You Count in Greek was too workbook-y in its presentation to really be inspiring but I thought that the general idea was a good one.
Although this is a picture book, it is more suitable for older elementary and middle school kids than for younger ones. There is a lot of text to a page. And it seems to me that one would get more out of it if you already had a basic grasp of counting and place value. The language is straightforward and shouldn’t pose any difficulty. And the author, who is an archaeologist, provides information about how we know these facts and the pieces of the historical puzzle that we don’t know. She also provides a convincing explanation for why numbers and number systems might have developed the way they did.
This book would be a good way to help kids develop abstract understandings of numbers and mathematical concepts. I can see how you might just play with some of the systems she describes. Although she doesn’t talk about other bases, you could develop the understanding of the importance of zero and the invented nature of a decimal system by playing around with other bases as Tigger and I did in the fall. Working out how to add, subtract, multiply and divide using a different number system, building a multiplication table, and working out how to do multi-digit calculations can move students beyond procedural facility to a deeper understanding of why certain procedures work.
And as I read more and more about mathematics, it seems that it is really important to nurture an interest in patterns and abstract properties of numbers. Learning about the history of numbers might lay a foundation for some of this. Perhaps learning that the number system we use is somewhat arbitrary opens the door to accepting the abstract rules of algebra and geometry later on.