Numerals invented by Kaktovik students can now be used digitally

 A set of dark blue cards with symbols printed on them arranged in an arc
The cards with Kaktovik numerals are displayed on a table Oct. 5, 2022. The cards are used in a game called Tallimakipiaġutaiḷaq, which means “99.” In the game, you add the cards as they are played, with the goal to avoid being the person that brings the pile above 99. (Photo by Chrisann Justice)

Almost 30 years ago, a group of Kaktovik students invented a numbering system that reflected the way they counted in Iñupiaq and made math more intuitive for them. Soon, anyone in the world will be able to type Kaktovik numerals on a computer.

“It’s not just a number system. It’s not just math. It was created and developed by a teacher of our district and our Iñupiaq students,” said Tennessee Qaġġuna Judkins, director of Iñupiaq Education at the North Slope Borough School District. “When you use it in a classroom, it’s most relatable to those students, to that population. When it comes to Indigenous methods and understanding, it just clicks. It makes a lot more sense.”

Today, the interest in culturally responsive education — and studying Kaktovik numerals in Iñupiaq schools — is growing, and so is the need for an easy way to use the numbers digitally. Starting this September, an international encoding standard, Unicode, included Kaktovik numerals in its latest version, which means that the numbers will be now universally accepted by computers.

“That means that anybody anywhere in the world on a computer can have access to producing stuff using the numerals,” said former Harold Kaveolook School math teacher William Clark Bartley, whose students invented the system in the ‘90s.

Creating the numerals

When Bartley was a math teacher in Kaktovik in 1994, his middle school students came up with the numbers to represent the Iñupiaq oral counting system.

“Before we made these numerals, we used the Arabic numbers, and, visually, it didn’t connect to our language,” said Alicia Solomon, who was an eighth grader at the time. “And we started asking our teacher, ‘What about our own numbers? Our own system?’”

Most countries use the Hindu-Arabic base-10 numbering system where numbers range from 0 to 9. But in Iñupiaq — as well as other Inuit and Yup’ik languages — the numbers go from 0 to 19, which makes it a base-20 system.

“The Iñupiaq word for the number 20 is iñuiññaq, which represents a whole person,” Judkins said. “You have all 20 appendages — your 10 fingers and your 10 toes. A lot of the classroom activities that we use now with this numbering system is in relation to those body parts and those appendages.”

Kaktovik students came up with digits from zero through 19, composed of straight strokes joined at sharp angles that you can write without lifting a pen.

“We didn’t want them to look like any other numbers,” Solomon said. “It was our whole math class that did it together.”

A table showing the Iñupiaq counting system from 1 to 59
Kaktovik numerals from 1 to 59, as they are seen in Edna MacLean’s Inupiaq dictionary. The lower numbers, 1 to 59. The Kaktovik numbers in the tens’ and fifteens’ rows are graphically simpler than those immediately above and below them, and the corresponding Iñupiaq numbers are lexically simpler than those above and below them.

The Iñupiaq counting system did not have zero, so the school district suggested a couple of names for the digit. A student who had a disability came up with zero’s visual representation.

“She just raised her hands above her head crossing them,” Bartley said.

The numerals are built following the structure of numbers in Iñupiaq: for example, 16 is akimiaq atausiq in Iñupiaq, which translates as 15 and 1. The Kaktovik numeral 16 is also composed of 15 and 1.

“The kids really did come up with a brilliant system,” Bartley said. “The numerals, you just have to look at them, and you can see what the numeral means.”

Because Kaktovik numbers visually reflect the composition of the number, using them in math problems was easier than Arabic numbers, Solomon said. Just by looking at the Kaktovik numerals, students could see how to add, subtract and even divide. For example, for long division, students used colored pencils to match the strokes of the divisor in the dividend.

“The numbers almost gave themselves away,” Bartley said.

After students started working with Kaktovik numerals, Bartley said their interest in math grew. They would rush to get through the regular math book to save time for working with Kaktovik numerals.

“It’s their culture that got all the kids far more involved in it,” he said.

Digitalizing the numerals

The effort to make Kaktovik numerals available on computers began in 2021, when several linguists and language enthusiasts wrote a proposal describing the relevance of the numbering system.

NowUnicode has a spot reserved specifically for Kaktovik numerals starting with Version 15.0 released on Sept. 13. Because the update is so recent, today’s computers, smartphones and other devices don’t come with a font that can display Kaktovik numerals, according to Deborah Anderson, research linguist at the University of California Berkeley who also helps preview new Unicode proposals before they are submitted.

“To access the numerals, users need a font with glyphs and an input mechanism, such as a keyboard,” Anderson said.

In the past, Google has developed free fonts for new Unicode characters that are in modern use. If this is done for the Kaktovik numerals, a font may become available in the next few months, said Craig Cornelius, a software engineer at Google who contributes to Unicode. Eventually, a font will also be available on mobile devices such as Android, but the process will take at least a year, Cornelius said.

“The next step, to make this really usable, is to build a keyboard that can be used on a laptop or desktop directly,” Cornelius said. “If people can type the characters, then someone will be able to see them if the font is installed on their device.”

For now, Cornelius built a digital keyboard for those who want to start using numerals today. The developers are working on training the Iñupiaq Education staff on how to access and use the numerals before the fonts are publicly available.

“The people who did the hard work of getting the Kaktovik characters into the Unicode standard have started the process,” Cornelius said, “but like with any product, it takes time for it to roll out to all the stores.”

Teaching the numerals

Teachers across the North Slope used Kaktovik numerals in math classes for a period after their invention. Their use has since been scaled back, with the influx of out-of-state teachers and the growth of standardized testing in the late ‘90s, but more and more teachers in Iñupiaq schools are now considering bringing the system back.

Adults and children sit around tables looking at numeral system cards
From left: Teachers Kayutak Julie Itta, Anausuk Timmothy Ferreira, Tukak Vernon Elavgak and Atuqtuaq Chrisann Justice play a number game using Kaktovik numerals during Immersion gathering in May 2022. (Photo courtesy of Tenna Judkins)

Next fall, the North Slope Borough School District hopes to roll out several pilot immersion classrooms that will include teaching students math concepts and math activities, using Kaktovik numerals. Moreover, this immersion program will be built on a place-based culturally relevant curriculum that will offer students classes in the Iñupiaq history and local governance.

“There’s this huge wave of Indigenous education and culturally responsive teaching,” Judkins said.

Kaktovik numerals are part of the Iñupiaq language curriculum in the district, and students learn to count and describe dates and ages using them, said Chrisann Justice, the Iñupiaq Education Department Specialist.

But creating educational materials with Kaktovik numerals right now means drawing them by hand or, in Justice’s case, copying and pasting screenshots of each numeral, which often leads to a pixilated image.

“It would be so handy to be able to just type them in!” Justice said.

Digitalizing Kaktovik numerals can also help preserve the use of numbers in Iñupiaq.

“Our words are long, and it’s just easier to see the numbers instead of saying the numbers,” Solomon said. “I think it would be awesome to have the kids try to learn the numbers, sort of get a feel for them and learn our numeral system. Just to stay in touch with our culture.”

This story originally appeared in the Anchorage Daily News and is republished here with permission.

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