Mathematical Thought and Application in Traditional Seminole Culture

Jim Barta

Utah State University

Author's note: During the past several years, I have been involved with an ethnomathematics research project studying the Seminole tribe of Florida. The project has evolved in two phases. The first phase involved interviewing Seminole elders and others to examine the traditional (historical) daily activities of the Seminole people in which mathematical principles were embedded. This data then (phase two) will be used to collaborative design with teachers at the Ahfachkee Seminole Elementary School on the Big Cypress Reservation culturally inclusive elementary math curriculum. The following describes findings related to the first phase.

The Seminole, a native people whose roots can be traced throughout the southeastern United States came into being during the 18th century (Garbarino, 1988). The name "Seminole" is thought to have originated from the European mispronunciation of the Creek word "simanoli" which meant runaway. The Seminole were comprised of both native and blacks who sought freedom in Florida from persecution and slavery at the hands of the increasing number of settlers in colony of Georgia. They successfully made their homes in the swamps and glades of central and southern Florida where they could freely maintain their traditional ways of life. Several times during a 25 year period ranging from 1817 through 1842, the United States declared war on the Seminole. Many natives resisted with their lives the Government's insistence that they give up their lands and accept relocation out west. Eventually, with numbers estimated to be less than 500, the cavalry grew tired and those natives remaining were left alone. The Seminole are the only native group to have never signed an official "peace treaty" with the United States. Traditional cultural practices are still evident among the people although there is concern among the Seminole that the most recent generation is losing touch with their ancestral culture. Today, a population of nearly two thousand live on several reservations across Florida.

Bishop (1991) has stated that many of the everyday activities of people (past and present) involve a substantial amount of mathematical application. Six "universal" activities that are thought to be practiced by any culture are: counting, measuring, designing, locating, explaining, and playing. These six universal activities (inclusive of D'Ambrosio's broad view of mathematics. 1987) provided the fundamental facets used to probe traditional daily living practices of the Seminole culture. The results of the research have allowed for substantial insight into traditional application of mathematical inventiveness within the Seminole culture. These universals (counting, locating, designing, measuring, explaining, and playing) were inseparably intertwined with other aspects of the Seminole culture. Through a study of these applications, we come to better know the wonder of these people and their early experiences using math. The following examples are outlined.

Counting appears to be predicated on a "Base Ten" system if one examines the numeric names. No written symbols existed, rather physical representations (seeds, pebbles, knots) or finger gestures were used to physically describe quantities when necessary. When gestures have been observed however, counting appears to be done in groups of five (a person will count and touch each digit of one hand while counting from one to five). Counting on from six to ten occurs by retouching digits on the first hand counted. The Seminole referred to zero as "having nothing." Extremely large numbers were not necessary and so no words for them were used. It was culturally inappropriate to have too much of anything. If one did, it meant that they were greedy and that they must share with others in the tribe. Reference was made to these numbers however in other ways. For example, when asked to describe the number of stars in the sky, an Elder stated, "There are so many that I could count for all of my life and never finish counting."

These words listed below are the counting names for the numbers 1-10 and 10-100 (Wilson, 1986).

1	Hum-kin		6	A-pa-kin
2	Ho-ko-lin		7	Ko-lo-pa-kin
3	Too-chin		8	Chin-na-pa-kin
4	Os-tin		9	Os-ta-pa-kin
5	Chaw-kee-bin		10	Pa-lin
20	Pa-lin-ho-ko-lin		60	Pa-lin-a-pa-kin
30	Pa-lin-too-chin		70	Pa-lin-ko-la-pa-kin
40	Pa-lin-os-tin		80	Pa-lin-chin-na-pa-kin
50	Pa-lin-chaw-kee-bin		90	Pa-lin-os-ta-pa-kin
			100	Chope-kee-hum-kin

Measurement involved the use of certain "standard units" found in the environment. Parts of the body provide convenience yet suitably standard units of measure. For instance, the distance from the nose to the end of an out stretched arm was used to measure units of cloth. Measurement for construction of their traditional homes known as "Chickees," used the po-cus-wv e-mv-pe (pronounced ba-giz-u-ah e-mobi) which when translated from the Creek language means the "length of an axe handle".

Other "units of measurement" such as the number of paces existing between objects in their environment (distance), the rate one traveled on foot or in a wagon to the trading post (speed), the length of shadow cast by a tree (time) reflect how these people applied their mathematical intelligence to solve relevant problems. It appears the Seminole possess an uncanny ability to measure "by the eye." Exact units were not necessary since minor allowances created few real problems.

Distances, were expressed as a function of the time it took one to travel from Point A to Point B. The speed (or distance) was determined by the mode of travel; walking was the slowest, wagons drawn by cattle was faster. Canoe travel resulted in the greatest speed. The distance from the village to the trading post may be only a half-day travel by canoe. Great distances were described as being so great that a man could walk his entire life and never arrive at the destination.

Seminole located places within their environment by constructing mental maps. Landmarks familiar to most acted as points of reference. Occasionally, maps drawn in the sand were used. Directions used to locate a position were literally named. The cardinal direction "East" for instance was named the place where the sun comes up.

Designs in the Seminole culture were abundantly evident. The patchwork clothing worn by many women and a few of the men resulted from sewing strips of colored fabric into geometric patterns which involved an implicit understanding of transformational geometry. These patterned designs were then stitched onto other clothing such as dresses and shirts.

Math was also used to explain concepts such as age and the time between certain importart events. The year was described as a cycle of two seasons and one's age was calculated by counting how many cycles had occurred since an event happened. Therefore, one might be 21 "summers" old. Age was also relative to those with whom one lived. A person might have lived many winters yet would not be considered an "Elder" if there were others still living who were older.

Playing was an important aspect of the Seminole culture. During the sacred "Green Corn Dance", a celebration welcoming the beginning of a new year, a type of stick ball is played (men against women) and scores are kept. The scoring could be additive (a point for each goal earned) or can be subtractive (a point subtracted from a predetermined originating score). A traditional children's game similar to mumble peg (Appalachian) was played. Children would use a sharpened stick and take turns pitching it into a pile of sand from places on the body. Points were scored when the stick landed vertically and remained upright in the sand. The knee bone of a cow was also used to play a similar game. Certain faces of the bone earned specific points when it landed with that part of the bone face upwards. Children added the combination of numbers earned and played until a predetermined number was reached.

There remains a great deal more to learn about Seminole application of mathematical practices. I feel a sense of great awe to be witness to the culturally-determined mathematics created by these people. Through this ethnomathematical study, we glimpse how math provided them the intellectual tools and language to survive and succeed in the swamps of southern Florida.

References

D'Ambrosio, U. (1987). Reflections on ethnomathematics. International Study Group on Ethnomathematics Newsletter, 3 (September).

Garbarino, M. (1988). The Seminole. New York: Chelsea House Publishers.

Wilson, M. (1986). The Seminoles of Florida. Philadelphia,PA.: American Printing House.