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Kaktovik Numerals

A base-20 counting system (aka vigesimal). The number symbols were created by a class of children in the town of Kaktovik Alaska.

Maggie Pollock spent five years teaching in the North Slope Borough. “They are the numerals that William Bartley and his middle school students created in Kaktovik,” Pollock said.

Their teacher, William Bartley, guided them. After brainstorming, the students came up with several qualities that an ideal system would have:

Visual simplicity: The symbols should be "easy to remember"

Iconicity: There should be a "clear relationship between the symbols and their meanings"

Efficiency: It should be "easy to write" the symbols, and they should be able to be "written quickly" without lifting the pencil from the paper

Distinctiveness: They should "look very different from Arabic numerals," so there would not be any confusion between notation in the two systems

Aesthetics: They should be pleasing to look at.

In base-20 positional notation, the number twenty 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 Kaktovik digit 0 should look like overhead crossed arms, meaning that nothing was being counted.

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 an iconic notation with the sub-base of 5 forming the upper part of the digit, and the count of ones forming the lower part. This proved visually helpful in doing arithmetic.

As the Kaktovik middle school students who invented the system graduated to the high school in Barrow, Alaska (now renamed Utqiaġvik), in 1995, they took their invention with them. They were permitted to teach it to students at the local middle school, and the local community Iḷisaġvik College added an Inuit mathematics course to its catalog.

In 1996, the Commission on Inuit History Language and Culture officially adopted the numerals, and in 1998 the Inuit Circumpolar Council in Canada recommended the development and use of the Kaktovik numerals in that country.