Kaktovik numerals

Iñupiaq, like other Inuit languages, has a base-20 counting system with a sub-base of 5. That is, scores are indicated by multiplication (as in French or Danish) with additional numerals for 5, 10, and 15. Arabic numerals, consisting of 10 distinct digits (0-9), are not appropriate for a base-20 system.

In the early 1990s, during a math enrichment activity at Harold Kaveolook school in Kaktovik, Alaska,[1] students said that their language used a base 20 system and that when they tried to write numbers with Arabic numerals, they didn't have enough symbols to represent the Iñupiaq numbers.[3]

Map of Alaska highlighting North Slope Borough, part of Iñupiaq Nunauruat

The students first addressed this by creating ten extra symbols, which made it difficult to remember, and elaborated that it took a long time to write down the numbers. The middle school in the small town had nine students, so it was possible to involve them in the discussion regarding creating the new system. The teacher, William Bartley, helped.[3]

After brainstorming, the students came up with several qualities that the system would have to have:

1. The symbols should be "easy to remember."
2. There should be a "clear relationship between the symbols and their meanings."
3. It should be "easy to write" the symbols. For example, being able to be written without lifting the pencil and should be able to be "written quickly."
4. They should "look very different from Arabic numerals," so there would not be any confusion between the two systems.
5. They should be pleasing to look at.[3]

In base-20 positional notation, the number for 20 is written with the digit for 1 followed by the digit for 0. The Iñupiaq language does not have a word for zero, and the students decided that the digit 0 should look like crossed arms, meaning that nothing was being counted.[3]

When the middle-school pupils began to teach their new system to younger students in the school, the younger students tended to squeeze the numbers down to fit inside the same-sized block. In this way, they created a notation with the sub-base forming the top part of the digit. This proved visually helpful in doing arithmetic.[3]

The numeral system has helped revive counting in Inuit languages, which had been falling into disuse among Inuit speakers due to the prevalence of the base-10 system in schools.[1][4]

In 1996, the Commission on Inuit History Language and Culture adopted the numerals to represent the Inuit language numbers.[3]

In 1995, the middle school students moved over to the high school in Barrow (now renamed Utqiagvik), Alaska, and took their invention with them. The high school students were permitted to teach the middle school students this system, the local community Iḷisaġvik College added an Inuit mathematics course to its catalog.[3]

In 1997, the student scores in the middle school on the California Achievement Test in mathematics, which was used to measure student success, increased dramatically. Previously, the average score was in the 20th percentile, and after the introduction of the new numerals, the scores rose to be above the national average.[3]

This dual thinking in base-10 and base-20 might be comparable to the advantages that bilingual students have in forming two ways of thinking about the world.[3]

In 1998, 20-month calendars were available with the new numbering system.[6]

The system has since gained wide use among Alaskan Iñupiat and has been considered in other countries where dialects of the Inuit language are spoken.[2]

This numeral system's development showed Alaskan-native students that math was embedded in their own culture and not simply imparted by western culture.[7] Those students going on to college saw studying mathematics as a necessity to get into college. Also, non-native students can see a practical example of a different world view, a part of ethnomathematics.[7]

The Kaktovik numerals have been provisionally assigned a block in the Unicode Supplementary Multilingual Plane (U+1D2C0-1D2DF).