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NASGEmn e w s l e t t e r

North American Study Group on Ethnomathemat icsV olume 1 Number 1 February 2003

IIIII NNNNN T T T T T H I SH I SH I SH I SH I S I I I I I S S U ES S U ES S U ES S U ES S U E

Articles2 Study of Solstice Marker Pictograph9 The Algorithm Collection Project

(ACP)1: An Exploration of theEthnomathematics of Basic NumberSense Acquisition Across Cultures

15 Dancing Numbers!: An AlternativeMathematics Instruction

16 Ethnomathematics Place in TeacherPreparation Programs

18 Survey on : Prevailing ClassroomCulture for School Mathematics

Have You Seen?17 Creeping Up in the Oddest Placeses18 Dream Catching 2003

From the Editors19 Evaluation of Culturally-Situated

Design ToolsHelp WantedSpecial Interest Groups

20 International Study Group onEthnomathematics

24 ISGEm Constitution26 ISGEm-NA Constitution32 “Become a Member”

WelcomeFrom Lawrence Shirley

Welcome to the new newsletter of theNorth American Study Group onEthnomathematics (NASGEm). Since thestart of the International Study Group onEthnomathematics (ISGEm) in 1985, theNorth Americans have been a big part ofthe membership and leadership ofISGEm. Part of this leadership has beenseen in the location of the ISGEm News-letter in North America. However, in aneffort both to strengthen the non-Americanaspect of ISGEm, the ISGEm Boardmoved the international newsletter to beproduced in Brazil. This left the NorthAmericans with the exciting opportunity tostart our own newsletter especially forNASGEm. We are also pleased that theinterim editor of the ISGEM Newsletter,Tod Shockey, has agreed to become thefirst editor of the new NASGEm Newslet-ter. We hope this newsletter can become aforum of news, research reports, articles,information on conferences, and a generalexpression of the ideas and activities ofNASGEm members. We would also liketo see this newsletter offer a livelyexchange of opinions in letters andcommentaries. One of the hardest tasks ofany newsletter editor is to obtain submis-sions for publication. I ask you to helpTod by sending him news of your researchand classroom activities and your thinkingon the directions of ethnomathematics inNorth America.

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The darkened sky begins an everincreasing lightening and the valley floorbegins to come alive in anticipation of thedawn. As the sharp rays of first light spillover the surrounding hills and mesas,pictographs tucked into an obscure cliff faceare now illuminated with the sunlight.Darkened lines of shadow move swiftly overthe ancient drawings to once again signal thechanging of seasons. The sun markerscontinue their long vigil over the revolvingseasons as they have done for the pastthousand years. Their sun watchers and thepeople to whom the canyon was once home,have been gone for hundreds of years, leavingtheir designs behind. In the river drainagevalley now known as Canyon Pintado, thepassage of the seasons is marked in relativeobscurity and solitude since the ancientpeople of the valley are gone.

The emerging fields ofethnomathematics, the study of mathematicsand its relation to cultural influences, andarchaeoastronomy, the study of ancient skywatchers and their astronomical practices,come together in the study of rock art sitesthat mark the passage of the seasons.

Evidence of substantial astronomicalknowledge by ancient peoples abounds inthe southwestern region of the United States.Rock art sites and ancient building remains

that exhibit astronomical activity arecontinually added to a database that nownumbers into the hundreds. The interactionof the light marks the equinox days, solsticedays, or, in some cases, the cross-quarterdays, in many different ways: sun daggers,or beams of light intersecting the drawing ina particular spot; beams of light displayedthrough the window of building to mark acertain spot on an opposite wall; a tangentline to a display of circles; a direct observa-tion with a horizon line marker and a sunmarker. All of these solar markers weremade by using specific geometry principlescoupled with observations of the heavenlybodies and related light interactions.

Since the “discovery” of the now-famous sun dagger site at Fajada Butte in1977, other sites have been studied anddocumented as solar observatory sites. Thesun dagger site in the Chaco Canyon, NewMexico complex shows the sun interactionduring both equinox and solstices(Williamson, 1984). Once thought to be aunique example of sunlight and rocksymbols, it became the first of manydocumented sites. Many of these sites havecommon elements in their designs, but eachone is unique in its placement relative to thegeography of its specific location. Equi-noxes and solstices are moments in time andthe interaction occurs at a particular time ofday; many of the rock art, or glyph markers,operate at midday. A comparison betweenthe time of interaction and the moment of theseasonal event can help in assessment of theprecision of the glyph as a solar marker.

To view glyphs or designs as possiblesolar markers requires persistence andpatience since there are only eight times eachthat possible interaction might occur: twoequinox days, summer and winter solstice,and the corresponding cross-quarter days,the days halfway between an equinox andsolstice. Cross-quarter days are often morein tune with changes in seasonal weatherpatterns than the actual seasonally desig-nated days of equinox and solstice. Whilethe solar interactions are much morecommon on the summer solstice and

Photo by: Cathy Barkley, Ph.D., Mesa State College

Study of Solstice MarkerPictographCanyon PintadoEast Fourmile Draw Site

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equinox days, interaction has also beenreported in a number of the summer cross-quarter days also. In a database of 219observations reported at 45 different sites, by29 different observers, Fountain reports thefollowing frequency of interaction: (1)summer solstice, 34%; (2) equinox, 32%; (3)winter solstice, 14%; (4) summer cross-quarter day; (5) winter cross-quarter day(Fountain, 1998).

Two categories of solar markers havebeen used to denote the changing seasons:direct, and indirect. A direct marker is onethat is observed by standing in a particularspot and viewing the sun rise or set over acertain landmark such as a notch in themountain (Malville and Putnam, 1989). Anindirect marker is one that is man made bypecking or painting a glyph onto a rocksurface. Precise observations would have tobe made to accurately draw the indirectmarker at the exact spot to mark the sun’spattern of travel. Gnomon markers can beused to establish a seasonal calendar but it iseasier to establish the rising azimuth byrecording the position of the rising or settingsun as it appears against a particular geo-graphic feature. This practice forms the basisof the horizon calendars used by the Puebloanpeoples of today (Charbonneau, 1999).

There is reliable evidence that certaintypes of circular glyphs were symbolicreferences to the sun. A series of concentriccircles, either pecked or painted, has longbeen regarded by the Puebolan peoples torepresent the sun (Charbonneau, 1999). Adot encircled by two rings is the mostcommon sun symbol of the modern Pueblopeople. The spiral form, such as the onefound by Anna Sofaer at Fajada Butte, isanother common symbol for the sun and itspassage. The number of spirals may alsohave special meaning for the either the sunpassages or the lunar cycles. The mostcommonly reported solstice interactionmarkers are either circular or spiral, but otherinteractions have been observed andrecorded that make use of geometric, animalshapes, and human-like forms. In thedatabase of 219 observations documented by

J. W. Fountain, Tucson, Arizona, thefollowing distribution of glyph types wasreported: (1) circular and spiral, 37%; (2)anthropomorphic, 21%; (3) zoomorphic,15%; (4) other, 27%.

Solar markers have been reported atsites all throughout the southwestern UnitedStates. The database of dramatic lightinteractions continues to grow as amateurarchaeoastronomers observe and documentthese sites. Looking for solar markersrequires full familiarity with the site underconsideration, a sense of the sun’s motionacross the sky, and the corresponding waysin which shadows fall across rock faces.Interactions are sometimes much morecomplex than originally expected.

When looking for a solar rock site, it isessential to note a distant landmark so thattrue north is located. Interaction possibilitiesdepend on the precise angle of the sun at aparticular time of the year. In the southwest-ern region of the United States, the sun risesnorth of east in the summer and south of eastin the winter; in summer, the sun is higherthan in winter. At equinoxes, the sun movesrapidly with regard to the celestial equator ata rate of approximately 0.4 degrees per day.The earth’s rotation leads to an apparentdaily motion of the sun at a constant angularvelocity of fifteen degrees per hour. Thesun’s equinox altitude at solar noon is equalto 90 - Æ where Æ is the observer’s altitude.The equinox to solstice altitude differencesat solar noon is approximately 23.5 degrees(Allen, 1998). Interactions change markedlyfrom day to day so observations for any solarinteraction must be made on that precise day.At the solstices, the sun seems to stop in itsmotion, as it changes directions of motionrelative to the celestial equator. Solarinteractions change little during the weeksurrounding the solstice. On the cross-quarter day, the sun’s motion is approxi-mately two-thirds of that at the equinox.

The solar interaction is not always at thecenter of a glyph; quite often the light passesthrough the edge of an object to form atangent line. The indirect solar markers donot always occur at times of the day special

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to us, such sunrise, or noon. Most of thedocumented interactions actually occurbetween 10 a.m. and 3 p.m.

This study examined a rock art siteattributed to the Fremont people, a culturethat existed in western Colorado and easternUtah. Their “cultural capitol” with extensiverock art sites seems to have been in thenorthwestern corner of Colorado andnortheastern corner of Utah centering aroundthe Dinosaur National Monument andUintah Basin areas (Castleton, 1984). Themajor portion of Fremont culture develop-ment seems to have occurred simultaneouslywith the Anasazi development. Fremontculture in this area is generally dated as A.D.650 – 1200. Sometime after A.D. 1300, itwas replaced by the Shoshonis who camefrom the west.

This study examined a Fremont rock artsite for possible solar interactions. Onedocument was found that labeled the site as a“sun dagger site.” The study was begun insummer, 2001. The site was located and ageneral description of the area was recorded.The study continued during the followingyear and will conclude in summer, 2002.Several similar circle/spiral sites are locatedin the northwestern corner of Colorado/northeastern corner of Utah. Few of thesehave been studied or documented as solsticemarkers but they may also exhibit sunlightinteraction similar to the one in this study.

The site in question is located inCanyon Pintado. The Canyon PintadoHistoric District is located in westernColorado in the Douglas Creek drainagebasin. More than fifty known rock art sitesare located in this area along the creek. Thecanyon was named by Spanish explorersFathers Dominguez and Escalante in 1776when they traveled through the region toCalifornia (Rangely Chamber of Commerce,1999). Because of the unusually largenumber of pictographs (painted panels),rather than the more common peckeddesigns, they noted the area in their diaries asthe “painted canyon.” Pictographs in thecanyon are done in two primary colors, redand white. The red tints usually come from

an iron oxide base and the white paint comesfrom gypsum, calcium carbonate, or lime(Mallery, 1886).

One of the most interesting sites in theCanyon Pintado Historic District is locatedin East Fourmile Draw. This site is approxi-mately .6 mile from the main road. It is anindirect solar observatory site with picto-graphs on two southeastern facing cliff faces.There is a noticeable notch in the cliff facethat allows shadows to fall across themarkings on the southernmost cliff duringsolstice. Markings on the left cliff faceinclude two concentric circles, a spiral, andat least six other geometric or anthro-pomorhic figures. The center of the spiral isapproximately 139 inches from the base ofthe cliff.

Some of the figures are petroglyphs andhave been pecked into the cliff face. Theconcentric circles are painted in red andwhite. The top circle has a “bull’s eye” of redwith a circle of white, then circle of red, thencircle of white around it, for a total of threerings of alternating colors around the center.Colors are still quite vivid in this pictograph.We used a stick to measure the approximatesizes of the paintings and compared our non-standard “stick measures” to a flexibleyardstick. A second set of measurements wastaken using a metal tape with an eight footlength. The top circle was approximately sixinches in diameter and the bands of colorsgrew smaller in width as the circle was drawnaround the bull’s eye center.

Directly below this set of concentriccircles was the spiral painted in a whitecolor. The white has faded and can be

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difficult to see if the light is too bright. Thespiral is a counter clockwise, or counter suntravel, rather oblong flattened spiral. Thereare seven turns in the spiral and a white“bull’s eye” beginning. It appears to betangent to the circle above it at a midpointfor both the concentric circles and the spiral.The spiral measures approximately 7 inchesacross and 11 inches high. In comparing themeasurements for the length and width ofthe spiral, the ratio equals approximately1.57. This number is surprisingly close tothat of the golden ratio, Æ, phi, that is usedextensively in the ancient Greek empire.Exact measurements are difficult as the faceof the cliff has a slight curve or bulge to itssurface and thus tends to “warp” the straightline geometry of the figures. Use of specificgeologic features is common among thedocumented solar sites; a curve on thesurface of the rock, a fissure in the cliff face,lichens or natural markings, are all used tohelp illustrate the movement of the sun atvarious solar sites.

The second concentric circle is locatedto the right of the spiral at a midpoint of thespiral and the circle. The two do not quitetouch. It appears that the set of concentriccircles were painted like the ones above thespiral but the paint seems to have faded overthe years. This set of circles is approxi-mately eight inches in diameter.

In addition to the circles and spiral, atleast six other figures are scattered about thecliff face. Some have paint on them, and oneof the figures is done in the reverse paint, or“negative photograph image” style. Thefigures are quite faded but seem to fit theclassic Fremont style of boxy, elongatedtorsos with missing arms or legs. A smallwhite figure appears at the top of cliff and isonly visible in deep shadows.

On the right side of the notch in the cliffface, there are three sets of geometric figuresvisible. A rectangle, an incomplete circle,and another incomplete rectangle holding arectangle is opposite the set of circles. Asmall pecked dot lies within the incompletecircle. This symbol of a dot within a circlehas been interpreted as “to hold here” or

stand still.” The rectangular symbolsindicate a field or place of a particular groupof people (Mallery, 1886). Taken as onereading, this could be interpreted as “the sunholding place.” Since the sun appears to stopat the summer solstice, this would beinterpreted as a site where this phenomenoncould be seen.

Beneath the cliff face, there lies anunusual boulder that tapers from its base onthe ground to a larger, flattened area at thetop. It is approximately four feet high.Several rows of peckings are visible on thefront side away from the cliff. On the leftside is an irregular pattern on dots. On theright side, the dots appear to be pecked intofive rows with a large space between rowstwo and three. The first four rows have sixdots each and the last row has four dots.This rock could have been used as a solarcount or solar observatory. The number ofdays in a month would vary since they wereobserving the changing moon in the skyrather than looking at the abstraction of thecalendar that we use. Sometimes a monthwould seem to be twenty-eight days longand at a different time, it might appear to bethirty-one days in length (Hudson, 1984).

A group of mathematics students fromMesa State College and I have visited thepurported solstice at four different times:Fall Equinox, September 21, 2001; WinterSolstice, December 21, 2001; January 15,2002 (a non-significant day in the suncalendar for comparison); Vernal Equinox,March 20, 2002. As predicted by the Solmardatabase, solstice interaction was evident atthe equinox times but not during the wintersolstice.

The first observation during the FallEquinox did show a spectacular use of theexisting landscape and the man-madedesigns. The interaction of the shadows withthe pictographs occurred at 9:55 MountainDaylight Time. The sunrise time from astandard chart does not correspond withthe actual sunrise time at the site due to theposition of the mountain to the east. Sunrisein Grand Junction, Colorado, September 22,2001 was 6:02 a.m Mountain Standard

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Time. The shadow interaction begins at theupper left of the first cliff and steadily movesto cover the entire face of the cliff. At about9:50 a.m. the shadow was tangent to the topconcentric circles. The shadow line appearstangent to both circles, one above and onebelow, and to the spiral by the end of themorning sunrise (9:55 a.m.). The line oftangency does not appear any other times;the shadows appear on the cliffs at the upperleft hand corner and travel downward untilthe lower edge of the shadow forms thetangent line. This interaction is differentthan the “sun dagger” bead of light thathighlights a particular spot on a wall orprojects the beam onto a petroglyph/pictograph figure. However, it does appearto be an interaction of significance since thisspecial tangent line does not appear on otherviewing days. The shadow line falls rightalong the crack in the cliff that splits thesymbols on the cliff face.

The viewing of the site at Winter

Solstice revealed no shadow interaction withthe figures on the cliffs. We viewed the sitefrom 8:00 a.m. until 10:30 a.m. and saw nointeraction during this time. The shadowswere not aligned with any of the figures onthe cliffs.

We again viewed the cliffs and shadowson Spring Equinox, March 20, 2002, to see ifthe shadow interaction would again bevisible. At approximately 8:40 a.m.Mountain Standard Time, the shadow lineappeared tangent to the top set of concentriccircles. This time was approximately anhour and ten minutes earlier than Fall

Equinox. At 9:10, the shadow was tangentto both circles and the spiral. The point ofthe shadow again followed the center crackin the cliff as it did during the Fall Equinox.Since the position of the sun was in themiddle of its celestial journey between thefarthest winter point to summer point, theangle of the shadows should have made thesame patterns on the cliffs as those made forthe Fall Equinox.

The site was again observed duringSummer Solstice on June 21, 2002. Sunriseaccording to the Grand Junction sunrisechart was 5:48 a.m. Mountain DaylightTime. At 8:01 a.m. the shadow fell acrossthe top bull’s eye. By 8:08, the shadow wastangent to the top bull’s eye and the spiral.By 8:17, the shadow had advanced tobecome a tangent line the second bull’s eyeand dropped below the second ring on thespiral. At 8:30, the shadow bisected thecenter of the spiral and the lower bull’s eye.There seemed to be significant interactionregarding the positioning of the shadow lineas a bisector but it was clearly not the sametype of interaction evidenced by the equinoxshadow play. From the farthest point atwinter solstice to the farthest point atsummer solstice, an angle of 60 degrees isformed; the equinox lies directly between thetwo, so it seems reasonable to have observedthe same type of interaction on both equinoxviewing days. Early records indicate thatsun shamans used an outstretched hand toapproximate the location of the sun relativeto its celestial year since the hand width isapproximately equal to 60 degrees also.

This site and its solar interaction hasbeen recorded in the Solmar database sincethe study has been completed following thesummer solstice, June 21, 2002. The site hasnow been viewed through the cycle of acomplete solar year.

A review of other Fremont sites in thenorthwestern Colorado/northeastern Utahregion reveals several sites with sun symbolsand spirals similar to those in the EastFourmile Draw site (Castelton, 1984). Thisstudy could be extended to include them inthe Solmar database (Fountain, 1998).

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Solstice interactions are cleverly done withthe designs placed in isolated spots, hiddenfrom the casual observer of today. Study ofthese sites is often difficult because of theirgeographic isolation and the weatherpatterns of the region (Wheelwolf, 1999).The opportunities for viewing solsticeinteractions occur, at most, eight times ayear, and the interactions may not occur oneach of the equinox, solstice, or cross-quarterdays.

By studying these ancient astronomysites and observing the solstice interactionon significant seasonal days, our picture ofthe ancient builders of the sites changes. Thepetroglyphs and pictographs used as markersof special times of the year were not placedon the cliff faces in a random manner.Observations were made of the sun and itstravel; then, careful attention was paid to theprecise angles needed for alignment onequinox and solstice days. Through the lensof ethnomathematics, we begin to see a morecomplete picture of these ancient peoples.

Bibliography

Allen, Hubert A., Jr. (1998)ThePetroglyph Calendar: An Archaeoas-tronomy Adventure. Albuquerque, NM.:Quality Books.

Ascher, Marcia. (1991).Ethnomathematics: A multicultural viewof mathematical ideas. Belmont, CA:Brooks/Cole.

Ascher, Martcia. (2002). Mathemat-ics Elsewhere: An exploration of ideasacross cultures. Princeton, NJ: PrincetonUniversity Press.

Aveni, Anthony F. (1980).Skywatchers of Ancient Mexico. Austin,Texas: University of Texas Press.

Barta, James. (1995, March).Ethnomathematics. Mathematics in School, 12-13.

Brecher, Kenneth and Michael Feirtag.(1980). Astronomy of the Ancients.Cambridge, Massachusetts: MIT Press.

Castleton, Kenneth B. (1984).Petroglyphs and Pictographs of Utah. Volume

One: The East and Northeast. Salt Lake City,Utah: Utah Museum of Natural History.

Charbonneau, Paul. (1999).www.hao.ucar.edy/public/education/archeoslides/slide_11.html.

D’Ambrosio, Ubiratan. (2001,February). What is Ethnomathematics andHow Can it Help Children in Schools?Teaching Children Mathematics, 7 (6),308-310. Reston, VA: NCTM.

Eddy, John A. (1977). Archaeoas-tronomy of North America: Cliffs,Mounds and Medicine Wheels. In E. C.Krupp, (Ed.),. In Search of AncientAstronomers. Garden City, New York:Doubleday and Company, Inc.

Eells, W.C. (1913), Number Systemsof the North American Indians. TheAmerican Mathematical Monthly, 20: 263-299.

Fountain, John. (1998). Rock Art SolarMarkers. www.azstarnet.com/~solmar/.

Hadingham, Evan. (1984). Early Manand the Cosmos. NY, NY: Walker & Co.

Hudson, Travis. (1984). California’sFirst Astronomers in Archaeoastronomyand the Roots of Science, (E)d. E. C.Krupp. Boulder, Colorado. Westview Press,Inc.

Joseph G. G. (1993). A Rationale for aMulticultural Approach to Mathematics. InD. Nelson, G. G. Joseph & J. Williams(Eds.), Multicultural mathematics: Teachingmathematics from a global perspective.New York: Oxford University Press.

Krahn, Gary. (2002). Interdiscipli-nary Culture – a Result not a Goal. In C.Arney and D. Small (Eds.), Changing CoreMathematics (pp. 49 – 53). MathematicalAssociation of America. Washington, D.C.

Mallery, Garrick. (1886). Pictographsof the North American Indians. Washing-ton, D.C.: Bureau of American Ethnology.

Martineau, LaVan. (1973). The RocksBegin to Speak. Las Vegas, Nevada: KCPublications.

Malville, J. McKim and ClaudiaPutnam (1989). Prehistoric Astronomy inthe Southwest. Boulder, Colorado:Johnson Printing Company.

Murray, William Breen (1986).

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THE ALGORITHM COLLECTIONPROJECT (ACP)1:AN EXPLORATION OF THEETHNOMATHEMATICS OF BASICNUMBER SENSE ACQUISITIONACROSS CULTURES

Daniel Clark Orey, Ph.D.California State University, Sacramento

AbstractThis discussion focuses on the interac-

tions between culture, the language(s) spo-ken, and the particular algorithms used byrecently arrived high school immigrant stu-dents attending an inner-city high school inNorthern California. Using a Brazilian re-

search paradigm employing strategies ofethnomathematics and mathematical mod-eling, students develop an understandingbetween the relationships of an individual’slanguage and the algorithms they use.

Theoretical FoundationsMany people experience mathematics

negatively. Many more students have difficultyin performing basic arithmetic operations thatmay ultimately exclude them from full partici-pation in society. Comparable populationsacross the world have fewer problems withmathematics than do American students(TIMSS, 1997). Facility with the algorithm oneuses, which includes its unique history andculture, most certainly contributes to one’ssuccess or failure in mathematics.

A fundamental aspect of this project re-spects the importance of this interaction, thatof the language(s) spoken and the algorithmused, that combine to form individual abilitiesand/or disabilities in mathematics. Success dur-ing early attainment of arithmetic operations,accomplished at the same time we learn lan-guage, forms the basis for how successfullywe can learn advanced mathematics. Work withmathematics learners in other countries (Orey,2000, 1999, 1998), combined with data gleanedfrom the Third International Math ScienceSurvey suggests that true reform, insuring suc-cessful mathematics attainment for all, is ex-tremely complex. An in-depth study of the typeof algorithms used has important internationalsignificance as well.

Project DesignThe design of the project encompassed

a three-step process:Collection: The ACP used a Brazilian

modeling protocol (Orey & Rosa, 2001)which conducts interviews of recently arrivedimmigrants in relation to their mathematics.Cohorts of graduate and student teachers wereasked to interview recently arrived immigrantstudents related to the attainment and use of

Numerical Repreentations in NorthAmerican Rock Art. Closs, Michael P.(Ed.) In Native American Mathematics.Austin, Texas: University of Texas Press.

Patterson, Alex. (1992). Rock ArtSymbols of the Greater Southwest.Boulder, CO: Johnson Books.

Rangely Chamber of Commerce (1999).Rangely Visitors Brochure. Rangely, Co:Rangely Chamber of Commerce.

Shaw, C.C. (1993). Takingmulticultural math seriously. Social Studiesand the Young Learner, 6(1), 31-32.

Sofaer, Anna, Volder Zinser, and RolfSinclair. (1979). A Unique Solar MarkingConstruct. Science 206.

Waters, Frank. (1963). The Book ofthe Hopi. New York, NY: Viking Press.

Wheelwolf Productions. (1999). SunCalendars of the Ancient Puebloans:Archaeoastronomy in the Mancos Canyonof Colorado [Film]. (Available fromWheelwolf Productions, Chico, California,www.wheelwolf.com).

Williamson, R. A. Living the Sky.(1984). Norman, Oklahoma: University ofOklahoma Press.

Zaslavsky, Claudia. (1996). TheMulticultural Math Classroom: Bringingin the world. Portsmouth, NH: Heinemann.

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the four basic facts in mathematics. As partof course assignments, students have askedquestions, and assisted in developing a vo-cabulary collection of over 35 languages, aswell as the learning and use of the four basicfacts in mathematics - addition, subtraction,multiplication and division.

Analysis: The PI interviews students atEncina High School, where he has been avolunteer visiting professor in the mathemat-ics department for over 4 years. The samplesare analyzed using interview data, for diverseprotocols, and error patterns distinctive toeach algorithm and its ethnomathematicalcontent. During the pilot study, 16 groupswere represented; it has grown to 35 found inthe Sacramento region. The initial pilot studyuncovered four patterns for long division usedby the high school students (see appendix).

Dissemination: Pilot study data, was usedto construct a new course objective for math-ematics methods students. Where students areasked to interview a newly arrived immigrant.Data gleaned from this work has been usedto develop curriculum strategies for teachereducators in both California and Brazilthrough numerous seminars and workshopsgiven by this writer. As well, the findings wereshared on Public Radio2, at the CaliforniaMathematics Council Asilomar Meeting,NCTM and though The International StudyGroup on Ethnomathematics3 network.

Research Question and SignificanceDo algorithms we use have cognitive, as

well as pedagogical significance for their us-ers? Recent research suggests that one’smother tongue influences one’s personal formof cognitive processing (Holtz, 2001; Devlin,2000). This unique interaction of languageand written language, suggests that Ameri-can children may possess unusual difficultywith the algorithms they learn. Educators inmany countries are surprised to find that com-

mon day-to-day algorithms differ by cultureand by national origin.

For example, the pilot study data sug-gested that there might be at least four majorpatterns used for long division in our region,where only one is taught formally. The ACPhas collected long division algorithms usedby newly arrived ninth graders that fall intofour major styles or patterns. For purposes ofthis study, they are called: North American;Franco-Brazilian; Indo-Pakistani; and Russo-Soviet (see appendix).

ContextEarly colonization enabled, for better or

worse, alternative ways of thinking and learn-ing to be exchanged between diverse groupsof people. This process continues in manyplaces where immigration and urbanizationhave brought together members of diversecultures. Northern California is part of thisphenomenon, where over 180 different cul-tures and languages interact. This is clearly acase for studying “what works” across cul-tures in relation to number sense acquisition.The pilot study uncovered relationships be-tween mono-, bi- and multilingualism, thealgorithm used and student ability and confi-dence. For example, some language groupsuse the comma (,) for the decimal, which canbe cause for some confusion for scientists,business people, students and educators. Mis-takes in measurement, often deadly, in trans-lation between standard and metric measure-ments are legendary. Thus, a strong case canbe made for studying “what works” acrosscultures in relation to number sense acquisi-tion. What is a surprise to many educators arethe successful methods for learning, memo-rizing, calculating and communicating an-swers that differ across cultures.

Much of what has been studied in bothethnomathematical and multicultural contextshas been related to the ancient ways of doingalgorithms. For example, it is common fortextbooks in many countries, to introduce

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Roman and Babylonian number systems,medieval-Russian peasant addition, Napier’sbones and other such activities as historicalcuriosities. It is also quite common to studycertain aspects of Aztec-Mayan math.

This study is built upon data collected,organized and developed from 1999 to thepresent, in an inner city public high school inSacramento, California. A Brazilian gradu-ate student, Milton Rosa, serving as a visit-ing foreign exchange teacher in mathemat-ics, was having difficulty in using and explain-ing the standard North American algorithmto his students as prescribed by the curricu-lum, and realized that his method also dif-fered from that of a number of his students(see examples from Brazil and Kazakhstan).He asked his students to demonstrate howthey learned to do long division in their formerschools.

What is Ethnomathematics andMathematical Modeling?

Ethnomathematics forms the intersectionbetween mathematics and cultural anthropol-ogy. It was introduced by UbiratanD’Ambrosio (2001) who explained thatethnomathematics is the “art or technique ofexplaining reality within a proper cultural con-text”, and describes all the ingredients that formthe cultural identity of a group: language,codes, values, jargon, beliefs, food and dress,habits, and physical traits. Ethnomathematicsdefines a broad view of mathematics, and in-cludes ciphering, arithmetic, classifying, order-ing, inferring, and modeling.

In this context, “ethno” and “mathemat-ics” are understood in the broadest possiblesense. Ethno refers to a broad concept of cul-tural groups, and not an anachronistic conceptrelated to race or exotic groups of people; math-ematics is to be seen as a set of activities suchas calculating, measuring, classifying, order-ing, inferring, and modeling. This perspec-tive, using ethnomathematics, enables us to seethe diversity around us as a resource.

The construction of mathematical con-cepts incorporates the reality of each individual.This begins by placing new situations and prob-lems in front of a child for them to masterwithin their own context and experiential real-ity so that math concepts are learned with afocus on the understanding and resolution ofproblems that we “do” mathematics. Learnersmust have experiences that enable them to learnhow to break a problem situation into man-ageable parts; create a hypothesis; test the hy-pothesis; correct the hypothesis; and maketransference and generalizations to their ownreality. Activities involving mathematics shouldenable opportunities for: open-ended explora-tion; appropriate project work; group and in-dividual assignments; discussion; and practiceusing a variety of mathematical methods, tools,and techniques. It is no longer acceptable thatthe intellectual activity of a child is exclusivelybased on memorization and testing, or for thatmatter only with the application of archaicknowledge, which serves only to increase mathavoidance.

Using an ethnomathematics based peda-gogy, a teacher can introduce their learners tonew tools and techniques directly connectedto the real life of the learner, help them to prac-tice becoming proficient in their use, and guidethem towards sophisticated mathematical ap-plications. It is through “context” that theteacher creates additional explanations andways to work within a “mathematically basedreality”.

This work within a mathematics reality isrelated to the “transforming action” (Freire,1997) that looks to reduce its degree of com-plexity through the choice of a model whererepresentations of this reality are derived byenabling the exploration, explanation, and in-creased comprehension of the concept. This iswhy cross-cultural study of basic algorithmsallows us to reflect on the inherent possibili-ties, and for these same possibilities to becomethe object of critical analysis by the learnersthemselves. The process in which we consider,

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analyze and make ongoing reflections is calledmodeling.

In making mathematics accessible for allstudents, educators must create conditions forincreased involvement by all students (Orey,1998; NCTM, 1999). Ethnomathematics sug-gests that modeling become a significant partof classroom pedagogy whereby good modelsare elaborated, demonstrated and shared freely,much as children discuss computer game tech-niques or soccer. Students learn as they applymodels and see mathematics as somethingpractical if it is valuable to them.

The way to introduce students to math-ematical modeling is to expose them to a di-versity of problems and models that includemathematical interpretations of problems,which in turn, are representations of modelsunder study. When we analyze a given situa-tion for its mathematical perspective, the teach-ing and learning process becomes more thanan over emphasis on rote memorization of ba-sic facts. One effective place to begin this studyis in the way that we personally compute orcalculate, that is, a study of the algorithms di-verse people use on a day-to-day basis. Math-ematical questions are used to explain and tomake forecasts on phenomena in the real world.What is interesting from an ethnomathematicspoint of view is that many of these explana-tions are unique from one culture to another,and of course, this works for algorithms thatpeople use to make basic day-to-day calcula-tions. Many of these diverse perspectives areused in representing situations for the study ofalternative techniques used to make calcula-tions.

Goals for Teachers and StudentsBy bringing alternative strategies together,

teachers and students learn to flexibly solveproblems, use alternatives when one strategydoes not work, and look at “best practices”from a global view. This project initially gath-ered a modest representative sample of thebasic arithmetic algorithms used by peoples

originating in diverse cultures. The data fromthis project was used to further refine this workand develop a number of curricular activitiesthat make use of this unique resource as foundin this author’s community. As describedabove, this data is used to develop the ACPwebsite and course materials that enable edu-cators to draw upon alternative forms of cal-culating by making use of options or choices,which are attuned to diverse linguistic, culturaland cognitive abilities of individual students.

ReflectionsA number of interesting things happened

as an outgrowth from this activity. A fewpreservice students were extremely nervousabout contacting someone to interview, “I donot know any one from another country” washeard a number of times. Together as a class,we brainstormed a number of possibilities.These included: going to the Student Union,sitting and listening, and politely introducingyourself and asking if the person speakinganother language was a foreign student, andif they would be interested in being inter-viewed; contacting parents of children in thestudent’s field placement, or a church or lo-cal groups; contacting the UniversityMulticultural Center; and contacting the De-partment of Foreign Languages.

Interestingly enough, students who ex-pressed the most reluctance, stated that theyenjoyed the activity the most. All intervieweesin the sample mentioned how happy they werethat Americans were interested in knowingsomething about their culture and ways ofdoing something as basic as arithmetic. Theclasses developed lists of vocabulary words,mathematical terms, numbers from 0-10 etc,wrote the words on index cards and hung themin the classroom, so we could compare eachlanguage.

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Additions to this activity often include:Conversion formulas - standard to metric,time zones, etc.; vocabulary lists in languagesnot represented by this study; the four basicoperations, square roots; tricks for resolvingproblems; and a discussion of how the par-ticipants memorized the basic facts. Almostall students who have participated in this ac-tivity have come away with a greater appre-ciation of “more than one way to solve a prob-lem” a greater appreciation for cultural di-versity, a new understanding for how hard itis for newly arrived students to adapt to lifein a new country.

Bibliography

Bassanezi, R. (1994). “Modeling as a teach-ing-learning strategy.” For the learning ofmathematics. 12(2), 31-35.D’Ambrosio, U. (2001). “What isethnomathematics, and how can it help chil-dren in schools?” Teaching Children Math-ematics, 7(6). Reston: NCTM._____________. (1985).“Ethnomathematics and its place in the his-tory and pedagogy of mathematics.” For theLearning of Mathematics. 5(1): 44-48.Devlin, K. (2000). The Math Gene: Howmathematical thinking evolved and whynumbers are like gossip. Basic Books.Freire, P. (1997). Pedagogia da Autonomia:Saberes Necessários à Prática Educativa

(Pedagogy that Gives Autonomy: Necessaryunderstandings towards a practical educa-tion). São Paulo: Editora Paz e Terra.Holtz, R. L. (2001, March 16). “Study: Somewritten languages intensify dyslexia.” Sac-ramento Bee, p. A20.NCTM. (1999). Every child Statement.Reston, VA: National Council of Teachersof Mathematics (www.nctm.org).Orey, D. & Rosa, M. (2002). Vinho e Queijo:Etnomatemática e Modelagem. Submited to:Boletim de Educação Matemática.Unversidaded Estadual Paulista - Rio Claro,Brasil.Orey, D. (2000). “Etnomatemática comoAção Pedagógica: Algumas Reflexões sobrea Aplicação da Etnomatemática entre SãoPaulo e Califórnia in Proceedings of thePrimeiro Congresso Brasileiro deEtnomatématica — CBEm1. Universidadede São Paulo, São Paulo, Brazil.______.(1999). “FulbrightEthnomathematics in Brazil.” InternationalStudy Group on Ethnomathematics News-letter. Las Cruces: ISGEm, 14 (1).______. (1998). “Mathematics for the 21stCentury.” In: Teaching Children Mathemat-ics, Reston, VA: National Council of Teach-ers of Mathematics.______. (1989). “Ethnomathematical per-spectives on the NCTM Standards.” Inter-national Study Group on EthnomathematicsNewsletter. 5(1): 5-7.______. (1984). “Logo goes Guatemalan: anethnographic study.” The ComputingTeacher, 12(1): 46-47.

Appendix I.Examples of Long Division Algorithms

(Footnotes)1 http://www.csus.edu/indiv/o/oreyd/Alg.html2 http://www.csus.edu/indiv/o/oreyd/exchange.html3 http://www.rpi.edu/~eglash/isgem.htm

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14

Dancing Numbers!: An AlternativeMathematics Instruction

Jim Barta – Utah State UniversityPerso (2002) contends that the

mathematics taught in schools exclusivelyreflects a “western-techno mathematics”. Its roots lie in the creation of a thoughtpattern resulting from a Cartesianworldview developed in the 15th centurythat has since been accepted as thestandard for not only mathematical andscientific endeavors, but has been infusedinto virtually every aspect of modernsociety around the world. This perspectiveincludes a perception of linear deductivelogic and separate objectification of theworld and things found in it.

For the Native American student, thiscultural disconnection poses additionalobstacles for achievement. It is as if thechild were being asked to see through twodifferent pairs of glasses; one whichincludes a perception of “reality” based ona reliance of the western worldview andthe other the subject, whose concepts,content, and information are all encased ina cloak of western impression and defini-tion. “Many Native children may strugglewith mathematics because for them thenumbers don’t dance.” (personal conversa-tion with Elmer Ghostkeeper, February 13,2000). From a western perspective, such acomment has little meaning, but not so ifone considers the insight from an indig-enous perspective. Pause for a momentand ask yourself how you would describea “dancing number”. Allow yourself toponder freely and draw your own conclu-sions. Juxtapose your impressions withthe traditional mathematics instruction youwere likely to have received as a child.Know that such prescriptive instructionstill occurs in some schools today.

Dancing Numbers is the name givento recent efforts to create culturallyinclusive mathematics curriculum forNative American students. DancingNumbers is more than instructionalactivities whose context emanates from aNative tradition or craft. Its perceptual

framework originates in an indigenousworldview. The challenge is to seekinstruction that treats knowledge asculturally situated and dynamic andlearning as relational and holistic. Here,the learner plays an active role in seekingpersonal understanding and meaningthrough the development of a relationalinvolvement in what is studied. A sense ofthe spiritual nature of human interactionwith one another all that surrounds andtied with a sense of service to others arebenchmarks of the curriculum. In subtleways using such a perspective, objects,numbers, concepts, and figures begin “todance” for and with the learner. Thisvision of education may be well suited forNative American students. This curriculummay be used to help rejuvenate thosestudents who have previously had todiscount their native ways of knowing tosucceed in schools, which heretoforeexclusively promoted a westernworldview.

Note: These efforts are in theirinfancy. This dream has just begun and Iam seeking others who might be interestedin working together to dream more deeplyand broadly. Please contact me if you sodesire – jbarta@coe.usu.edu

References:

Perso, T. (2002). Investigating currentresearch and systemic approaches toimproving the

numeracy of indigenous children.Churchill Fellowship Report. 1-38. West

Perth, AU: Churchhill FellowshipTrust. http://www.churchilltrust.com.au/

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Ethnomathematics Place in TeacherPreparation Programs

By: Amy Dyal - Graduate student at theUniversity of Florida,

I was a first semester graduate student atthe University of Florida, before I was everintroduced to the idea of Ethnomathematics. Idecided to enroll in a Multicultural Mathemat-ics course that introduced the idea of connect-ing math to the student’s culture.

There were two main components to thisclass: activities and core course component pre-sentations. First, the activities introduced meto ethnomathematics and sparked my curios-ity. The activities were lesson plans or activi-ties that involved mathematics and were de-veloped based on one of five regions: Africa,Asia, Europe, North America, and Central andSouth America. The activities identified thevarious ways people used mathematics in theirday-to-day activities, such as sewing and/orquilting, games, trade, building construction,calendars and time, etc. Secondly, the presen-tations gave me more information onethnomathematics, including background onwhat it is, why we should use this method inthe classroom, groups or individuals related toinvention of ethnomathematics, etc. For thepresentations we were divided into groups oftwo and assigned a topic to present to the class.My partner and I received “ethnomathematics,”and up until this point we had only discussedmulticultural education and had never beenintroduced to the term ethnomathematics.However, we quickly learned they were closelyrelated. We researched the topic a lot for ourpresentation, but my curiousity did not stopthere. Afterwards, I still continued to researchthe topic because it seemed like a great ap-proach to teaching mathematics.

As a child, I was often intimidated bymathematics because it seemed so abstract and/or distant from my everyday life. As a child,you wanted and possibly even need to makepersonal connections to truly understand the

idea. While I always received good grades inmathematics, I never truly understood the ideaspresented to me, I simply did the algorithmsand procedures given to me by the textbook orthe teacher. However, this only led to a super-ficial understanding of the material and I wasunable to apply those concepts into other situ-ations. Often I would have to be re-taught thosesame procedures in later mathematics classes.However, if I would have been taught usingethnomathematics, I feel things would havebeen better or easier for me. I would havegreatly benefited from the connections betweenmath and my day-to-day life. Mathematics canbe found in sewing, calendars, architecture,trade, and many other things that I willinglyparticipate in without even realizing the math-ematics that is involved. Participating in ex-plorations, as an elementary student like thosein my multicultural mathematics class, wouldof allowed me to build self-confidence in math-ematics, realize that it can be “conquered” andthat I can be successful in mathematics.

Not only did these explorations, presen-tations, and individual research I did make methink about my mathematics as a young stu-dent, but it also made me think critically aboutmy previous mathematics methods course.Why had I not been introducedethnomathematics before? Creating a personalconnection for students is a central componentof all my other methods courses. Why areteacher preparation courses in mathematicsbehind, when mathematics is a subject thatmost often alienates or intimidates students?

Ethnomathematics has so many positivebenefits for students. First, as stated before, itcreates a personal connection that other teach-ing styles or methods simply do not provide.Students, especially at the elementary schoollevel, need to see the material they are learn-ing is useful in their everyday lives. They needto see the value of learning the material pre-sented to them. Students will be more inter-ested and engaged in activities they feel ben-

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efit them in some way. Secondly, it allows stu-dents to develop a sense of pride in their cul-ture. When students see contributions theirculture has made to mathematics, no matterhow big or small, they will develop a sense ofpride about who they are and where they comefrom. This pride will transfer over into self-confidence and will help them to take risks thatthey were unwilling to take before. Also, stu-dents acquire self-confidence by realizing theyhave been using mathematics, without evenknowing it, in many of their daily activities.Ethnomathematics also helps to foster toler-ance and acceptance among the children be-cause they learn that each culture is valuable.As you can see, helping the students to createa personal connection with the mathematicalmaterial will affect so many aspects of thatchild’s life.

As a student of mathematics, I was ableto experience the positive benefits ofethnomathematics firsthand. I am extremelydisappointed that I had not been introduced tothis method, or teaching approach, beforegraduate school. Ethnomathematics should bepart of all teacher preparation courses. Thereare many future teachers who did not attendgraduate school or who decide to enroll in an-other math methods course and as a result theymissed the opportunity to learn aboutethnomathematics. I have several friends whojust graduated from another university, and Iasked them if they had ever heard ofethnomathematics. Unfortunately, they all an-swered no. As a result, their students will notbe receiving this type of instruction. I believelearning about and implementingethnomathematics in the their future curricu-lum will allow their students to truly under-stand mathematical content and make them allwant to become life-long mathematicians.

Contact: amydyal@yahoo.com

Survey onPREVAILING CLASSROOMCULTURE FOR SCHOOLMATHEMATICS

Back in 1987, the following passage,which appears below, stood out to meboldly while I was reading AlanSchoenfeld’s Cognitive Science andMathematics Education. Over the years, Ihave shared the passage with numerousaudiences of mathematics educators, schoolteachers, and with graduate and under-graduate students. I have continued to bestruck by the consistent resonance it seemsto have had throughout that time withmembers of those groups. Recently, Ishared the quotation with those attending asession I presented at the NortheasternRegional NCTM Conference in Boston inNovember. As usual, attendees signaledthat it seems to be a reasonably accuratethumbnail description of the general patternof teaching and learning mathematics inschools in the United States.

I didn’t gather any data from thoseattendees, and I began to wonder whatmathematics educators would write downas a reaction to these words by Schoenfeld.After all, the state of mathematics educa-tion in the US today is seemingly complex.NCTM has published four standardsdocuments since 1989, a number of reformcurriculum development initiatives havepublished materials that are in use invarious schools around the country,apparently lackluster performances of USstudents on international mathematics testshave captured attention in US public,policy, and professional circles, andassessment of student performance inmathematics is a statutory requirement inmany states. The assessment movementand the tests it has spawned have generatedcontroversy over the extent to which thetesting facilitates or disrupts studentlearning of mathematics.

To explore this matter, I have turnedto you, mathematics educators in the

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quickly. Having had that experience overand over again, you might eventuallycodify it as the following (implicit) rule:When you understand the subject matter,any problem can be solved in 5 minutes orless. The stronger form of this rule is evenworse: If you fail to solve a problem in 5minutes, give up. Unfortunately, this storyis not hypothetical: My research indicatesthat this belief and a number of equallycounterproductive beliefs about mathemat-ics are all too common among our stu-dents.

Creeping up in the oddest places:These are two publications whose

writers capture Gloria Gilmer’s passion forethnomathematics.

“Cornrow calculations (or Math isBeauty)” by Toni Wynn in Tenderheaded:A Comb-bending Collection of HairStories (edited by) Juliette Harris andPamela Johnson. Pocket Books, New York,2001, pp. 63 - 69.

“Gloria: A Mission inEthnomathematics” in When the membersare the Missionaries: An ExtraordinaryCalling for Ordinary People by A. WayneSchwab. Member Mission Press, Essex,New York, 2002, pp. 61 – 68.

readership of the Newsletter of the NorthAmerican Study Group onEthnomathematics for reflections andcomments on Schoenfeld’s observation. Ifyou would like to participate in thisinquiry, please send your response to meby email or by surface mail:

Fredrick L. “Rick” SilvermanDepartment of Elementary EducationCampus Box 107University of Northern ColoradoGreeley, CO 80639flsilver@aol.com

If you don’t mind doing so, pleasegive your name, contact information(phone, surface mail address, and email),position you hold, a statement about yourexperience as a mathematics educator,your assessment of Schoenfeld’s words,and ways in which ethnomathematicsmight have influenced your perspective.

Thank you very much, RickSilverman

Comments by Alan H. Schoenfeld onPREVAILING CLASSROOM CUL-TURE FOR SCHOOL MATHEMAT-ICS

Schoenfeld, Alan H. (1987). CognitiveScience and Mathematics Education,Lawrence Erlbaum Associates, p. 27.

Suppose that during your entireacademic career, every mathematicsproblem that you were asked was in fact astraightforward exercise designed to testyour mastery of a small piece of subjectmatter. You were expected to solve suchproblems in just a few minutes: If you didnot, it meant that you had not understoodthe material and the material should beexplained to you again. Suppose inaddition that this scheme was reinforced inclass: Problems were expected to besolved rapidly, and teachers gave you thesolution if you did not produce the answer

Dream Catching 2003

Conference Information – DreamCatching 2003 is a professional develop-ment workshop focusing on First Nation’sperspectives and educational initiatives.Here you can explore math, science, andIT integration in a hands-on, interactivesetting. The workshop is sponsored by theNative Access to Engineering Program atConcordia University, Montreal, Canadaand will be held from February 19 untilSaturday, February 22, 2003. For moreinformation visit: http://www.dream-catching.com/start.htm

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DreamCatching 2003http://www.dream-catching.com/

“DreamCatching 2003 is a professionaldevelopment workshop where you canexplore math, science, and IT integration ina hands-on, interactive setting. Ourworkshop facilitators and speakers willspend 4 days helping you discover newways to spark and capture the dreams ofyour students. Come join us to share whatyou know with others and to learn abouteffective methods and innovative resourcesthat will bring new life and excitement toyour class room.” This workshop issponsored by the Native Access to Engi-neering Program at Concordia University,Montreal, Canada and is held from 19February through 22 February.

Have you seen these recent publications?Eglash, R. “Race, Sex and Nerds: from

Black Geeks to Asian-American Hipsters.”Social Text, 20:2, pp. 49-64, Summer 2002

Eglash, R. “A Two-Way BridgeAcross the Digital Divide.” Chronicle ofHigher Education, pg. B12, June 21 2002.

Eglash, R. and Bleecker, J. “The Racefor Cyberspace: information technology inthe black diaspora.” Science as Culture,10:3, 2001.

“The Kolam Tradition”, by MarciaAscher in American Scientist , Jan-Feb2002, pp. 56-63. An abstract of this can befound at www.americanscientist.org/articles/02articles/ascher.html

The Distributed E-Learning Communityfor First Nations Science Education, Na-tive Access to Engineering Program

Scholars and practitioners at the NativeAccess to Engineering Programme (NAEP)at Concordia University in Montreal havebeen working since 1993 to address theunderrepresentation of Aboriginal people inthe pure and applied sciences in Canada.The program has been developing anddistributing culturally appropriate math and

From the EditorsHere is volume one, number one of

the North American Study Group onEthnomathematics Newsletter. Thanks toRon Eglash for the wonderful cover.

We need your help with the success ofthe newsletter. For folks that have been“away” Ethnomathematics is gainingmomentum and respect. If you visitenc.org and do a site search you will findin excess of forty listings. The AnnualNational Council of Supervisors ofMathematics meeting is hosting theAnnual Ethnomathematics Reunion andthere are numerous sessions at the upcom-ing National Council of Teachers ofMathematics Annual Meeting that dealwith Ethnomathematics.

Our own ISGEm session at the annualNCTM meeting will be on Thursday, 10April 2003 from 8:30 a.m. until 10:00 a.m.in room 007 of the convention center. Wehave a promising panel of presenters: Dr.Dawn Andersen, California State –Fullerton; Dr. Ron Eglash, RensselaerPolytechnic Institute; Dr. Daniel Orey,California State University – Sacramento;Mr. Milton Rosa, Encina High School,Sacarmento, CA; and Dr. Jerry Lipka,University of Alaska – Fairbanks.

For our colleagues working withgraduate student please suggest that theyconsider submitting to the newsletter. To

science curriculum in hard copy for sixyears. Designed and written with inputfrom the Native communities, the curricu-lum makes connections between “aca-demic” math and science, traditionalpractice, and community economicdevelopment.

Program Director Corinne Jette’strongly believes that all children can andwill succeed if the instruction they receiveincorporates values, beliefs, and physicalexamples of the cultural community’s livedexperiences. The site offers a variety ofinformation and activities for teachers witha specific focus on First Nation’s perspec-tives. For more information visit: http://nativeaccess.com/

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HELP WANTED!

Translators of publications Displayed at ICEM-II .

SIG coordinator, Gloria F. Gilmer, seekstranslators and/or interpreters of about twenty publications - written inPortuguese- which she brought from theSecond International Congress onEthnomathematics (ICEM-II). Thesepublications should inform a proposedSIG project to popularizeethnomathematics in North America. Ifyou can assist in any way, pleasesend comments to Ggilme@aol.com.

To sign up for membership in the Mathand Arts SIG, please write to Ggilme@aol.com.

our colleagues teaching courses withEthnomathematics in the course title orEthnomathematics threaded through yourcurriculum please consider submittingclassroom insights, experiences, andpedagogical and curriculum issues. If youare presenting Ethnomathematics workplease consider sending us your presenta-tion abstract and the venue.

Even as this newsletter is beingfinalized Jim Barta, on sabbatical atConcordia University 2002 – 2003,submits a web site well worth visiting.

http://193.75.136.14/~dhuylebrouck/Ishango_web/Ishango_web.htm

Please accept our invitation to joinNASGEm. Daniel and I look forward tothe upcoming NCSM and NCTM meetingsand the opportunity to say hello.

Tod ShockeyMesa State Collegetshockey@mesastate.edu

Daniel OreyCalifornia State – Sacramentoorey@csus.edu

Evaluation of Culturally-SituatedDesign Tools in the Recruitment andRetention of Under-represented Minori-ties for Information Technology CareersRon Eglash and Audrey Bennett,Rensselaer Polytechnic Institute

Research on under-represented minoritystudents making their way through the ITcareer “pipeline” has located specificfeatures of the educational experience inwhich these students are lost. Many of theseproblems can be attributed to a tendency tosee their cultural identity as separated from(and even antagonistic to) the curriculumleading to IT careers. The PI’s previousresearch has initiated the development ofculturally-situated design tools that addressthis conflict. These software tools useethnomathematics—the mathematicalpractices embedded in artifacts such asnative american beadlooms, african americancornrow hairstyles, graffiti, etc.— to teachstudents how their cultural background canbecome a bridge, rather than a barrier, toinformation technology careers. Thisresearch will finalize the software develop-ment for integration into standard curricula,and evaluate its use by secondary students inRPI’s local GEAR-UP program over a threeyear period. The software is available onlineat http://www.rpi.edu/~eglash/csdt.html.

Special Interest Groups (SIGs)Gloria Gilmer

Have you ever contrasted previews ofcoming attractions at the cinema withreviews of math books? Well, a newNASGEm – SIG will be doing just that!Watch NASGEm create a new standardfor book reviews.

Each member of the ME – SIG willreview a chapter of Marcia Ascher’s book:Mathematics Elsewhere, with his or hercolleagues and students and prepare a

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INTERNATIONAL STUDY GROUPON ETHNOMATHEMATICS

International Board of Directors Meet-ing—6 August 2002—Ouro Preto, Brazil

MINUTES

The President, Paulus Gerdes, wasunable to attend the Second InternationalCongress of Ethnomathematics and hencewas unavailable to chair the Boardmeeting. Lawrence Shirley, one of thethree Vice-Presidents, presided.

The President shall appoint a Secretaryfor the Board. In the meantime, Shirley isrecording minutes of this meeting.

For the immediate future, the ActingTreasurer of ISGEm shall be the Treasurer ofthe North American chapter (North Ameri-can Study Group on Ethnomathematics—NASGEm), since the North Americanchapter has been operating the account forISGEm. This Treasurer position is currentlyheld by Cathy Barkley.

Having obtained acceptances from thenominees, the Board appointed PedroPaulo Scandiuzzi as Editor of the ISGEmNewsletter, and Marcelo Borba as Assis-tant Editor. Both are from Brazil. (Forreference, Scandiuzzi’s e-mail address is

pepe@edu.ibilce.unesp.br.) The Boardthanked Tod Shockey, who has beeninterim Editor for the past several issues(He will continue as the Editor of the newNASGEm newsletter).

The Board delayed decision on aproposal for ISGEm to sponsor a scholarlyjournal of ethnomathematics, pendingfurther discussion with the President andothers who were unable to attend themeeting. However, the following werenominated as a preliminary editorial board:Bill Barton, Maria Luisa Oliveras, FrancoFavilli, Daniel Orey, Rick Scott, TodShockey, and Maria do Carmo Domite.

The Board also delayed action on anyamendments of the ISGEm Constitution,pending further discussion. Some of thesuggested amendments relate to clarifica-tion of the separate roles of the overallISGEm and the regional chapter.

The Board agreed that all whoregistered for the Second Congress wouldhave automatic ISGEm membership untilthe next Congress.

Since the early 1990s, ISGEm hasbeen an affiliate of the (American)National Council of Teachers of Math-ematics (NCTM) organization. However,now that the North American chapter hasbeen organized and handles ISGEmbusiness in the region of the NCTM, theBoard approved making effort to shift theaffiliation with NCTM from ISGEm to theNASGEm.

The Board accepted the invitationfrom Bill Barton to hold the Third Interna-tional Congress of Ethnomathematics inNew Zealand. The conference will be in2006, probably in January (summer seasonin New Zealand), though the exact dateswill be announced later. A Program Chairand International Program Committee willbe selected later.

The Board noted that the TenthInternational Congress on MathematicalEducation (ICME-10) will be held inCopenhagen, Denmark, in July, 2004. BillBarton and Marcelo Borba are ISGEmmembers who are on the ICME International

“new wave” presentation for the NASGEmbusiness meeting in San Antonio. The idea isto elaborate in a meaningful way uponsignificant ideas that may only be alluded toin typical reviews but which actually connectin some way with the ethnomathematics ofthe general reader. The SIG members willalso publish and introductory monograph ontheir work. In this way, we may begin toimpact mathematical reviews and popularizeethnomathematics as well.

The SIG members are: Cathy Barkley;Oshon Temple; Milton Bond; Ron Eglash;and Claudia Zaslavsky. Others are invitedto join by contacting Gloria Gilmer by e-mail at Ggilmer@aol.com.

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Minutes from the ISGEm Board MeetingMonday, April 22, 02, 12 noon.Venetian Hotel

Present: Tim Crane, Marilyn Frankenstein,Gloria Gilmer, Swapna Mukhopadhyay,Daniel Orey, Larry Shirley, Tod Shockey,Rick Silverman, HollyWenger.—————————————————Committee on NASGEm Affiliation:

After exchanging initial pleasantries,the group focused discussion on establish-ing a committee for the North Americanchapter to take over from the InternationalStudy Group of Ethnomathematics as anaffiliate of NCTM. The members of thecommittee are: Gloria Gilmer, DanielOrey, and Larry Shirley. Rick Silvermanmade the motion and it passed unani-mously.

New Journal:Larry Shirley brought up the issue of a

new journal and the group decided thatthere needs to be more discussion with theinternational group at the II-CIEM inBrazil in August. Since the North Americagroup doesn’t have any funds of its own,starting a journal could not be financiallyfeasible. Tod Shockey thanked Jim Bartafor his effort in having the newsletterprinted in a journal-type format.

NASGEm Membership dues:After some discussion, the revised

annual dues for NASGEm is decided to be$20.00 for fully employed individuals. For

Program Committee. They (and otherISGEm members) are asked to work for agood ethnomathematics presence at theCongress. However, it appears the TopicGroup structure may be changed such thatthere is no specific group forethnomathematics as there was in Japan atICM-9.

Respectfully submitted,

Lawrence Shirley

students and less than fully employedindividuals, the subscription rate is 50%discounted and is $10.00.The NASGEmdues will cover the ISGEm dues as well.

This motion passed unanimously too.

Constitution:Larry Shirley will send the bylaws

and constitution of ISGEm electronicallyto the board members.

Gloria Gilmer, on behalf of hercommittee, will reexamine the constitutionand by-laws for NASGEm.

Certificate:Gloria Gilmer handed over the

certificate from NCTM to ISGEm to LarryShirley.

New NCTM RepRick Silverman was appointed as the

new NCTM rep.

Acting TreasurerAs Jim Barta starts his sabbatical from

Summer ’02, Cathy Barkley agrees to takethe position (she was contacted bytelephone during the meeting). MarilynFrankenstein suggests to start a newcommittee on financial affairs.

Gloria Gilmer recommends thatNCTM be contacted for membershipcampaign.

There was substantial discussion re aretreat for the board members. MarilynFrankenstein needs to be contacted re theretreat prior to the NCTM Regional inBoston in November, 02.

SIG coordinators: Gloria Gilmer will coor-dinate all four SIGs.I. Curricula and classroom application—Tim CraneII. Out of classroom application—SwapnaMukhopadhyayIII. Theoretical and epistemological consid-erations—no oneIV. Research in diverse environments—Daniel Orey

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Gloria Gilmer suggested launchingstudy tours to increase interest andparticipation in ethnomathematics.

Tim Crane spoke about a courseMathematics from Diverse Cultures that hehad taught from 1998 to 2000. This coursesatisfied the multicultural/internationalrequirement for his institution. Currentlyconducting a survey on such courses, heshared his survey instrument with theattendees.

Marilyn Frankenstein described the roleand goals of the new SIG, Ethnomathematicsand arts. John Sims, one of the presenters atthe mini-course, solicited support for hisupcoming show. He also shared his idea oflaunching an annual publication (journalformat) on Mathematical Art which wouldfeature articles on ethnomathematics andwould be published by Ringling College. Hisprojected time line indicated first distributionof the journal in Fall 03. The journal wouldmost likely focus on themes such as “repre-sentations in ethnomathematics.”,“Pythagorean math and art”.

For further information, John Sims couldbe contacted by email : jsims@rsad.edu

Upcoming meetingsII International Congress on

Ethnomathematics, Aug. 5 - 7, in OuroPreto, Brazil

Ubiratan D’Ambrosio invited everyoneto attend the II International Congress onEthnomathematics, Aug. 5 - 7, in OuroPreto, Brazil. Since ethnomathematics is

Tod Shockey: Editor of the newsletter forNASGEmDaniel Orey: Co-editor of the newsletter forNASGEm.

Upcoming meetings:NCTM 2003, San Antonio. Tod

Shockey & Jim Barta submitted a proposalfor the minicourse.

Larry Shirley announced the dates forother meetings.

MinutesNASGEM Annual Business meetingNCTM 2002Las VegasTuesday, April 23, 02, 7:00 PM

President Larry Shirley greeted theattendees and explained the switch over ofname from ISGEM (International StudyGroup of Ethnomathematics) to NASGEm(North American Study Group ofEthnomathematics). Dr. Shirley stronglyemphasized that NASGEm was notseceding from the parent organizationISGEM and will fully support them astheir North American chapter,

SIGs (Special Interest groups) for theNASGEm

Gloria Glimer named as the coordinator ofall the SIGs.

The SIGs and their corresponding coordi-nators were announced:

SIG Title Coordinator1. Curriculum & Classroom applicationsTim Crane, Central Connecticut University

2. Out of School ApplicationSwapna Mukhopadhyay, San Diego StateUniversity

3. Theoretical and EpistemologicalConsiderations, Vacant

4. Research in Cultural/Diverse EnvironmentsDaniel Orey, California State UniversitySacramento

5. Ethnomathematics and the ArtsMarilyn Frankenstein, U Mass, Boston

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Switching to NASGEM from ISGEmThe new “name” indicated strengthen-

ing of the North American chapter. Newconstitution need to be developed.

Membership dues$20 annual membership dues for

NASGEm. The committee at the interna-tional conference will decide on the duesstructure.

One of the attendees suggested to thinkabout the nonprofit status for the group.

VacanciesTwo vacancies in the office:(1) Treasurer, although Cathy Barkley

agreed to be the acting treasurer.(2) NCTM rep. Anyone interested

should contact Larry Shirley atlshirley@towson.edu.

Treasurer’s reportJim Barta shared his report as the

ISGEm treasurer.

Since roughly 80% of the totalmembership is from the US, Tim Cranesuggested that NASGEm take the respon-sibility for carrying the financial burden ofthe newsletter for the non-US members.One of the attendees (Jack London) urgedthe group to think in terms of electronicpublishing. Larry Shirley invited sugges-tions from the group.

During the last part of the meeting,the participants introduced themselves andshared their personal interest inethnomathematics.

Meeting adjourned at 8:30 PM.

Respectfully submitted

Swapna Mukhopadhyay

studied widely in Brazil and a bulk ofresearch on ethnomathematics is conductedthere, this conference would be most suitableto attend for an interest in the subject. LarryShirley reminded the participants that onecould still submit a proposal for a posterpresentation since the dead line was ex-tended.

For the benefit of a wider audience,Gloria Gilmer requested to have the non-English papers translated in English.

She also invited the attendees tocontribute their thoughts and ideas for theNASGEm newsletter.

Larry Shirley offered his email as acentral hub or locator for future emailcommunications.

Marilyn Frankenstein suggested to usethe ISGEm list as a place for discussionson poster presentations and other similarideas.

NCTM 2003, San Antonio, TX, April, 03.NCTM allows the group one three-

hour mini-course at the annual meeting.

A proposal for a mini-course oncurriculum development for K - 16 hadbeen submitted by Daniel Orey, Jim Bartaand Tod Shockey.

NCTM 2004, Philadelphia, PA, April, 04.If interested in submitting a proposal

for the mini-course, Larry Shirley shouldbe contacted.

ICME Copenhagen, July 04The website ? A topic group on

ethnomathematics needs to be launched.

III. ICEM, 2006Possibility of hosting the meeting in US?Delegate AssemblyRick Silverman agreed to serve as the

NCTM Representative and to attend the2003 Delegate Assembly in that capacity.

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lthe NCTM representative, the editor of thenewsletter, the immediate Past-President, thePresident-Elect, the Program Assistant andthe Assistant Editor.

Section 2. The Executive Board shallattend to any business of the organizationthat may require attention in the intervalbetween business meetings.

Article V. Officers.

The officers of the organization shall bePresident, First Vice-President, Second Vice-President, Third Vice-President, RecordingSecretary, Corresponding Secretary andTreasurer.

Article VI. Duties and Election of Officers.

Section 1. The President shall presideat all meetings of the organization and shallbe chairman, ex-officio, of the ExecutiveBoard, and shall appoint an NCTM repre-sentative, the editor of the newsletter and theAssistant Editor.

Section 2. The First Vice-President shallperform the duties of the President in theabsence of the President and shall act as pro-gram chairman. The First Vice-Presidentshall appoint as necessary a program com-mittee and a Program Assistant or specifyprogram representatives to promote presen-tations on Ethno-Mathematics at relevantprofessional meetings.

Section 3. The Second Vice-Presidentshall perform the duties of the President inthe absence of the President and the FirstVice-President and shall act as membershipofficer.

Section 4. The Third Vice-Presidentshall perform the duties of the President inthe absence of the President, the First Vice-President and the Second Vice-President andshall act as coordinator of the Special Inter-est Groups (SIGs) in ISGEm and communi-cated with members-at-large concerning

ISGEm CONSTITUTION

Article I. Name.

The name of this organization shall bethe International Study Group onEthnomatematics (ISGEm).

Article II. Purpose.

The purpose of the organization shallbe to encourage and maintain interest in theteaching and learning of mathematics in cul-tural contexts and to promote professionalgrowth, fellowship and communicationamong its members.

Article III. Membership.

Section 1. Membership shall be opento all persons interested inethnomathematics.

Section 2. (A) Members shall pay regu-lar dues and be entitled to all privileges ofthe organization. (B) The dues shall be setby the Executive Board subject to approvalof the membership. (C) At the discretion ofthe Executive Board, any person shall begranted an honorary membership upon re-quest without payment of dues.

Section 3. The membership period co-incides with the calendar year from January1 to December 31.

Section 4. All members shall indicatethe region to which they belong. The regionsshall be: A. Africa; B. Asia (including theMiddle East); C. South Pacific (includingAustralia, New Zealand and the Pacific Is-lands); D. Europe; E. The Americas (North,Central, South, and the Caribbean).

Article IV. Executive Board.

Section 1. The Executive Board shallconsist of the officers and members-at-large,

25

conferences relevant to ISGEm in their re-spective regions.

Section 5. The Secretary shall keep theminutes of the business meetings and shallpass these along to the newly elected secre-tary as a permanent record of the actions ofthe organization.

Section 6. The Treasurer shall receiveand account for all monies of the organiza-tion, disburse all sums on order of the Presi-dent, and render a financial report at the lastmeeting of the year. A yearly audit must beconducted by two members appointed by theExecutive Board.

Article VII. Meetings.

At least one business meeting shall beheld during each calendar year. The time andplace of these meetings shall be set by theExecutive Board. All meetings are open toany member of the Group.

Article VIII. Rules of Order.

The organization shall be governed byRobert’s Rules of Order except in mattersotherwise provided for by the Constitution.

Article IX. Amendments.

This Constitution may be amended at anymeeting of the Group by a two-thirds majorityvote of the members present and voting, pro-vided notice of the proposed amendment hasbeen given at the previous meeting.

Article X. Dissolution.

If at any time the International StudyGroup on Ethnomathematics (ISGEm) shallcease to carry out the purposes herein stated,all assets held by it in trust or otherwise, shall,after the payment of its liabilities, be paid overto an organization selected by the final Ex-ecutive Board of the International Study

Group on Ethnomathematics which has simi-lar purposes and has established its tax-ex-empt status under Section 501 (c) (3) of theInternal Revenue Code of 1954 as now en-acted or hereafter amended, and such assetsshall be applied exclusively for such chari-table, scientific, and educational programs.

By-Laws

Article I. Executive Board.

Section 1. Two of the members-at-largeshall be elected from the South Pacific, threefrom Africa, three from Europe, three fromAsia (including the Middle East), and threefrom the Americas.

Section 2. Additional members of theExecutive Board shall include the Immedi-ate Past-President, the President-Elect, theNCTM Representative, the Editor of thenewsletter, the Assistant Editor, the ProgramAssistant, and the officers.

Article II. Election of Officers and Members-At-Large.

Section 1. The terms of office for allofficers and members-at-large shall be fouryears with half the members-at-large electedevery two years.

Section 2. All elections shall be held byballot prior to the end of each even-numberedcalendar year and shall be carried by a plu-rality vote of the ballots returned. Nomina-tions for the officers and members-at-largeshall be made by a Nominating Committeeof five members, appointed by the Presidentand approved by the Executive Board. TheNominating Committee shall recommend atleast one candidate for each office to be filled.Other nominations shall be received as write-ins on the election ballot at the time of theelection. The consent of each candidate, otherthan write-ins, must be obtained before thename is placed in nomination.

26

ISGEm-NA CONSTITUTION

Article I. Name.

The name of this organization shall bethe International Study Group onEthnomatematics-North America Chapter(ISGEm-NA).

Article II. Purpose.

The purpose of the organization shall beto work in close collaboration with ISGEmto encourage and maintain interest in theteaching and learning of mathematics in cul-tural contexts and to promote professionalgrowth, fellowship and communicationamong its members. ISGEm-NA shall be sub-ordinate to ISGEm and its constitution onmatters petaining to activities sactioned bythis constitution.

Article III. Membership.

Section 1. Membership shall be opento all persons interested inethnomathematics.

Section 2. (A) Members shall pay regu-lar dues and be entitled to all privileges ofthe organization.

(B) The dues shall be set by theExecutive Board subject to approval of themembership.

(C) At the discretion of the Execu-tive Board, any person shall be granted anhonorary membership upon request withoutpayment of dues.

Section 3. Officers shall be elected inyears divisible by four.

Section 4. Officers shall begin to servetwo years after being elected.

Section 5. Members-at-large shall be-gin to serve on January 1 of the odd-num-bered year immediately following election.

Section 6. Officers shall be elected bythe entire membership.

Section 7. Members-at-large shall beelected by the members from their region.

Section 8. All officers and members-at-large can be re-elected.

Article III. Amendments.

These by-laws may be amended by writ-ten ballot by a majority vote of the ballotsreturned, provided notice of the proposedamendment has been given at the previousmeeting.

First Amendment

In order to broaden the membership inthe International Study Group onEthnomathematics (ISGEm) and increasethe participation in research inETHNOMATHEMATICS around theworld, the following provisions arepermitted:

1. ISGEm chapters may established ineach region delineated in this constitution,Article III, Section 4, or in countries withinthose regions, for the purposes of furtheringthe aims of ISGEm. Each chapter so formedmust adopt an organizational structure par-allel to the structure of ISGEm.

2. Each chapter created under the aus-pices of this amendment must abide by thisconstitution. Furthermore, all members andofficers of each chapter must be membersof that chapter or members at large of

ISGEm.

3. Each chapter is permitted to set itsown membership dues structure accordingto its own socio-economic conditions. ThePresident of the chapter must communicateto the President, or to the Second Vice Presi-dent, of ISGEm the membership policiesgoverning her/his chapter.

27

Section 3. The membership period co-incides with the calendar year from January1 to December 31.

Section 4. All members shall indicatethe region to which they belong. The regionsshall be: A. Canada; B. Mexico; C. UnitedStates of North America.

Article IV. Executive Board.Section 1. The Executive Board shall

consist of the officers and members-at-large,the NCTM representative, the Editor of theNewsletter, the immediate Past-President,the President-Elect, the Program Assistant,and the Assistant Editor.

Section 2. The Executive Board shallattend to any business of the organizationthat may require attention in the intervalbetween business meetings.

Article V. Officers.The officers of the organization shall be

President, First Vice-President, Second Vice-President, Third Vice-President, RecordingSecretary, Corresponding Secretary andTreasurer.

Article VI. Duties and Election of Officers.Section 1. The President shall preside

at all meetings of the organization and shallbe chairman, ex-officio, of the ExecutiveBoard, and shall appoint an NCTM repre-sentative, the Editor of the Newsletter, andthe Assistant Editor.

Section 2. The First Vice-President shallperform the duties of the President in the ab-sence of the President, and shall act as pro-gram chairman. The First Vice-President shallappoint as necessary a program committeeand a Program Assistant or specify programrepresentatives to promote presentations onEthno-Mathematics at relevant professionalmeetings in North America and elsewhere.

Section 3. The Second Vice-Presidentshall perform the duties of the President inthe absence of the President and the FirstVice-President and shall act as membershipofficer.

Section 4. The Third Vice-Presidentshall perform the duties of the President inthe absence of the President, the First Vice-President and the Second Vice-President andshall act as coordinator of the Special Inter-est Groups (SIGs) in ISGEm-NA and com-municate with members-at-large concerningconferences relevant to ISGEm-NA in theirrespective regions.

Section 5. The Secretary shall keep theminutes of the business meetings and shallpass these along to the newly elected secre-tary as a permanent record of the actions ofthe organization.

Section 6. The Treasurer shall receiveand account for all monies of the organiza-tion, disburse all sums on order of the Presi-dent, and render a financial report at the lastmeeting of the year. A yearly audit must beconducted by two members appointed by theExecutive Board.

Article VII. Meetings.At least one business meeting shall be

held during each calendar year. The time andplace of these meetings shall be set by theExecutive Board. All meetings are open toany member of the Group.

Article VIII. Rules of Order.The organization shall be governed by

Robert’s Rules of Order except in mattersotherwise provided for by the Constitution.

Article IX. Amendments.This Constitution may be amended at any

meeting of the Group by a two-thirds major-ity vote of the members present and voting,

28

provided notice of the proposed amendment hasbeen given at the previous meeting.

Article X. Dissolution.

If at any time the International StudyGroup on Ethnomathematics (ISGEm) shallcease to carry out the purposes herein stated,all assets held by it in trust or otherwise, shall,after the payment of its liabilities, be paid overto an organization selected by the final Execu-tive Board of the International Study Groupon Ethnomathematics which has similar pur-poses and has established its tax-exempt sta-tus under Section 501 (c) (3) of the InternalRevenue Code of 1954 as now enacted or here-after amended, and such assets shall be appliedexclusively for such charitable, scientific, andeducational programs.

By-Laws

Article I. Executive Board.

Section 1. One of the members-at-largeshall be elected from each of the followingregions: (a) Canada; and (b) Mexico.

Section 2. Additional members of theExecutive Board shall include the Immedi-ate Past-President, the President-Elect, theNCTM Representative, the Editor of theNewsletter, the Assistant Editor, the ProgramAssistant, and the officers.

Article II. Election of Officers and Members-At-Large.

Section 1. The terms of office for allofficers and members-at-large shall be twoyears.

Section 2. All elections shall be heldby ballot at a regular meeting of ISGEm-NA and shall be carried by a plurality voteof the ballots returned. Nominations for theofficers and members-at-large shall be made

by a Nominating Committee of five mem-bers, appointed by the President and ap-proved by the Executive Board. The Nomi-nating Committee shall recommend at leastone candidate for each office to be filled.Other nominations shall be received as write-ins on the election ballot at the time of theelection. The consent of each candidate,other than write-ins, must be obtained be-fore the name is placed in nomination.

Section 3. Members-at-large shall be-gin to serve on January 1 of the year imme-diately following election.

Section 4. Officers shall be elected bythe entire membership.

Section 5. Members-at-large shall beelected by the members from their region.

Section 6. All officers and members-at-large can be re-elected.

Article III. Amendments.

These by-laws may be amended by writ-ten ballot by a majority vote of the ballotsreturned, provided notice of the proposedamendment has been given at the previousmeeting.

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NASGEm 2003 Elections

Elections for the slate of proposedofficers will occur at the Annual Meetingof the National Council of Teachers ofMathematics being held in San Antonio,Texas, 09 – 12 April 2003.

FINAL SLATE of NASGEm OFFICERSfor 2003-2005

Larry ShirleyOffice -President Affiliation - Professor of Mathematics andAssociate Dean of the College ofGraduate Education and Research,Towson UniversityNASGEm Activities - President 2000-2002;USA Member ICEM-II InternationalProgram Committee; Coordinator ofICEM-II Roundtable on Ethnomathematicsand Teacher’s QualificationVision for NASGEM - To strengthenNASGEm’s affiliation with NCTM andISGEm

****************************Arthur PowellOffice - 1st Vice-president (ProgramChair) -Affiliation - Professor, MathematicsEducation, Rutgers UniversityNASGEm Activities - 1st Vice-President2000-2002; USA Member ICEM-IIInternational Program Committee;Coordinator of ICEM-II Roundtable onEthnomathematics and Urban Education;ICEM-II ConferenceLecturer on Paulo Freire’s Contribution toan Epistomology of EthnomathematicsVision for NASGEm for next two years -To Increase NASGEm’s visibility atconferences

****************Louise GouldOffice - 2nd Vice President ( MembershipOfficer)Affiliation - Professor in Department ofMathematical Sciences, Central

Connecticut State University, New Britain CTNASGEm Activities - Presentation /Roundtable V: Ethnomathematics andTeacher’s qualification Use ofEthnomathematics Topics in NorthAmerican College Programs at ICEM-II.Vision for NASGEm for next two years -To bring increased visibility toNASGEm through the NCTM affiliationand conference related presentations, andbuild a resource base for educators of pre-service teachers and wage a vigorouscampaign to increase memberships inMexico, Canada, and the USA

*********************Gloria F. GilmerOffice - 3rd Vice-president (SIG Coordina-tor)Affiliation - Math Curriculum Consultant,Math - Tech MilwaukeeNASGEm Activities - 3rd Vice- President2000-2003; USA Member ICEM-IIInternational Program Committee; ICEM-II Closing SpeakerVision for NASGEm for next two years -To create at least four strong SIGs thatresearch and publish their findings onethnomathematical issues in NorthAmerica

**********************Holly WengerOffice - Recording SecretaryAffiliation: Mathematics Teacher, 9-12public school, Sacramento, CANASGEm Activities: member, participantsince ICEM-1 in Granada. Occasionalpresenter at local functions in behalf ofethnomathematics study and usage in K-12Vision for NASGEm: strengthenNASGEm’s presence among K-12classroom teachers; encouraging dialogand contact among teachers who wish touse an ethnomathematical perspective intheir daily work with kids.

30

Interested in Math and the Arts?

See the preliminary edition ofMATH DANCE by Karl Schaffer,Erik Stern and Scott Kim. For moreinformation visit their website http://www.mathdancs.org or e-mail Karl atschafferkarl@fhda.edu . Pleaseconsider signing up for the Math andArt SIG, send Gloria Gilmer an e-mail at Ggilmer@aol.com to getsigned up.

************************Claudette Bradley -Office - Corresponding SecretaryAffiliation - Professor, University ofAlaska - FairbanksNASGEm Activities -Vision for NASGEm for next two years - To disseminate updated rosters andconstitutions to all members and to e-mailquarterly NASGEm news alerts toall members,

************************Cathy BarkleyOffice - TreasurerAffiliation - Professor of Mathematics,Mesa State CollegeNASGEm Activities - Treasurer 2002Vision for NASGEm for next two years:To remind all members to pay duesannually

****************************Office - Members-at-largeMarilyn FrankensteinAffiliation - Professor College of Publicand Community Service, Universityof Massachusetts - BostonNASGEm Activities - Member-at-Large2000-2002; Coordinator for the Math andArts SIG; Organizer of NASGEm MiniCourse in Las Vegas in 2002; ICEM-IIConference Lecturer on Paulo Freire’sContribution to an Epistomology ofEthnomathematicsVision for NASGEm for next two years -To strengthen the Math and Arts SIGand to help strengthen the organizationalstructure of the group

*************************************Oshon TempleAffiliation - Mathematics Teacher, De LaSalle Academy, Manhattan, New YorkNASGEm Activities - Presentation atICME-II with Arthur Powell. “BridgingPast and Present: Ethnomathematics, TheAhmose Mathematics Papyrus,and Urban Students.” II International

Congress on Ethnomathematics. OuroPreto, Brazil, 7 August 2002; Presentationat 78th Annual Meeting of the NationalCouncil of Teachers of Mathematics. Chicago, USA, 14 April 2000 withArthur Powell on “Ethnomathematics:Examples and Justification of CurricularModules.”Vision for NASGEm for next two years -To work to maintain and increaserelationships with young teachers as ameans of sustaining and growingmembership in NASGem and to serve as aPortuguese and Spanish translator.

******************************** Patrick ScottAffiliation - Associate Dean, College ofEducation, New Mexico State UniversityNASGEm Activities - As past Editor(1985-1998) of ISGEm Newsletter havemaintained availibility of past ISGEmpublications ; Attended ICEM-II.Vision for NASGEm for next two years -Advance knowledge of and use ofethnomathematics in math courses at alllevels.

************************Note: ICEM - II is the Second Interna-tional Congress on Ethnomathematicsheld 5-7 August 2002 in Ouro Preto,Minas Gerais, Brazil

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NASGEm Newsletter Submissions

It is up to YOU to make this newslet-ter a success. We want to be informedabout your research, publications, grantwork, teaching, and what your under-graduate and graduate students are doing.Please send your input electronically to:

Tod Shockey Ph.D.Assistant ProfessorMesa State CollegeDepartment of Computer Science,Mathematics & Statistics1100 North Ave.Grand Junction, CO 81501

tshockey@mesastate.edu

OR TO:

Daniel Orey Ph.D.ProfessorMathematics and Multicultural EducationCollege of EducationCalifornia State University, Sacramento6000 J StreetSacramento, CA 95819 - 6079

Special Interest Groups (SIGs)for the NASGEm

Chaired by Gloria Gilmer,Ggilmer@aol.com

SIG Title CoordinatorCurriculum & Classroom ApplicationsTim CraneCentral Connecticut Universitycrainet@mail.ccsu.edu

Out of School ApplicationsSwapna MukhopadhyayPortland State Universityswapna@pdx.edu

Theoretical & EpistemologicalConsiderations

Vacant

Research in Culture/DiverseEnvironments

Daniel OreyCalifornia State – Sacramentoorey@csus.edu

Ethnomathematics and the ArtsMarilyn FrankensteinU Mass – Bostonmarilyn.frankenstein@umb.edu

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Become an NASGEm/ISGEm

member !Dues for the International Study Group on Ethnomathematics are$15 per year and may be paid for up to three years. Contributionsmay be made in order to allow others to receive the ISGEm Newslet-ter. Please fill out the form below and mail it along with a check toDr. Cathy Barkley, Department of Computer Science, Mathematics& Statistics, Mesa State College 1100 North Ave., Grand Junction,CO 81501, USA. Make checks payable to ISGEm.

name _________________________________________________________________

address________________________________________________________________

city ____________________ state/province _______________ postal code ________

country _______________________________________________________________

phone __________________ e-mail ________________________________________

amount enclosed __________

may your name/address be distributed to organizations that request copies of the ISGEmmailing list? ___________ yes ___ no

please briefly describe any projects in which you are involved that may be related toethnomathematics.