WigwametryTeaching Geometry through the

Scale-Model Construction of a Tradtional Native American

Structure

Definining Mathematics

Mathematics reveals hidden patterns that help us understand the world around us…Mathematics is a

science of pattern and order…Its domain is…numbers, chance, form, algorithms, and change.

Pattern

You have noticed that everything an Indian does is in a circle, and that is because the Power of the World always works in circles, and everything tries to be round. The Sky is round, and I have heard that the earth is round like a ball, and so are all the stars. The wind, in its greatest power, whirls. Birds make their nest in circles, for theirs is the same religion as ours....

Even the seasons form a great circle in their changing, and always come back again to where they were. The life of a man is a circle from childhood to childhood, and so it is in everything where power moves.

Black Elk, Oglala Lakota, 1863-1950  *This quote comes from the book Black Elk Speaks by John Neihardt. Though critics, Native and non, scrutinize the authenticity of his research and translation, many of the philosophies in it reflect a humanistic understanding of life.

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Background

The achievement gap between Native American and non-Native American students is especially alarming in the areas of math and science.

*Wisconsin Department of Public Instruction (1999-2000)

While curriculum in general is not to blame, many educators in Indian Country1 feel that cultural relevancy can refine teaching material as well as methods (Cambpell, 2003).

Accountability

1. A vague but common reference to Native American populations residing in the United States in cities, rural areas, and on reservation.

*Campbell, Linda. “Increasing the Achievement of Native American Youth at Early College High Schools” March, 2003. http://www.newhorizons.org

Learning Style

Furthermore, it has been demonstrated that Native American children learn differently than their non-Native peers (Read, 1999).

*Read, Dr. Sue Ellen. “Learning Styles of American Indian Students in Northeastern Oklahoma” April, 1999. http://arapaho.nsuok.edu/~oil

Consequently the delivery of curriculum and its accommodation of Native American learning styles is vital to the learning success of Native American students (Bergstrom, 168).

Accommodation

* Bergstrom, Amy, Linda Miller Cleary, and Thomas D. Peacock. The Seventh Generation. Charleston, WV: Clearinghouse on Rural Education and Small Schools, 2003.

Identifying geometric patterns in a hemi-sphere.

Origin

RadiusWigwametry

How can you design the base shape of your structure so that the distance around is about 37 inches? How wide is the shape of your structure?

Problem Example

Area

What pattern do you notice about square area and the area of a square?

radius

length

A = A X 3.14

Group Work

Origin

Radius

Diameter

Circumference

Performance Assessment and Rubrics

Category 4 3 2 1

Construction-Materials

Appropriate materials were selected and creatively modified in ways that made them even better

Appropriate materials were selected and there was an attempt at creative modification to make them even better

Appropriate materials were selected.

Inappropriate materials were selected and contributed to a product that performed poorly.

Quality of Construction

Great care taken in construction process so that the structure is neat, attractive and follows plans accurately.

Construction was careful and accurate for the most part, but 1-2 details could have been refined for a more attractive product.

Construction accurately followed the plans, but 3-4 details could have been refined for a more attractive product.

Construction appears careless or haphazard. Many details need refinement for a strong or attractive product.

Function Structure functions, extraordinary well, holding up under atypical stress.

Structure functions well, holding up under typical stresses.

Structure functions pretty well, but deteriorates under typical stresses.

Fatal flaws in function with complete failure under typical stresses.

Design Structure is of appropriate size and shape, arranged well from front to back. Creatively arranged.

Structure is an appropriate size and shape, arranged well from front to back with arrangements not all appearing balanced.

Structure is an appropriate size and shape, but arrangements not very attractive.

Structure is untrimmed OR inappropriate size, little attention to arrangements.

Time and Effort Class time was used wisely. Much time and effort went into the planning and design if the collage. It is clear the student worked at home as well as at school.

Class time was used wisely. Student could have put in more time and effort at home.

Class time was not always used wisely, but student did do some additional work at home.

Class time was not used wisely and the student put in no additional effort.

TOTAL POINTS