Normally I pass on the murky political waters my profession dips into, but Scott McLeod sent me a link I couldn’t resist discussing because it regards historical mathematics.

First, the original source of confusion:

Mayan numbers taught in Somis school to help students learn math

A group of sixth- and seventh-graders still crack open their textbooks and practice regular math skills most days. But once a week, they turn their math attention to history, culture and places far from Somis.

Teacher Jill Brody’s class started learning about Mayan math in September, part of the school’s efforts to incorporate “ethno-mathematics” into some of its classes.

It is clear to me as a teacher that this is referring to an enrichment activity, and not some sort of overarching system (like New Math or Reform Math). Again from the article:

The school isn’t replacing regular math classes, just adding the ethno-mathematics lessons, she said.

I am also guessing the classroom did not study only Mayan numerals (it’d be hard to fill even a quarter) but the newspaper gave the impression it was the only area being studied.

Otherwise the only thing that bothers me is designating math history lessons under the term “ethno-mathematics” — I find the claim dubious that one part of math history is different from another, so I’d prefer the umbrella term.

Now, the reaction:

Stupid education fad of the day: “Mayan Math”

Today’s stupid education fad of the day?

“Mayan Math.” I kid you not . . .

This is creepily similar to the idiotic “lattice multiplication” lessons in Everyday Math that justify using incoherent, inefficient methods of multiplying because that’s the way the ancient Egyptians did it.

1. The newspaper never called it “Mayan Math” in the same category as “New Math”. It simply is a type of lesson.

2. Teaching mathematics history is not a “fad” and has been present even in highly traditional classrooms for a while. I have Mayan worksheets floating around from the 1950s.

3. Lattice multiplication doesn’t come from the Egyptians (either the Indians or Arabs, depending on your reference). The blog 360 has written up the subject in detail. One of the authors of the blog has also defended the use of the practice. What I should emphasize is that lattice multiplication intrinsically has nothing to do with Reform anything; it’s another algorithm just like the “traditional” one, with the disadvantage that it takes longer to set up and the advantage that it is easier to spot mistakes. The fact that Everyday Math does include the algorithm is unrelated to the overall philosophy, other than a willingness to change the status quo.

I do have sympathy for those suspicious of “discovery” curriculum, in that it can go very badly with an unskilled teacher, but that doesn’t mean essentially unrelated material should be pulled into the same critiques.

Filed under: Education, History, Mathematics

josh g., on January 26, 2010 at 10:10 am said:The word “ethnomathematics” is clumsy, but I don’t think it’s safe to just push it aside. It reminds us that we need to deliberately analyze, dissect, and correct our colonial lens on history, including the history of mathematics. It’s all well and good to wish that math history would be treated justly and without any traces of racism, but old habits die hard. We’re not there yet, and pretending the problem isn’t there will not make it go away.

Anyway, yay for Mayan math. I used it as an extension of teaching how to convert to/from non-decimal number systems. It turned out not only to be a fun enrichment, but it made teaching the core material much, much easier. Students eyes were too used to reading 142 as a decimal number no matter what subscript I added at the end, and they were getting lost. By using Mayan numbers to teach the conversion process, it was visually obvious which numbers were “normal” and which were not, and they could follow my explanation on the board.

Jason Dyer, on January 26, 2010 at 10:55 am said:Point taken, although out of all the math history curriculums I’ve seen for high school, I haven’t seen a single Western-centric-only one (including ones from decades ago).

The stuff that gets left out tends to be the more obscure stuff (Pre-Elamite, for example).

Nice story on the Mayan!

Jenny, on January 26, 2010 at 6:08 pm said:Interesting…

As an aside, I have to say that I love lattice multiplication. I offered it to my fourth and fifth graders in the past as one option and quite a few used it all the time.

jd2718, on February 20, 2010 at 9:35 am said:I get 1. And agree. I get 2. And agree. But 3? Lattice is often used with the specific intent of deprioritizing the standard algorithm.

Jonathan

Jason Dyer, on February 20, 2010 at 9:04 pm said:I included “other than a willingness to change the status quo” to account for that, but the point is it intrinsically doesn’t have anything to do with “discovery”, so it doesn’t make sense to attack lattice multiplication as a stand-in for all discovery curriculum. (If you want to claim “the only reason lattice multiplication was included in X was because of the author’s need to mess with things”, sure, but that’s not really an attack on the method itself.)

jd2718, on February 20, 2010 at 9:24 pm said:OK, I see how Malkin just tossed it in. You’re responding to a nut, and you’ve got a good point.

I do want to claim that the ‘reformers’ lean on lattice exactly because it is not standard. And I see real value in having a standard algorithm.. But I’ll readily agree that neither lattice nor standard are intrinsically superior from the standpoint of execution or performance.

Jonathan