USING
ETHNOMATHEMATICS
IN YOUR CLASSROOM:
PRACTICAL SUGGESTIONS

This webpage supports the presentation at:

Maryland Council of Teachers of Mathematics
Annual ConferenceEastern Technical High School
October 17, 2008—11:30am – 12:30pm, Room 215, Session 37

Lawrence Shirley, Professor of Mathematics and Associate Graduate Dean
College of Graduate Studies and Research

Towson University, Towson, Maryland 21252
e-mail: LShirley@towson.edu ; phone 410-704-3500
personal webpage: http://pages.towson.edu/shirley

Handout (click here)

Abstract

Ethnomathematics is the mathematics of cultural groups-all cultural groups.
We will see examples of what this means and how you can use ethnomathematics to enrich your mathematics classes at any grade level.
Useful resources will be included.

Outline

1. Introduction: the meaning of ethnomathematics   Isn't mathematics culture-free?

2. Two models to help find ethnomathematics examples

A broader meaning of mathematics:
  pure applied
formal ACADEMIC TECHNICAL
informal RECREATIONAL EVERYDAY
                                                                        (Shirley, 1995)

Bishop's list of the activities of societies:
counting explaining
measuring designing
locating playing
                                                                        (Bishop, 1988)

3. Historical development of ethnomathematics
(see "Ethnomathematics Looks Backward and Looks Forward" (a paper from ICME-11)

--early 20th Century (anthropologists)
--the era of civil rights (especially in US) and decolonization
--Zaslavsky, D'Ambrosio
--International Study Group on Ethnomathematics (North American Study Group on Ethnomathematics)
--International Conferences
--Successes in multiculturalism, curriculum materials, instruction, and continued study

4. Ethnomathematics for social justice, global understanding

5. General activities for the classroom

--counting--other languages, numeration
--measuring--units, techniques
--locating--finding your way? in the South Pacific, in video games
--explaining--algorithms, stories, kinship (see Ascher, 1991)
--designing--freizes, textiles (e.g.kente), fractals
--playing--magic squares, Mu Torere, Oware—Mancala

6. Who are you? What is your own ethnomathematics? How does your culture influence your teaching?

Links

From the pages of the International Study Group on Ethnomathematics (North American Study Group on Ethnomathematics), you can jump to several ethnomathematical links.  Here is a collection of ethnomathematics links from ISGEm and more references and links for ethnomathematics and even more ethnomathematics links.  Also see the Ethnomathematics Digital Libary

You can find counting words for one to ten in over 5000 languages(!) here.

Eulerian path sand drawings from Slavik Jablan & Paulus Gerdes (see Gerdes' books below)

Akan cultural symbols project, organized by George F. Kojo Arthur and Robert Rowe

Ron Eglash's African Fractals including activities for classrooms (see the Eglash book reference below)

You can play Mancala against the computer on the web! The rules are slightly different from ours, but are well explained.  Another mankala page has more variations.

RadicalMath looks at blending mathematics content and issues of social justice. Similarly, the Algebra Project considers algebra and the opportunity to learn mathematics as civil rights.  Rethinking Schools--a nonprofit educational publisher on school reform (including mathematics)with a focus on issues of equity and social justice (See Gutstein below)

The Fourth International Conference on Ethnomathematics (ICEM-4), Towson, Maryland, July 2010

Bibliography   (most with on-line ordering links)

Ascher, Marcia (1991) Ethnomathematics: a multicultural view of mathematical ideas, Wadsworth.

Ascher, Marcia (2002) Mathematics Elsewhere: an exploration of ideas across cultures, Princeton University Press.

Bishop, Alan (1988) Mathematical Enculturation: A Cultural Perspective on Mathematics Education, Kluwer.

Bazin, Maurice, Tamez, Modesto, and the Exploratorium Teacher Institute (2002) Math and Science Across Cultures: Activities and Investigations from the Exploratorium, The New Press (Norton).

D'Ambrosio, Ubiratan (1985) Socio-cultural Bases for Mathematics Education, University of Campinas (Brazil).

Eglash, Ron (1999) African Fractals: modern computing and indigenous design, Rutgers University Press.

Gay, John, and Michael Cole (1967) The New Mathematics and an Old Culture: A study of learning among the Kpelle of Liberia, Holt, Rinehart, and Winston.

Gerdes, Paulus (1997) Lusona: Geometrical Recreations of Africa, Editions L'Harmattan. 

Gerdes, Paulus (1998) Women, Art, and Geometry in Southern Africa, Africa World Press.

Gerdes, Paulus (1999) Geometry in Africa, Mathematical Association of America.

Gutstein, Eric and Peterson, Bob (editors) (2005) Rethinking Mathematics: Teaching Social Justice by the Numbers, Rethinking Schools, Ltd.

Ifrah, Georges (1994) The Universal History of Numbers, Wiley

National Council of Teachers of Mathematics (1995) Connecting Mathematics Throughout the Curriculum (1995 Yearbook), NCTM.

National Council of Teachers of Mathematics (1997) Multicultural and Gender Equity in the Mathematics Classroom: The Gift of Diversity (1997 Yearbook), NCTM.

Nelson, D., Joseph, G.G., and Williams, J. (1993) Multicultural Mathematics, Oxford University Press.

Powell, Arthur and Frankenstein, Marilyn (editors) (1997) Ethnomathematics: Challenging Eurocentrism in Mathematics Education, State University of New York Press

Shirley, Lawrence (1995) "Using Ethnomathematics to Help Find Multicultural Mathematical Connections" in House, Peggy (editor) Connecting Mathematics across the Curriculum (1995 Yearbook), National Council of Teachers of Mathematics.

Shirley, Lawrence (2001)"Ethnomathematics as a Fundamental of Instructional Methodology" Zentralblatt fur Didaktik der Mathematik--International Reviews on Mathematical Education, issue 2001/3 (June 2001), [ZDM].

Shirley, Lawrence (2006) http://pages.towson.edu/shirley/global.htm presented at the Third International Conference on Ethnomathematics, Auckland, New Zealand.

Zaslavsky, Claudia (1973, 1995) Africa Counts: Number and Pattern in African Culture, Lawrence Hill Books.

Zaslavsky, Claudia (1996) The Multicultural Mathematics Classroom, Heinemann.

---(also see a full Zaslavsky bibliography)

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last updated 21 October 2008, links checked 13 October 2008 (please report any broken links to LShirley@towson.edu )

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Note: Some pages of the conference handout are not available in electronic form. Here are the pages that are available.
USING ETHNOMATHEMATICS
IN YOUR CLASSROOM:
PRACTICAL SUGGESTIONS

Maryland Council of Teachers of Mathematics
Annual Conference—Eastern Technical High School
October 17, 2008—11:30am – 12:30pm, Room 215 (Session 37)

http://pages.towson.edu/shirley/ethnomathematics.htm

Lawrence Shirley, Professor of Mathematics and Associate Graduate Dean
College of Graduate Studies and Research
Towson University, Towson, Maryland 21252
e-mail: LShirley@towson.edu ; phone 410-704-3500
personal webpage:
http://pages.towson.edu/shirley

OUTLINE

  1. Introduction: the meaning of ethnomathematics
  2. Two models to help find ethnomathematics examples (Shirley, Bishop)
  3. Historical development of ethnomathematics
    (see http://pages.towson.edu/shirley/ethnomath%20looks%20back,%20forward.htm )
  4. Socio-cultural-(even political) applications of ethnomathematics
  5. General activities for the classroom
    a. Counting—Yoruba and Mada; Spanish, Vietnamese,?,?
    b. Measuring—local units, estimation of size (Kpelle vs Yale)
    c. Locating—maps, here, in South Pacific, in video games?
    d. Explaining—kinship; how to…
    e. Designing—kente; textile patterns
    f. Playing—mu torero, mancala, even tic-tac-toe!
  6. Who are you? What is your own ethnomathematics?

Fourth International Conference on Ethnomathematics, July 25-30, 2010, at Towson University
http://pages.towson.edu/shirley/ICEM-4.htm
    (Participate?  Help?)

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ETHNOMATHEMATICS:

A BROADER MEANING OF MATHEMATICS

 

PURE

APPLIED

 

 

FORMAL

 

 

Academic

technical

 

 

INFORMAL

 

 

recreational

everyday

Shirley (1995)

 

 

Bishop’s (1988) list:

 

Counting            Measuring          Locating

 

Explaining          Designing           Playing


---------------------------------
Counting words in two Nigerian languages

YORUBA(southwest)

1 okon
2 eeji
3 eeta
4 eerin
5 aarun
6 eefa
7 eeja
8 eejo
9 eesan
10 eewa
11 okanla
12 eejila
13 eetala
14 eerinla
15 aarundinlogun
16 eerindinlogun
17 eetadinlogun
18 eejidinlogun
19 ookandinlogun
20 ogun
21 ookan le logun
22 eeji le logun
23 eeta le logun
24 eerin le logun
25 aarun din logbon
26 eerin din logbon
27 eeta din logbon
28 eeji din logbon
29 ookan din logbon
30 ogbon
31 ooka le logbon
35 aarun din logoji
39 ookan din logoji
40 ogoji

41 ookan le ogoji
45 aarun din aadota
47 eeta din aadota
50 aatota
60 ogota
70 aadorin
80 ogorin
90 aadorun
100 ogorun
110 aadofa
120 ogofa
130 aadoja
140 ogoja
150 aadojo
160 ogojo
170 aadosan
180 ogosan
190 aadowa
200 igba
300 oodunrun
400 irinwo
2000 egbewa









 

MADA/ NINZAM/NINDEM(north-central)

 1 gir
2 wwa
3 tar
4 nzhe
5 tunn
6 tanni
7 tamgba
8 tahnda
9 tir
10 gur
11 poh
12 tsoh
13 se gir b’gir
14 se gir was
15 se gir b’tar
20 se gir b’tahnda
23 se gir b’poh
24 se wa
25 se wa b’gir
30 se wa b’tanni
35 se wa b’poh
36 se tar
40 se tar b’nzhe
50 se nzhe was
60 se tunn
75 se tanni b’tar
80 se tanni b’tahnda
90 se tambga b’tanni
100 se tahnda b’nzhe
108 se tir
120 se gur
132 se poh
144 naa

HINDI BINARY COUNTING

BASE TEN      BASE TWO

NUMERAL       NUMERAL      COUNTING WORD

 1                      1                      EK

 2                     10                     DO

 3                     11                     DAK

 4                    100                    DAWWA

 5                    101                    DAWWEK

 6                    110                    DAWWADO

 7                    111                   DAWWADAK

 8                  1000                   DODAWWA

 9                  1001                  DODAWWEK

10                 1010                   DODAWWADO

11                 1011                  DODAWWADAK

12                 1100                   DODAWWADAWWA

13                 1101                    DODAWWADAWWEK

14                 1110                   DODAWWADAWWADO

15                 1111                   DODAWWADAWWADAK

16                 10000                         ? ? ?

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OWARE           

Oware is a counting and strategy game from West Africa.  Similar games, with the generic name of mancala, are played throughout Africa and other parts of the world, with variations in the rules and with many different names.  This version, oware, is from Ghana, and is similar to others played in West Africa.

Materials and set-up: The playing board is an arrangement of twelve small pits in two rows of six.  An egg carton is a good example and can be used for the board or use the board on the next page.  In West Africa, the game is played on boards ranging from twelve small holes dug in the dirt to elaborate wooden carved boards with storage bins, stands, and sometimes hinges so they can be folded closed.  One row of six pits belongs to each of the two players.  Counters, which may be pebbles, seeds, bottle caps, shells, coins, or even (for the affluent) jewels, are shared into the twelve pits.  In this version, four seeds are put into each of the twelve pits to start the game.

Rules of play: The players take turns playing. One turn consists of picking up all the seeds in one of the players's six pits.  The seeds are then distributed one into each pit, moving around the board counter-clockwise, including the use of the pits of the opponent if necessary, or even, if there are enough seeds, going all the way around the board (in this case, the original pit is skipped as a recipient of a seed).

 Collecting seeds: If the last seed lands in a pit on the opponent's side which had exactly one or two seeds already, thus making its new total two or three, all the seeds in that pit are collected by the player and stored out of play.  For a continuous chain of pits on the opponent's side, going back from the last, if the pit now has two or three seeds exactly, those sides can also be collected.

End of the game: If the opponent has no seeds left, the player must try to play so as to put at least one seed into a pit of the opponent.  Otherwise, if a player has no seeds, the game ends and the other player keeps any remaining seeds.

Winning: The winner is the player with the most seeds collected at the end of the game.

Etiquette: It is considered improper to pick up and count the seeds in any pit, most especially a pit of the opponent!

Strategy: Try to keep track (mentally!) of the number of seeds in each pit and hence where the last seed would land if the seeds in that pit were to be played, aiming at collecting seeds from a long string of pits back from the last.  Sometimes building up many seeds in one pit can be helpful.  The end-game can be very important.

Learning: counting, mental adding and subtracting, estimation, the geometry of the board, problem-solving, strategic thinking, etc.  Also, analyses can be made of possible plays, even to designing a computer program of the game.

Web-Mancala: Another version of mancala is on the Web.  It’s rules are slightly different but well-explained.  It allows you to play on-line against the computer!  Look at: http://imagiware.com/mancala/

Have fun!

Mancala (Oware) board (start with 4 “seeds” in each “pit”)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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WHO ARE YOU?

1.  The following is derived from the official US Census form for identifying ethnicity.  In 1990, the instructions were to check one category only, but in 2000, respondents could check all that apply (in fact, there were more categories than this; this will again be the case in 2010).   Please check the categories that describe you, checking as many as you consider accurate descriptions of yourself.

___  Black                    ___  American Indian                    ___  Asian or Pacific Islander

                          ___  Hispanic                          ___  White

2.  In the blank space below, describe your own cultural heritage, without being restricted to the items from the Census Bureau.  Use any terms that describe you--ethnic, religious, social class, geographic, or whatever.  Be creative!

 

3. How could you use your own cultural heritage in your teaching?

 

4. How does your own cultural heritage influence your teaching?   Should it?

 

5. Can you use your students' cultural heritages as resources for your teaching?  How?

 

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Bibliography

Ascher, Marcia (1991) Ethnomathematics: a multicultural view of mathematical ideas, Wadsworth.

Ascher, Marcia (2002) Mathematics Elsewhere: an exploration of ideas across cultures, Princeton University Press.

Bishop, Alan (1988) Mathematical Enculturation: A Cultural Perspective on Mathematics  Education, Kluwer.

D'Ambrosio, Ubiratan (1985) Socio-cultural Bases for Mathematics Education, University of Campinas (Brazil).

Eglash, Ron (1999) African Fractals: modern computing and indigenous design, Rutgers University Press.

Gerdes, Paulus (1999) Geometry in Africa, Mathematical Association of America.

National Council of Teachers of Mathematics (1997) Multicultural and Gender Equity in the Mathematics Classroom: The Gift of Diversity (1997 Yearbook), NCTM.

Powell, Arthur and Frankenstein, Marilyn (editors) (1997) Ethnomathematics: Challenging   Eurocentrism in Mathematics Education, State University of New York Press

Shirley, Lawrence (1995) "Using Ethnomathematics to Help Find Multicultural Mathematical Connections" in House, Peggy (editor) Connecting Mathematics across the Curriculum (1995 Yearbook), National Council of Teachers of Mathematics.

Zaslavsky, Claudia 1996) The Multicultural Mathematics Classroom, Heinemann. (also see other Zaslavsky books and articles)