The students built base-20 abacuses. These were initially intended to help convert decimal numbers to base 20 and vice versa, but soon the students started using them to do arithmetic in base 20.

The upper section of their abacus has 3 beads in each column for the values of the sub-base of 5, while the lower section has 4 beads in each column for the remaining units.

(2/n)

The students discovered their new system made arithmetic easier than it was with Arabic numerals. Adding two digits together often gives a result that *looks* like the combination of the two digits!

(3/n)

The students also found that long division was more fun with Kaktovik numerals! They noticed visually interesting patterns. They discovered that they could keep track of intermediate steps with colored pencils.

(4/n)

After the students of Kaktovik invented their new numerals, their scores on standardized math tests improved dramatically! Before, their average score was down in the 20th percentile. Afterwards, their scores shot above the national average.

Some argue that being able to work in both base 10 and base 20 was helpful - much like being bilingual.

I suspect that even more important was the sheer process of developing their own system of numerals! Getting engaged in mathematics is so much better than learning it passively.

But this was just the start of the story. The new numerals began to catch on... but then:

"Under the federal No Child Left Behind Act, from 2002 to 2015, schools faced severe sanctions—or even closure—for not meeting state standards, provoking a “scare” that some local educators say squeezed the Kaktovik numerals into a marginal role despite the system’s demonstrated educational impact."

For more, read this:

https://www.scientificamerican.com/article/a-number-system-invented-by-inuit-schoolchildren-will-make-its-silicon-valley-debut/

(5/n)

Why is Scientific American talking about Kaktovik numerals just *now*? It's because some linguists working with the Script Encoding Initiative at U.C. Berkeley recently got them added to Unicode! See here:

https://en.wikipedia.org/wiki/Kaktovik_Numerals_(Unicode_block)

For more on the cool mathematical properties of Kaktovik numerals, try the Wikipedia article on them:

https://en.wikipedia.org/wiki/Kaktovik_numerals

I suspect there's more to be said. Maybe someone has worked out all the details somewhere?

Below is another example of long division.

(5/n)

Finally, here's a map of Inuiit languages! The Kaktovik numerals were invented by high school students in northern Alaska who spoke Iñupiaq, one of these languages.

For more on Iñupiaq:

https://en.wikipedia.org/wiki/I%C3%B1upiaq_language

For more on Inuit languages, try this:

https://en.wikipedia.org/wiki/Inuit_languages

(6/n, n = 6)

@johncarlosbaez

Your findings are really very interesting and I think I might be able to share some facts about the cognitive reasons why base 5 is so effective.

However, I do not want to promote a link that contains a word that is considered offensive by the ethnicity involved.
May I second that you change the E word to #Inuit?
Thanks a lot for your consideration.

@HistoPol - Fixed! I thought I'd gotten rid of that word everywhere a week ago, but one instance survived.

I hope folks change Wikipedia, which is where I got that term.