Got it!

[velvetpage]

I just came up with the most fabulous project EVAR to combine social studies and math.  Get a load of this:

Project:

 

With your partners (groups of 3) you will research number systems in at least three ancient civilizations.  One of those three must be the Hindu-Arabic system; the others are up to you and will depend on what resources you can find to learn about the number systems.  I've included a list of links, available on our class's First Class page, to get you started.

1. Write a paragraph explaining the main features of the three number systems you chose (each group member should write one paragraph; I will be looking for rough work during conferences.)
2. Use number cubes or other manipulatives to model each number system.  (It may be easiest to pick one number and model it in all three number systems.)  Take pictures of your models.  Don't forget to include a group member in each photo so that we know who the pictures belong to when we download them off the cameras!
3. Make a chart that explains the main features of each number system, and compares it to our base-ten system.  Some suggestions for headings on your chart:

Use of zero

Base number

Strengths

Limitations

4. Write another piece in the format of your choice, explaining which parts of those ancient number systems are still in place today, giving examples for each.  (Use the cameras or images from the internet to back up your points!)  If any of those systems have been completely abandoned, explain why you think that happened.
5. Each group will do a brief oral report on their findings for their classmates.  Every group member should be able to discuss any aspect of the project - even if somebody else worked on it - so be sure to teach each other what you learned!

I'll be making up a rubric and some lesson plans when I get back from my swim, and I've already got a thorough list of expectations that can be assessed using this project.  When I'm done I'll post the whole thing to Ontario_teacher.  Any suggestions appreciated; this is the first, very rough draft. 

Comments

[siobhan63.livejournal.com]

Don't have any suggestions, but your post reminds me of this really interesting series that aired on BBC World a few months ago - the Story of Maths.

http://www3.open.ac.uk/media/fullstory.aspx?id=14437

[velvetpage.livejournal.com]

I'm going to have to get my hands on that. It looks wonderful. Thanks for the link!

[forthright.livejournal.com]

OK, I'll bite, since I did write a book on the subject, after all. :) I think it's a great exercise and combines a historical focus with a good study of the structure of each system.

- If one of the three systems is the Hindu-Arabic system, then point 3 is confusing, because "our base-system" is the Hindu-Arabic system and can't be compared to itself. I understand what you mean (compare H-A to two other systems) but because you keep talking about three systems, it could be confusing. Indeed, probably best to replace "our base-ten system" with "Hindu-Arabic numerals" because of course one of our 'base ten' systems are the English number words, and that is presumably not the comparison you are lookking for.
- I'd scrap the word 'ancient' in the intro and point 4. After all, Hindu-Arabic numerals aren't ancient (at least not in the ordinary sense)
- I'm not quite sure what you mean by "which parts of those ancient number systems are still in place today". Could you give me an example of what you mean?

[velvetpage.livejournal.com]

The original hindu-arabic system changed over the course of several millenia to include a zero, and the look of the numbers changed somewhat, too. I want them to compare the way they were used long ago to the way they changed into our current base-ten system. Clearly there will be many similarities, but they're not quite the same thing.

By the parts still in place, I mean things like the 360 degree circle, which is a legacy of the Babylonian system of base sixty.

[forthright.livejournal.com]

The original hindu-arabic system changed over the course of several millenia to include a zero, and the look of the numbers changed somewhat, too.

Hmm, I understand what you are saying but the formulation is confusing. It certainly can't be called Hindu-Arabic before it gets to the Arabs in/around AD 800, by which time it already had a 0. The system used in India prior to AD 600 or so is usually called Brahmi numerals and lacks place value - really other than some vague similarities in the signs for 1-9 the system is completely different. But again I'd avoid using the word 'base-ten system': both Brahmi and Hindu-Arabic numerals have a base of 10 - the difference (primarily) is the use of place value in the latter. In any event, this raises a further issue: if you are defining it all as one system from 300 BC to the present day then you need to ask how the system changed through the period of its use.

[velvetpage.livejournal.com]

I hadn't realized how long ago those changes had occurred. You're right, I'll have to rethink how that is phrased and which research I direct them to. I probably will insist that they do the Brahmi numerals because they're the direct ancestors, and I'll want them to investigate the history of the Hindu-Arabic system at least a little bit.

[forthright.livejournal.com]

I would be happy to help with sources if you like. Because I'm lazy, I've never put together a good page on numerical notations on the Phrontistery (just a massive bibliography which is no use to your students). The Wikipedia pages on numerical notations are mediocre at best, I'm afraid.

(Of course, my *actual* recommendation would be for me to send you the entirety of my 500-page book by PDF ... but probably that would be taking your research too far for this project!)

[velvetpage.livejournal.com]

I would be interested in reading it, at some point - but not now. :) I would appreciate a few straightforward sources. There are plenty of books about ancient civilizations in our school library, but they all ignore mathematics more or less completely. Last year's project was a brochure on an ancient invention. You wouldn't believe how difficult it is to come up with research about wheelbarrows and water clocks.

[forthright.livejournal.com]

I suppose the best one is this link:
http://www-groups.dcs.st-and.ac.uk/~history/Indexes/HistoryTopics.html
although it still makes me wince at various places. And I suppose some of the Wikipedia articles are all right.

Honestly you could do worse than the 1911 (now out of copyright, available at http://www.gutenberg.org/ebooks/22599) book by Karpinksi and Smith, The Hindu-Arabic Numerals.

Out of curiosity, what are you using currently?

[velvetpage.livejournal.com]

Whatever internet resources came up on Google, and dim memories from my undergrad fifteen years ago. :) Thanks for the links!