Ethnomathematics Unit and other resources
Updated on
Please alert stoloffd@easternct.edu to any non-functioning links. You might do your own web search if the links are not functioning to find where the topic had moved.
From an email from Orey, Daniel C [email:orey@csus.edu]
I might invite your students to look over the Algorithm Collection
Project: http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/Alg.html
and Ron
English's: Culturally Situated Design Tools:
teaching math through
culture: http://www.rpi.edu/~eglash/csdt.html
Ethnomathematics Unit developed by Katherine Patterson
Multicultural Ideas for your Math Class
Ethnomathematics
Ethnomathematics refers to any form of cultural
knowledge or social activity characteristic of a social and/or cultural group
that can be recognized by other groups such as 'Western' anthropologists, but
not necessarily by the group of origin, as mathematical knowledge or
mathematical activity" Geraldo Pompeu, Jr. (Pontifica Universidade Catolica de Campinas, Brazil- ISGMe 12.2)
A Definition of Ethnomathematics
Gloria Gilmer, Math-Tech Inc.
The following definition of Ethnomathematics has been prepared for a dictionary of multicultural education:
(1) Ethnomathematics is the study of the mathematical practices of specific cultural groups in the course of dealing with their environmental problems and activities; For example, the manner in professional basketball players estimate angles and distances differs greatly from the corresponding manner used by truck drivers. Both professional basketball players and truck drivers are identifiable cultural groups that use mathematics in their daily work. They have their own language and specific ways of obtaining these estimates and ethnomathematicians study their techniques.
The prefix 'ethno' refers to identifiable cultural groups, such as
national-tribal societies, labor groups, children of a certain age bracket,
professional classes, etc. and includes their ideologies, language, daily
practices, and their specific ways of reasoning and inferring.
Mathema' here means to explain, understand and manage
reality specifically by ciphering, counting, measuring, classifying, ordering,
inferring and modeling patterns arising in the environment.
The suffix 'tics' means art or technique.
2) Thus, ethnomathematics is the study of
mathematical techniques used by identifiable cultural groups in
understanding, explaining, and managing problems and activities arising in
their own environment.
ISGEm Newsletter. Vol.11 No.1, Dec.,1995
Ethnomathematics - http://iml.math.wvu.edu/portals/0/NtForums_Attach/Ethnomathematics%20revised.ppt
Ethnomathematics: an absolutely essential key for Mathematics Education
A brief introduction to Ethnomathematics
is given with some valuable links.
Why Do We Teach Ethnomathematics?
Brief discussion of the 1. educational view;2. anthropological
view 3. modeling view;4. historical
view; 5."science studies; 6. historical-modern;
7. mathematical view
ISGEm
Newsletters The International Study Group in Ethnomathematics
publishes a newsletter which is a vast resource for those interested in ethnomathematics. In these newsletters you will find
articles and research by the people that are making this a field of
mathematics. Not only are there interesting articles contained in these
volumes but also bibliographies. I shall briefly list areas that may be
of interest in each volume.
Volume 2 No.
1: "Learning, Aboriginal World View, and Etnomathematics"
by Robert Hunter
"An
Experience with Mathematics Testing Bilingually in Guatemala"
Volume 3
No.1: "Reflections on Ethnomathematics" by Ubiratan D'Ambrosio
Volume
4 No.2: "Candy Selling and Math Learning" by Louis
Ortiz-Franco
"Integrating Math with the Study of Cultural Traditions" by Claudia Zaslavsky
Volume 5 No.
2:" Ethnomathematical Perspectives on the NCTM
Standards" by Daniel Orey
Volume 6 No.
1:" Critical Math Network Convenes at Cornel" by Paul Ernest
"A
Multicultural Mathematics Curriculum" by Beatrice Lumpkin
"HIMED
Conference" by Claudia Zaslavsky
Volume 6
No.2: "Video Games for Math: A Case for 'Kid Culture"" by
Lawrence Shirley
UNESCO
Mathematics Curriculum in Guinea-Bissau" by Beatriz D'Ambrosio
"Games
Played Around the World"
"The
Philosophy of Mathematics Education" by Dr. Paul Ernest
"Recent
Ethnomathematical Research in Mozambique"
Volume 7
No.1: "Women as the First Mathematicians" by Claudia Zaslavsky
"
'Mathematics' & Ethnomathematics: Zimbabwean
Student's View" by David Mtetwa
Volume
8 No. 1: "Working Group 10 on Multicultural/Multilingual
Classrooms"
Volume 8
No.2: "A View of Ethnomathematics" by P. Rajagopal
"Connecting the Ethnomath of Carpet Layers with
School Learning" by Joanna Masingila
Volume 9
No.1:" Mayan Geometry" by Leomel Morales
"Shape
Hunting" by Maria Ponza
Volume 9 No.
2:" Connecting Math Practices In and Out of School" by Gloria Gilmer
"How
Students can Own Mathematics: Three Tales" by James Rauff
Volume
10 No.1: " Mathematics and roller blades" by Rick
Silverman
volume 10
No. 2: "Mathematics Pedagogy in the 3rd World: The Case of a Guatemalan
Teacher" by Richard Kitchen
"Report
on Ethnomathematics Research" by Joanna Masingila
Volume
11 No.1: "Ethnomathematics,
Complementarily and Bhutan" by Jerome turner
"An Ethnomath Approach to Curriculum Development" by
Gloria Gilmer
Volume 11
No. 2:"Ethnomathematics and Multicultural Mathematics" by Bill
Collins
"The
Mathematics of Nature: the Canamate Quadrivertex" by Rogelio Diaz
Volume 12
No. 1 :"Geometry in the Middle Grades: A Multicultural Approach" by
Fredrick Uy
"Symmetry Patterns of the Wisconsin Woodland Indians" by Kim Nishimoto and Bernadette Berken
Volume 12
No. 2:" Ethnomathematics Production in
Brazil" by Gelsa Knijnik
Mathematics
and Beadwork: Notes from a Conversation with a Sioux Artist" by Jim Barta and Rick Silverman
Volume 13
No. 1: "An Investigation of Muskogee Creek Indian Counting Words" by
Richard DeCesare from SCSU
Mathematics
and Crafts in Andalusia: An Anthropological-Didactic Study" by Maria
Contreras
African
Mathematical Union This is their homage with a
description of the union and the various parts of which it is composed.
Of particular interest is AMUCHMA which is the commission on the History of
Mathematics in Africa. They offer a newsletter which is available online.
History of Mathematics
Africa's Science and Indigenous
Knowledge Systems Listed by UNESCO as one of
the top 50 African web sites three areas of particular interest are given here.
1) Mathematics in pre colonial Hausaland (including Ilm al-Awfaq -the science of
magic squares) by Ahmad Kani 2) African
Fractals-Modern computing and Indigenous Design by Ron Eglash
and 3) Geometry from Africa by Paulus Gerdes
Ancient Egyptian
Planning Mathematics of Egyptian planning
COLOR: History of Mathematics in Africa Dedicated to dispersing many misconcepts about Africa and in particular math in Africa, this site offers many valuable entries on African math history.
Development
of Mathematics in Ancient China
Chinese math as defined as the art of calculation, being both practical and
spiritual.
Earliest Known Uses of Some of the
Words of Mathematics A
Egyptian mathematics
History of
Mathematics Home Page After a brief introduction, math history in Greece,
Europe, China, Japan, India, Egypt, Babylon and the Arab sphere are linked
through regions at the bottom of the page.
History of Mathematics This is the site of the MacTutor
History of Mathematics archive offered by the
History of Mathematics in the Americas Mesoamerican cultures discussed.
Mathematics History This site comes from Seoul, Korea with areas both on the development of mathematics and mathematicians. Site is designed so that you can take tests as you do along.
Mathematics in Latvia Through the Centuries
Mesopotamian
Mathematics A site for a St. Lawrence U. professor offering some math
history
Math Forum: Famous Problems in the History of Mathematics Offering some of the great Historic problems of math, these problems are appropriate for middle and high school students.
The first Use of Zero and Negative Numbers
Tokens: the
origin of mathematics From about 800 B.C.
found all over the
Web sites relevant to the History of Mathematics
Mathematicians
Biographies of
Women Mathematicians
This is a good place to start when looking for information on women in
mathematics. Both an alphabetical and chronological index is given
Mathematicians
of the African Diaspora
From SUNY at
Mathematical Quotation Server Quotes from the great and not-so-great mathematicians
Past Notable Women of Mathematics biographies of 12 notable female mathematicians are given as this Yale site.
.
Time and Measurement
A Brief Introduction to the Islamic (Hijri) Calendar This site gives the history, and method of calculating the Hirji calendar.
Calendars - Historical information and FAQ about many calendars A look at Christian, Jewish, Islamic, Chinese, Mayan, French and other calendars exploring the 7 day week, and the year.
Counting in Babylon These are lecture notes from a professor at UVa in physics. Good basic introduction to the number system used by the first to use written language. View his other notes on math and science by going to Galileo and Einstein
Hindu Calendar Not only the months in the Hindu calendar are given at this site, but also "Today in the Hindu Calendar" and "This month in the Hindu calendar".
Metric Units and Measurement Hosted by the Math League, this is a good site for students providing not only explanations, but also problems.
Time Function An explanation of time and how it is measured, and three calendars used. A Walk through Time Ancient Calendars, Early Clocks, Revolution in timekeeping, world time scales, NIST time calculations and the atomic age are explored here
Zoroastrian Religious
Calendar Brief descriptions of the three main calendars-Fasli, Shahanshahi, and Qadimi- are given.
.
Systems of Numeration
The Abacus: Index A
History of the abacus, directions for adding and subtracting using the abacus,
and a comparison of the Chinese and Mesoamerican abacus is given here.
Abacus in various number systems Explores the abaci in China, Japan and Russia.
Ahmes: Rhind Mathematical Papyrus is the major source of our knowledge of mathematics in early Egypt. Not only does it contain 80 math problems but a table of fractions.
Khipus, or quipocamayos, a unique Huarochiri Legacy: this is part of the Huarochiri, a Peruvian Culture in Time web site which offers an ethnographic and historical tour of the community. Here the "quipocamayos" are treasured. Wonderful photos available here.
The Maya Astronomy Page Located here are Mayan Mathematics, the Maya Calendar, Maya Writing and Maya Astronomy .
Numbers Arabic and duodecimal numerals, the decimal system, Egyptian, Greek, Roman, Babylonian and the Hindu Arabic numeral systems are covered.
The Numbers in Various Writing Systems Not only is there over a lists of numbers from 1-10 in over a thousand languages, but the author briefly discusses the writing system of morphosyllabic script, syllabic script, modified syllabifies, consonantal scripts, alphabets and the feudal system as well as American sign language.
Lesson
Plans
ANASAZI/MESOAMERICAN/ANDEAN:
TIME AND CULTURAL PASSAGES
A middle school (grade 7) lesson plan where students become a member of one of
six (Olmec. Teothihucan-Toltecs,
Mayan, Aztec, Inca or Anasazi)ancient
cultures and tell their story.
Extreme Elevation A seventh grade lesson exploring the lowest and highest elevations in the world.
Fractions and Paper Folding Lesson designed to teach fractions through origami.
From Prairie Ecosystem to Prairie Architecture; Good unit for about 4th grade doing a whole math approach with geometry and architecture also may tie in some literature.
Geometric Systems in Architecture A 2 week unit designed for middle school to help students build an awareness of geometry and space.
Iditarod
Webquest Upper elementary webquest
It's Your Life Grade levels 6 and 7 utilizing census information.
LeGrand-Equisite Excursions A lesson for
several class period for Gr. 4-6. Students plan a trip
to 6 world
Ma Baker's Origami and Paper folding Web Quest Page.
The History of Mathematicians and Physicists. Webquest
Pennsylvania Dutch Hex Signs 4th gr. lesson exploring hex signs
Native American Geometry A site formed for 4-9 graders linking Native American symbols to specific polygons. It is divided into three areas: Education, Design and Anthropology.
Math History Lesson plans for 7-9 graders taking four periods covering famous mathematicians.
Math Forum- spanish language math resource
Mathematical Patterns in African American Hairstyles Using Technology to Explore
Mathematical Patterns in African American Hairstyles: explores the tessellation, box braids, and triangular braids used by African Americans and gives suggestions for classroom activities.
Multicultural Lesson Plans and Resources Everything is covered here, not just math.
The Quipu, an Incan Data Structure Marcia Ascher gives a brief description and history of the quipu.
Suzanne's
Mathematics Lessons; Web Units available for: circle Design,
Tantalizing
Tessellation 10 lesson plans for a grade 5 class culminating in the
making of a quilt.
What In the World Would You Have? A lesson involving money exchange rates for grades 4-7. Includes links to the Pacific Exchange Rate Service or Yahoo Exchange.
Architecture
Euclid's Elements discussion of deductive logic as used in geometry and the classroom.
Geometry
in Art & Architecture Syllabus
Excellent site with examples liberally given. Check this one out. Suggested activities also provided.
This is part of Architecture Design Images, History, 3D Models and more-Artifice Great Buildings Online which documents a thousand buildings and hundred of architects with photographs, bibliographies, web links, 3-D models and architectural drawings.
Sacred Geometry in Building Harmony in Architecture and its influence
Sacred Geometry and Armenian Architecture The essentials- a circle, a square, a rectangle and the myriad permutations remain the same. Sacred geometry is explored and examples are shown in Armenian architecture.
The Washington National Monument In Perspective: Learn the "Math-magic" of this monument. Take this opportunity to view some of the authors other articles at the home site of the Philosopher's Stone.
Basketry
American Indian Baskets American Indian baskets are some of the most expensive and finest . Each tribe has its own designs and styles. Explore many of them here.
A History of Basket
Making in Somerset Basket making in
Hopi Basketry History, techniques and uses of the basket.
Native Tech: Weaving & Cordage Nipmuc Split Basketry, coil Basketry, Pine Needle Basketry, and finger Weaving are covered in this site.
Splint
basket splint baskets in
The Amazing Story of Kudzu This is just a fun spot, discussing the plant Kudzu that man introduced into the south. It has taken over like a weed, but some people are finding interesting uses of it-including basketry.
Calligraphy
The Art of Arabic Calligraphy:
Islamic Calligraphy
Explore many Islamic scripts.
Games
African Games information/links Numerous descriptions of games; tournaments; sites for on line playing; as well as information on purchasing games.
Chinese and Korean Chess Information on Two Player Chinese and Korean Chess
The Chess Variant Pages This site offers Oriental, historic, multiplayer, small and large chess variations.
Dedicated to Shax- The preferred game of Somali nomads
International Omweso Society Omweso
is the national game of
Introduction
to Bao A game of
International Draughts Site Introduction to the game and its many versions, links to on-line games.
Mancala On-line game is offered as well as descriptions of a variety of ways to play. Mancala Web v2.0 How to play Mancala and playing on line are the advantages of this site
Mathematics and Chess Page The connection between math and chess are pointed out here including strategic thinking and calculation.
Mathematically Interesting Games Interactive games against the computer include Nim, The Tower of Hanoi, and the Monty Hall problem.
Native American Games & Toys A brief history, description and explanation of how to play the games are available.
Parcheesi
National game of
Traditional Games Extensive site that covers the history of games; agility games, ancient games, Board and table games, card games and dice games.
The history, rules of play and variations are given here.
The variation known as Hnefatafl-the strategic board game of the Vikings can also be played.
String Figures
International String Figure Association A wonderful site with string figures from many cultures with brief histories given.
Rain Forest String Figures From Guyana WaiWai and Wapishana tribes people demonstrate their string figures.
Jewelry
Celtic Jewelry, Ancient Symbols by Ancient Circles Jewelry designed using the Celtic knot.
Refractal Designs Although a commercial site, fractals in the world of jewelry are explored at this site.
Kinship
Kinship Glossary
From the Dept. of Anthropology at the
Kinship Logic Problems A few problems from the ethnomathematicians Marcia Ascher.
Kinship and Social Organization A tutorial on social organization going into some ethnographic examples.
Decoration
Eloquent Elegance Beadwork in the Zulu cultural tradition-very informative linking bead work designs with communication. Make sure you look at "Brief History of Traditional African BeadCraft".
Fringed Loomwork: The Mathematical Approach
Native American Beadwork Meaning in Native American Life. The Techniques and Analysis are given at Native Tech
Northern Plains Beadwork No synthetic materials are used.
Geometry of Carpets
Silk
and Wool:Ottoman Textile
Designs in Turkish Rugs An article that examines the use of
Ottoman textile designs in Turkish rugs.
Symmetry and Pattern: The Art of Oriental Carpets - Patterns in Islamic Art, Making Pile Carpets, Rug Knots and Major Rug Producing Regions of the World are discussed at this site from Swarthmore.
Ironwork
New Orleans Ironwork
Explore both wrought iron and cast iron, an art form itself, as used in
The Village Smith-History A brief history of blacksmithing is given and its tie in to decorative ironwork.
Knots
The
Knot Plot Site If you are interested in knots then this is the place
to be with: fancy knots, nifty knots, torus knots,
fancy knots, Brunnian knots, carpet knots, Celtic
knots, and many others.
Masks
African Art: Masking Not only are masks shown here, but the reasons for their use are discussed.
The Art of the African Mask Another wonderful exhibit of masks including faces of spirits, images of ancestors, icons of power and portraits of rulers.
Novica Although a commercial site, this site offers a
wealth of masks as well as other handcraft items from South and
Music
Pythagoras:Music and Space A brief introduction to the relationship Pythogoras saw between number and music
Origami, Paper Folding and Cutting
Hexaflexagons Description on what they are and directions on how to make them
Joseph Wu's Origami Page commissioned to do the official origami mascots for the Nagano Olympics, Joseph Wu has a wealth of information and directions at this site.
Kirigami Explore Kirigami, the Japanese art of paper cutting,on line, allowing one to try different symmetries.
The Geometry Junkyard-Origami Links to many articles and projects are available here.
Paper Folding Visual method to teach math including geometry, fractions, conic sections, tessellation, and tangrams.
Paperfolding.com Not only will you find history here, but directions on how to fold, origami and math, and directions for making insects and dinosaurs.
Papel Picado: The Art of Mexican Cut Paper Investigate the traditional art of decorative cut paper banners.
Symmetric
Patterns at the Alhambra: With Math Problems A
look at a walled city and fortress in
The Topaki scroll: Geometry and Ornament in Islamic
Architecture The theory and practice of geometry in Islamic art is
explained in one of the oldest scrolls still in existence.
Why is Origami so Good for You? Excellent reasons are given to include origami in your curriculum.
What is Pergamano- Although a relatively new folk art,
parchment craft was done as early as the 15th century in
Wycinanki Paper cutting from
Textiles
African Kuba Cloth 12 woven designs are shown
Chronology of Textiles and Fiber Art in New Mexico A thumbnail sketch of history with many valuable links to such things as textiles as art, indian trade blankets and navajo weaving can be found here. Also many beautiful links to Native American contemporary art. for the meaning of Native American symbols go to Indian Symbols
House of Tartan A database of world tartans as well as a link of Scottish surnames to clans may be found here.
Kuba
raffia Cloth
The embroidered and appliqué cloth traditions of the
Kuba people of the
Social Fabric An exhibit of West African textile at the University of Denver Museum.
Tartans of
Scotland-Scottish Tartan...the Register of All Publicly Known Tartans.Very complete
site going into many details of Scottish Tartans
Sewing
Egyptian Fork Art Tapestries The Wissa Wassef Experiment is one of creativity originally using children, who once taught the techniques of weaving, and now creating beautiful pieces. Further explained in The Egyptian Tapestry Weaves: A Few Details
Geometry in Hawaiian History and Culture The areas of lines, angles and planes; polygons, circles; conic sections; cylinders and cones; symmetry and translation are shown.
Hawaiian Quilting with Poakalani History, designs, traditions and superstitions discussed.
Indonesian Ikats and Batiks View many lovely textiles here, as well as an explanation as to how they are made.
International Quilt Study
Center The
Ivars Peterson's Math Trek-Geometry Out of Africa Interesting information on geometry quoting books by two well known ethnomathematicians.
Lefkara Lace embroidery and silver handicrafts from the Island of Cyprus Lefkara Lace making and embroidery crafting is an ancient craft that has been passed down for centuries. Explore the designs at this site.
Math Quilts Explore geometry, perspective, irrational numbers, fractals, tessellations and tiling as well as the "feathered Star" all on quilts.
Passementeries D'Egypte This site was chosen because is shows an excellent example of passementery (hand-made tassel and tie back). There are many available sites, but most are in foreign languages.
Porcupine Quill Embroidery the oldest form of Native American embroidery, not yet a lost art because it is still practiced by some nations. Techniques are explained at this site.
Quilt Ethnic fiber related arts and textile traditions of ethnic groups is portrayed and discussed.
Quilt Blocks: Geometry with a Cultural Warmth: A lesson that can be taught at any grade level, is better done in middle or high school. A brief history of quilt history is given also.
Raksti Latvian Cross-Stitch Designs
Rug Maker's Homestead Rug making from many cultures, although mainly followed in US history, 16 types of rag rugs are explained.
Susanis:Central Asian Dowry
Embroideries A site defining susanis and
how it was made in
A Timeless History of Tapestry and Wall Hangings: an illustrated history of the art of tapestry from Ancient Gree to Modern Day- links given.
Tatting History Doing a search for tatting history here will provide you with numerous links, some are by the century
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Islamic Art Introduction Good description of Islamic art.
Wallpaper Groups: Plane Symmetry Groups Site discusses transformations of the plane, lattices, symmetry groups, plane symmetry groups and the History of wallpaper
Sacred Geometry
The Classical Labyrinth found in many churches in Europe
The Code of Carl Munck, and ancient Gemeatrian Numbers-Part one Facts are given concerning some of the major mysteries of the world using an ancient system of numbers called "Gematria"
Labyrinth of Knossos An introduction Sacred Geometry "Everything in the universe follows the same fundamental geometric pattern." Follow the links to the Flower of Life.
Sacred Geometry Home Page Follow geometry in nature at this site with a number of available links.
Sacred Landscape Geometry An
exploration of sacred landscaping in ancient
Stonework
Stoneworks of Italy.
View beautiful stonework and tiles from Italy
Tattoo
They were their Tattoos : Body Marking Lore of Tribal New Zealand for the Maoris their tattoo was their name. Link also provided for the article"The Changing Cultural Status of Tattoo Art in American
Tessellations
Inversions Teacher Resources for Inversions Classroom activities based on Inversion to use in grades 3-12 for teaching geometry, symmetry, art and creative thinking.
Islamic Art: An introduction to the world of Islamic art , making a connection to tessellations
M.C. Escher-Interlocking Shapes and Tessellations From Ciao website, and extensive list of links on tessellations used in different cultures and crafts.
Symmetry in
Tessellations Discussion of translational symmetry, rotational
symmetry and
glide reflection is given with examples.
Tilings from Historical Sources View tiles from
Persian,
Totally Tessellated Wonderful
site. In the history section you will learn the role that
tessellations have had in the cultures and history around the world, not only
in art but mathematics and science. View modern and
ancient tessellations and to to a gallery.
Bibliographies (other than those given at the
sites listed here)
BiFoEtMa
(Bibliography finder for EnthnoMathematics)
Misc.
(agriculture)
The
Geometry of Rice Profile of rice fields in harmony with nature.
The Geometry of
War A fascinating museum
site dedicated to geometry of warfare during the period from 1500 to
1750. three areas are covered: 1) Gunnery, Range
finding and surveying, 2) fortification and 3) troop formations and the telescope.
SANGAKU Sangaku means a mathematics table in Japanese. These were often made to thank the gods the the discovery of a geometric theorem. Japan has the only ones left in the world and this site provides pictures of many of them originally published in Scientific American (May 1998).
How to Make Ukrainian Easter Eggs Explore the many designs used on eggs. For symbols used go to Symbols and Colors
Symmetry in Nature at the Butterfly website. View butterflies around the world and enjoy their symmetry. Links to other insects at the end.
Basic Numeracy Learning In and Out of School: Maths
on the Streets-Brazil Street math gets them through daily living by coming
up with their own strategies.
The
Mathematics of Cartography The use of scale, coordinates and projection are
explored at this site as well as map history.
Critics
Mathematically Correct
An organization consisting of parents, educators and scientist concerned about
the New New Math and the need to restore basic skills
to the classroom. Read what they have to say, and be aware of their
concerns. How can you teach basic skills using ethnomathematics?