Math Lessons for Language People

One of the books I read over the summer was  When Languages Die: The Extinction of the World's Languages and the Erosion of Human Knowledge by K. David Harrison.  This book tackles the issue of languages with only a few speakers remaining, and asks--what do we lose when we lose these languages? Overall, I thought the book was interesting but uneven. At times the author tries too hard to prove that we lose a lot. (I sort of thought that was obvious, but maybe it's not.) There were two sections that I found very thought-provoking. One of those sections is very rich reading for math teachers.

Sign Languages

Harrison does have a fascinating discussion at the end of the variety of sign languages that are being lost. As he writes:

So far, there are 121 identified and named sign languages used in deaf communities around the world, but potentially a great many more remain completely undocumented. Many sign languages are now rapidly vanishing. This is in part because many deaf communities possessing unique sign languages are small, indigenous, and rural. . . Signed communication systems arise spontaneously wherever deaf people live. . . as soon as there is a community of deaf people. . . these systems develop into full-fledged languages, rapidly becoming as complex as spoken languages (pp. 230-231).

Numbers and Language

The other chapter of the book that really got me thinking was the chapter on numbering systems. Here, I believe there is an opportunity for some really great math lessons (Chapter 6, pp. 167-200--I'm only going to talk about bases here, but for math teachers there is some really great food for thought in this chapter about all kinds of math concepts).

I was a very good math student, but a better "English and other languages" student. And one part of math that I never fully understood (I got it, but I never really "got" it) has to do with counting in other bases. Yes, we learned to count in base 2, and base 5, and base 12. . . but the truth is that my mind was really "converting" from base 10 to the other bases.

From reading this book, I started understanding that languages embody their math bases, and that not every language uses base 10. Chapter 6, Endangered Number Systems, is all about this. In the Pomo language of California (which now has fewer than 60 speakers), the counting system is in base twenty. The number 20 is "1 stick," and 400 is "1 big stick."

Some languages count with body parts. Fingers and toes seem obvious, but other counting systems rely on arms, elbows, and even nostrils and collarbones. The Kewa people of Papua New Guinea count in base 4, using the hand as the basic unit--but they omit the thumb!

It goes on--there are many languages in Papua New Guinea, and among them the Aiome employ a base-2 counting system; the Loboda use both base-5 and base-20 systems; the Huli use a base-15 system; and the Bukiyip use base 3 and base 4.

Harrison notes that non-base-10 languages may have a cumbersome way to say a number that we think is important, like 1,000, but on the other hand, "non-decimal bases make it easy to say other numbers. In base-15 Huli, 225 is expressed simply as ngui ngui (15 x 15). Compare this to the relatively complex English expression 'two-hundred and twenty-five (2 x 100) + (2 x 10) +5. (p. 191)."

As I read this, it occurred to me that developing lesson plans that teach the way some other languages think about counting would be a natural way to teach about various math bases. For instance, could students design their own (non-base 10) counting system using body parts or other things that we find around us? Which

And at the same time, it would achieve one of my ulterior motives--to keep U.S. students from thinking that what we do in our country, and in English, is the only or best way to do things.*

*Fueled by a recent conversation I had with a graduate of a local high school who told me she never took any foreign language because "I'm American, and I live here, and we use English, and I don't need it--it's not important."