A traditional man displaying body part positions in the Oksapmin 27-body part counting system. To observe the the use of “fu!” in the completion of all 27-body part positions, click here.

To count (traditionally) beyond the 27th position one loops to the wrist (the 23rd position), which becomes the 28th position.

Two men visit that Baptist Mission Station trade store in Tekin, 1978.

This video captures part of a purchase of tinned fish at the Baptist mission trade store in Tekin in 1978. The customers are making successive requests and payments of the fish.

This woman is displaying the Oksapmin 27-body part counting system (see figure at left). In the video, you will see her enumerate body part names beginning with the thumb on one hand (1) proceeding up to the nose (14) and down to the little finger on the other side of her body (27). At the end of the count, as has been standard practice, she exclaims a fists raised "tit fu!", indicating that she's completed all of the body parts of the system.* Similar 27-body part systems have been used traditionally throughout the larger Mountain-Ok region of central New Guinea (see map below). Note the direction of the count is arbitrary and meaning is linked to the act -- the woman is using a right-to-left trajectory whereas the upper left schematic shows the opposite direction. Traditionally, if people need to count beyond the 27th body part, they loop back to tan dopa (28), or the wrist on the other side (28th position). For more information, please see my book, Cultural Development of Mathematical Ideas: Papua New Guinea Studies.

This film was taken in 1980. The man interviewed is a trade store owner who has developed new ways of using the body part counting system to solve arithmetic problems. He is presented with the problem that he has one kina and sixty toea and spends seventy toea. In the video, he represents one kina sixty toea as 16, distributing the value as shoulder (10) on one side of his body and wrist (6) on the other. Then from the side for which he has registered shoulder (10), he indicates that he spends the equivalent of seven or forearm (7), leaving the elbow (8th body part), biceps (9th body part), and shoulder (10th body part). He then  "moves" these remaining body parts from one side to the other (to the side that already contains a representation of wrist (6): First he moves the remaining elbow (8) to the forearm (7), (to the forearm (7) since he has already a representation of wrist (6); then the biceps (9) to the elbow (8), since he now has accumulated forearm (7); he finally moves the shoulder (10) to the biceps (9). Biceps (9) then is the solution of the problem. In the Cultural Development of Mathematical Ideas, this approach is referred to as a "halved body" strategy. The man was not taught the approach; it's an approach that emerged as Oksapmin people engaged in novel practices of economic exchange with currency.

To support filming, the teacher agreed to have a 4th grade class moved outside for an arithmetic lesson. For a closer look at body strategies that children used, see this link.

School reforms in Papua New Guinea were initiated in the late 1990s. In post-colonial education, instruction was to be solely in English and traditional knowledge forms were devalued. With the reforms, teachers were to build upon local knowledge in moving towards Western-knowledge and representational systems. Here the students display their use of indigenous body counting now valued in the early grades.

The man is presented with one kina and ten toea in the form of two 50 toea coins and one ten toea coin. Because of a prior history detailed in the book, the value of 10t is treated as a unit. The man represents the value as gwer or neck (11th position) in the Oksapmin body part counting system, the equivalent of eleven 10 toea coins. For more information, please see my book, Cultural Development of Mathematical Ideas: Papua New Guinea Studies.

The video shows a child who was interviewed as a part of a larger study. The video shows ways in which Oksapmin school children were adapting their body system to solve arithmetic problems in 1980. During this period of schooling, children were not allowed to use the vernacular on school grounds. In the interview, the child is presented with the following problem: You have 16 pigs; you give seven away; how many left? The 4th grader begins his solution of the problem with the ear-on-the-other-side (16). He indicates that this (ear (16) is given away, and corresponds to the thumb (1); the eye on the other side (15) is given away, and that corresponds to the index finger (2); the nose (14) is given away, and that's the middle finger (3)... the child proceeds to the shoulder (10) is given away and that's the forearm (7), leaving biceps (9), the answer. In the Cultural Development of Mathematical Ideas, this approach is referred to as a "double enumeration" strategy. Children are not taught the approach; it's an approach that emerged as Oksapmin children made efforts to make sense of the mathematics taught in school in the post-colonial approach to schooling.

From 1978 through 2001 there was a development of a money economy in the Oksapmin area. One source of currency for people was to sell vegetables they grew in their gardens to the Ok Tedi mine (sent by small plane). The video shows people being paid for their vegetables by brokers.

The man is presented with one kina and ten toea in the form of two 50 toea coins and one ten toea coin. Because of a prior history detailed in the book, the value of 10t is treated as a unit. The man represents the value as gwer or neck (11th position) in the Oksapmin body part counting system, the equivalent of eleven 10 toea coins. For more information, please see my book, Cultural Development of Mathematical Ideas: Papua New Guinea Studies.

In 2014, teachers described the continued use of the body system in classrooms. The continued use is supported by Papua New Guinea school reforms initiated in the late 1990s.