Cards with Kaktovik numbers are displayed on a table on October 5, 2022. The cards are used in a game called Tallimakipiaġutaiḷaq, which means “99”. In the game, you add the cards as they are
Nearly 30 years ago, a group of Kaktovik students invented a number system that mirrored the way they counted in Iñupiaq and made math more intuitive for them. Soon anyone in the world will be able to type Kaktovik’s numbers into a computer.
“It’s not just a digital system. It’s not just math. It was created and developed by a teacher from 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 more relevant to those students, to that population. When it comes to Indigenous ways and understanding, it clicks. It makes a lot more sense.
Today, interest in culturally appropriate education – and the study of Kaktovik numbers in Inupiaq schools – is growing, as is the need for an easy way to use numbers numerically. From September, an international encoding standard, Unicode, included Kaktovik ciphers in its latest version, which means that ciphers will now be universally accepted by computers.
“It means that anyone, anywhere in the world, on a computer can have access to producing things using numbers,” said former school math teacher Harold Kaveolook , William Clark Bartley, whose students invented the system in the 1990s.
Creation of figures
When Bartley was a math teacher at Kaktovik in 1994, his middle school students figured out the numbers to represent the Iñupiaq oral counting system.
“Before doing these numbers, we were using Arabic numerals and visually it didn’t match our language,” said Alicia Solomon, who was in eighth grade at the time. “And we started asking our teacher, ‘What about our own numbers? Our own system?
Most countries use the base-10 Hindu-Arabic numbering system where numbers range from 0 to 9. But in Iñupiaq – as well as other Inuit and Yupik languages - numbers range from 0 to 19, making makes a base 20 system.
“The Iñupiaq word for the number 20 is iñuiññaq, which stands for a whole person,” Judkins said. “You have all 20 appendages – your 10 fingers and 10 toes. A lot of the classroom activities that we use now with this numbering system relate to these body parts and appendages.
Kaktovik students came up with numbers from zero to 19, consisting of straight strokes joined with sharp angles that you can write without lifting the pen.
“We didn’t want them to look like other numbers,” Solomon said. “Our whole math class did it together.”
The Inupiaq counting system didn’t have zeros, so the school district suggested a few names for the digit. A disabled student proposed the visual representation of zero.
“She just raised her hands above her head crossing them,” Bartley said.
Numbers are constructed according to the structure of numbers in Iñupiaq: for example, 16 is akimiaq atausiq in Iñupiaq, which translates to 15 and 1. The Kaktovik number 16 is also composed of 15 and 1.
“The kids really came up with a brilliant system,” Bartley said. “The numbers, you just have to look at them, and you can see what the number means.”
Because Kaktovik numbers visually reflect number composition, using them in math problems was easier than Arabic numbers, Solomon said. Just by looking at Kaktovik’s numbers, students could see how to add, subtract and even divide. For example, for long division, students used colored pencils to match the lines of the divisor in the dividend.
“The numbers almost came through,” Bartley said.
After the students started working with Kaktovik’s numbers, Bartley said their interest in math grew. They would rush to skim through the regular math book to save time working with Kaktovik’s numbers.
“It’s their culture that has made all the kids so much more involved,” he said.
The effort to make Kaktovik figures available on computers began in 2021, when several linguists and language enthusiasts wrote a proposal describing the suitability of the numbering system.
Now, Unicode has a place reserved specifically for Kaktovik ciphers starting with version 15.0 released on September 13. Because the update is so recent, computers, smartphones and other devices today do not come with a font capable of displaying Kaktovik digits, according to Deborah Anderson. , a research linguist at the University of California, Berkeley, who also helps preview new Unicode proposals before they are submitted.
“To access numbers, 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 usage. If that’s done for Kaktovik’s digits, a font could become available within the next few months, said Craig Cornelius, 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 in making this really usable is to create a keyboard that can be used directly on a laptop or desktop,” Cornelius said. “If people can type the characters, someone will be able to see them if the font is installed on their device.”
So far, Cornelius has built a numeric keypad for those who want to start using numbers today. The developers are working on training Iñupiaq Education staff on how to access and use the numbers before the fonts are released to the public.
“The people who worked hard to get the Kaktovik characters into the Unicode Standard started the process,” Cornelius said, “but like any product, it takes time to roll out to all stores.”
North Slope teachers used Kaktovik numerals in math lessons for a period after their invention. Their use has since been reduced, with the influx of out-of-state teachers and the growth of standardized testing in the late 1990s, but more and more teachers in Iñupiaq schools are now considering to restore the system.
Next fall, the North Slope Borough School District hopes to implement several pilot immersion classes that will include teaching students math concepts and math activities, using Kaktovik numbers. Additionally, this immersion program will be built on a culturally appropriate curriculum that will provide students with lessons in Iñupiaq history and local governance.
“There’s this huge wave of Indigenous education and culturally appropriate teaching,” Judkins said.
Kaktovik numbers are part of the Iñupiaq language program in the district, and students learn to count and describe dates and ages using them, said Iñupiaq Department of Education specialist Chrisann Justice.
But creating teaching materials with Kaktovik figures currently means drawing them by hand or, in Justice’s case, copying and pasting screenshots of each figure, which often leads to a pixelated image.
“It would be so convenient to just be able to type them in!” Justice said.
Digitizing Kaktovik numerals may also help preserve the use of numbers in Iñupiaq.
“Our words are long, and it’s just easier to see the numbers than to say the numbers,” Solomon said. “I think it would be great for kids to try to learn numbers, kind of get an idea of themselves and learn our number system. Just to keep in touch with our culture.
• • •