[This is the text of a presentation I made on October 7, 2017 at the kick-off event for Global Math Week, held at the Courant Institute of Mathematical Sciences in New York City. Earlier in the day, James Tanton gave his usual brilliant presentation on Exploding Dots, so in my talk I was able to assume that the audience knew what Exploding Dots is about; they also recognized my riff on Tanton’s signature line “I’m going to tell you a story that isn’t true”, as well as the significance of the word “Kapow!” (and its variants) in the Exploding Dots story. You might want to visit YouTube and sample Tanton’s Exploding Dots videos to get a feel for what it’s all about. For the full Exploding Dots spiel, try https://vimeo.com/204368634. There are two videos of this talk: there’s https://www.youtube.com/watch?v=x8wcbONcGHk (the one made by the Global Math Week folks back on October 7) and there’s https://www.youtube.com/watch?v=G8vVDrxcIi8 (my PowerPoint slides, narrated by me). The latter has better visuals, and it has captions, but it’s missing the audience reactions.]

I’m going to tell you a story that’s as true as I know how to make it. I don’t have a background in ethnomathematics, or the history of mathematics, or the history of math education, so please forgive any mistakes, omissions, distortions, or mispronunciations (and let me know about them, but not now!). The story I’m going to tell is as old as civilization, or at least as old as money — because as long as currency has existed in different denominations, there’s always been a need to make change, and to find systems for making change efficiently and accurately. The story I’m about to tell involves many parts of the world over the course of many centuries. And in many ways it’s a story about sand.

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