Educators of Native American Students (eonas)

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Educators of Native American Students (EONAS)

  • Richard Sgarlotti, Ed.S.
  • Hannahville Indian School
  • Jim Barta, Ph.D.
  • Bemidji State University

Educators of Native American Students has applied to be a SIG of TODOS.

  • The mission of TODOS: Mathematics for ALL
  • is to advocate for an equitable and high quality
  • mathematics education for all students — in particular, Hispanic/Latino students —
  • by increasing the equity awareness of educators
  • and their ability to foster students' proficiency
  • in rigorous and coherent mathematics.
  • If this was a strand of beads,
  • and was 100 beads long,
  • what color is the 100th bead?
  • What are the next three numbers
  • in this sequence?
  • 1, 4, 7, 10, ____, ____, ____
  • 1, 4, 7, 10, 13, 16, 19
  • If that sequence was continued,
  • is 100 one of the numbers
  • in the sequence?
  • X Y
  • 1
  • 4
  • 7
  • 10
  • 100?
  • Using points A and B as midpoints of opposite sides, construct a square using only a cord, straightedge and pencil.
  • A
  • B
  • Using points A and B as midpoints of opposite sides, construct a square using only a cord, straightedge, and pencil.
  • A
  • B
  • How do you know it is a square?

The Kwakiutl of Vancouver Island used a configuration of pegs and cords to lay out the plan for square houses. As reported by Franz Boas in the 19th century and reinterpreted by a modern scholar, the builders would start by driving two stakes to define a line marking the centers of the front and rear walls of the house. They would then stretch a cord between these two stakes and, having obtained the distance, double the cord on itself to identify its midpoint. With the midpoint known, it is placed at one of the two stakes with the cord’s ends extended roughly perpendicular to the line marked out by the two stakes. A second cord is run from the second stake consecutively to each of the first cord’s ends to make sure that the ends are located precisely to bring the cord exactly perpendicular to the line between the two stakes. These endpoints are then marked and the whole process repeated with the first cord centered on the second stake to locate the remaining two corner points of the square. From: American Indian Mathematics Traditions and Contributions, Michael P. Closs

American Indians generally have had a pragmatic orientation to the use and study of mathematics. In most Indian cultures, mathematics traditionally was practiced by most of our ancestors, … for its value in daily life rather than for its own sake or as an intellectual challenge.

  • Portland Public Schools Geocultural Baseline Essay Series, Landon, 1993
  • Center for Research in Education, Diversity & Excellence
  • (CREDE)
  • University of California, Berkley
  • Standards for Effective Pedagogy.
  • Strategies that work well with Indian students
  • (Minority students)
  • Joint Productive Activity
  •   Teacher and Students Producing Together
  • Language Development
  •   Developing Language and Literacy Across the
  • Curriculum
  • Contextualization
  •   Making Meaning: Connecting School to
  • Students' Lives
  • Challenging Activities
  •   Teaching Complex Thinking
  • Instructional Conversation
  • Teaching Through Conversation
  • Making Meaning:
  • Connecting School to Students’ Lives
  • Connect teaching and curriculum to students'
  • experiences and skills of home and community.
  • The teacher:
  • begins activities with what students already know from home, community, and school.
  • designs instructional activities that are meaningful to students in terms of local community norms and knowledge.
  • acquires knowledge of local norms and knowledge by talking to students, parents or family members, community members, and by reading pertinent documents.
  • assists students to connect and apply their learning to home and community.
  • “Creating Sacred Places for Children” is a National Indian School Board Assoc. effort to provide an Indian model of school reform that includes:
  • *The Effective Schools framework
  • (Larry Lezotte)
  • *The integration of Indian culture in the curriculum:
  • CSP Curriculum-6 Volumes by
  • Dr. Sandra Fox
  • Creating Sacred Places -
  • Means responding appropriately to students’ academic, physical, social, emotional, and spiritual needs. Research by Cummings, “The Empowerment of Indian Students”, lists four characteristics that schools must include if Indian students are empowered to learn. Cummins, Jim, 1986
  • Empowering Minority Students: A Framework for Intervention. Harvard Educational Review, v56 n1 p18-36
  • Language and Culture must be incorporated into the school program.
  • Research suggests that for minority groups experiencing school failure, the extent to which students’ language and culture are incorporated into the school program constitutes a significant predictor of academic success.
  • 2. There must be an unbreakable bond between school and community.
  • When educators involve parents as partners in their children’s education, parents communicate to their children a positive attitude toward education that leads to improvement in the students’ academic achievement.
  • 3. Appropriate
  • Instruction must be
  • provided.
  • The experiential-interactive model of instruction focuses on giving students hands-on classroom experiences that provide students with a basis for understanding more abstract academic curricula. Learning styles of students must also be taken into account.
  • 4. Appropriate
  • Assessment must be
  • Provided.
  • There should be more emphasis on performance based assessment.
  • Minority students are over represented in special education.
  • Creating A Sacred Place for
  • Students In Mathematics
  • Grades Pre-K - 12
  • Edited by Richard Sgarlotti, Ed. S.
  • Published by the National Indian School Board Association
  • 2006
  • The units are related to one or more of the following topics:
  •    Indian Contributions to Mathematics
  •    Mathematical Concepts in Traditional
  • Culture (Mathematics as the science of patterns)
  •    Mathematical Concepts in Present Day
  • Cultural Activities
  •    Math as the Language of (Indian) Science
  •    Math in the Study of Indian People
  •    Indian Mathematicians/Scientists
  • -Past and Present
  • Shota and the
  • Star Quilt
  • A Native American story, Shota and Ester are about to part, but before they do they make a star quilt with Shota's grandmother at Pine Ridge Reservation.
  • Ontario produces between 908,000 and 1,362,000 liters of maple syrup and between 9,000 and 11,000 kg. of maple sugar annually.
  • About 4 in 10 of the nation's 1.9 million American Indians identified their tribe as either Cherokee (308,132), Navajo (219,198), Chippewa (103,826), or Sioux (103,255), according to figures released today by the Commerce Department's Census Bureau. The census tabulations present population counts for 542 tribes for the United States, its regions, divisions, and states.
  • Jim Thorpe Winning Performances 1912 Olympic Pentathlon
  • Event Place Distance/Time
  • Long Jump 1 23 ft. 2.25 in
  • Javelin 3 153 ft 2 in.
  • 200 m 1 22.9 sec
  • Discus 1 117 ft 3 in
  • 1500 m 1 4 min 44.8 sec
  • Fred Begay (Navajo), Nuclear Physicist
  • My mother is from the Lakota tribe, and life wasn’t always so cheery for an Indian kid in a small rural school. When I was a child, the Indian stereotypes from the Western movies were still very strong. Some teachers and fellow students didn’t believe that Indians would need education or that Indians would eventually compete for the top jobs in our society. One year I ended up in the “slow” section of the class just because of my Indian background.
  • (Robert Megginson, SACNAS biography project)

Robert Megginson, Professor of Mathematics, University of Michigan

  • Robert Megginson, Professor of Mathematics, University of Michigan
  • On the way up Bear Peak in the Colorado Rockies
  • One of my greatest passions is mountain climbing, and my current project is to climb all of Colorado's Fourteeners, the mountains in Colorado whose summit elevations exceed 14,000 feet.
  • We have not wings, we cannot soar; But we have feet to scale and climb By slow degrees, by more and more, The cloudy summits of our time.
  • - From The Ladder of St. Augustine, by Henry Wadsworth Longfellow

John Herrington (Chickasaw) received a bachelor of science degree in applied mathematics from the University of Colorado at Colorado Springs, in 1983, and a master of science degree in aeronautical engineering from the U.S. Naval Postgraduate School in 1995. ORGANIZATIONS: Life member of the Association of Naval Aviation, University of Colorado at Colorado Springs Alumni Association. Sequoyah Fellow, American Indian Science and Engineering Society.

Edna Paisano

  • A talented mathematics and science student, Paisano attended the University of Washington and earned a graduate degree in social work, studying statistics in the process.
  • As a result of visiting tribal areas and of examining the data from both a questionnaire she developed and the 1980 census, Paisano discovered that American Indians in some locations were undercounted. Because the allocation of important federal funds to tribal units is based on census figures, Paisano used modern statistical techniques to improve the accuracy of the census. By encouraging education in relevant mathematics-related fields such as computer programming, demography, and statistics, and by coordinating a public information campaign, she and her colleagues alerted American Indian communities to the importance of the census. As excerpted from Agnesi to Zeno, Key Curriculum Press, P.O. Box 2304, Berkeley, CA 94702
  • When Edna Lee Paisano (b 1948) was growing up on the Nez Perce Indian Reservation in Sweetwater, Idaho she learned to preserve her families traditions and make them a part of her daily life. For example, her grandmother taught her how to make moccasins and beaded purses, which they sold to help support the family. Additionally, owning the fishing, hunting, and mineral rights to the land in the Nez Perce area made it easier for the tribe to be self-sufficient, and in the teepee in the backyard of Paisano's home, the family regularly prepared, dried, and smoked the meat of deer, elk, and moose.

Arrow Flight and the Quadratic Equation Brent Sauve, Hannahville Indian School

  • Native Americans used the bow for defense and for the taking of game animals for food. Many aspects of the flight of the arrow can be described using mathematics. When shot, the general flight of an arrow is a parabolic arc. Of course, any parabola can be described using a quadratic equation. This lesson helps to define for students how a, b, and c affect the graph of the quadratic equation, and should be considered as an introduction into graphing of quadratics.
  • This looks like the graph of an arrow in flight.
  • In fact, if the distance between each grid line is equal to one yard,
  • our arrow rose 1 yard while it flew 20 yards.

  • The North American Study Group on Ethnomathematics
  • (NASGEm) strives to increase understanding of the cultural diversity of mathematical practices, including that of traditional American Indian knowledge and to apply this knowledge to education and development.

Ethnomathematics is the term used to describe the mathematical practices of identifiable cultural groups. Mathematical practices include:

  • Ethnomathematics is the term used to describe the mathematical practices of identifiable cultural groups. Mathematical practices include:
  • symbolic systems,
  • spatial designs,
  • practical construction techniques,
  • calculation methods,
  • measurement in time and space,
  • specific ways of reasoning and inferring, cognitive and material activities which can be translated to formal mathematical representation.

  • Virtual Beadloom
  • Ron Eglash

Earl Otchingwanigan A Concise Dictionary of Minnesota Ojibwe

  • Earl’s Wigwam
  • …it has been documented that certain materials such as wood strips, also "string-like" strips of inner basswood bark were used as measurement tools....also, the use of certain body parts were used in measurement such as canoe making....but specifically ningodoninj refers to the length of the forefinger from the knuckle to the joint nearest its finger nail,  e.g;  if you were to bend your forefinger as it would look much like an upside down "L", it approximates an inch more or less on the average male/female and, also then, you can also note how easy it is to use that bent forefinger to apply to a surface for a fairly general but not exact measurement ---- Earl O
  • Wigwam Measurement
  • finger width izhinoo'iganinjiikanjige vai, determine
  • width/length in a certain way with forefinger measurement.  knuckle to knuckle length dibikwaakoninjiikanjige vai,
  • determine width/length by knuckle to knuckle measurement. finger tip to elbow dibadooskwanikanjige vai, determine
  • width/length by using elbow to finger tip measurement. chest to fingers inikaakiganaangikanjige vai, determine
  • width/length in a certain way by chest area to finger tip
  • measurement.
  • Kwezage’win
  • The game (kwezage’win) was played only by women, and mostly in the winter in place of double-ball. Like the two preceding games, this one is also sponsored by a woman in honor of her guardian spirit, and similar ceremonial preliminaries are held. After the feast, a blanket is spread out on the floor and the women sit in a circle, but divided into two teams with each side sitting in a semi-circle facing the other. As many women can play as want to, but there are only four prizes: yard goods of red, blue, green, and white. The gaming equipment consists of a wooden bowl and eight dice, six of which are thin, circular discs; one is carved in the form of a turtle and one represents a horse’s head. Dice were formerly made of buffalo rib, but horse’s ribs are used at present. One surface of each die is colored blue (red may also be used). Thus each die has a colored and a white side. The bowl is held with both hands, and the dice shaken to the far side of the bowl which is given one flip, set on the floor, and the score counted …
  • Hannahville Indian School
  • Click on Classroom Projects,
  • then Math Wall

“Using Native Legends to Teach Mathematics” Judith Hankes UW-O

  • Children's Mathematics: Cognitively Guided Instruction Based on more than twenty years of research, this eye-opening book will help you understand how children's intuitive mathematical thinking develops and how children can build up their concepts from within. Thomas Carpenter, Elizabeth Fennema and others
  • Math at the Museum
  • Ethnomathematics of the Eiteljorg
  • For
  • Educators of Native American Students
  • And other interested people
  • Eiteljorg Museum
  • of American Indians and Western Art
  • (Adjacent to NCTM Conference Center)
  • 3:00-5:00
  • Friday, April 15, 2011
  • American Indian Science
  • and Engineering Society
  • (AISES)
  • National American Indian
  • Science and Engineering Fair
  • -Mathematics Competition
  • Society for the Advancement of Chicanos and Native Americans in Science
  • (SACNAS)
  • Changing the Faces of Mathematics: Perspectives on Indigenous People of North America
  • This volume is meant to give class-
  • room teachers, administrators and principals, curriculum supervisors and program developers, ethno-mathematicians, and researchers a deeper understanding of indigenous people's mathematics and pedagogy. (Published by NCTM)
  • Math, Science, and Art
  • Presented at NAISEF, 2009


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