Berken, Bernadette Anne

Humanistic Mathematics Network Journal

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Humanistic Mathematics Network JournalIssue 14 Article 1311-1-1996Book Review: Ethnomathematics: A MulticulturalView of Mathematical Ideas, by Marcia AscherBernadette Anne BerkenSt. Norbert CollegeFollow this and additional works at: http://scholarship.claremont.edu/hmnjPart of the Mathematics Commons, and the Music CommonsThis Book Review is brought to you for free and open access by the Journals at Claremont at Scholarship @ Claremont. It has been accepted forinclusion in Humanistic Mathematics Network Journal by an authorized administrator of Scholarship @ Claremont. For more information, pleasecontact scholarship@cuc.claremont.edu.Recommended CitationBerken, Bernadette Anne (1996) "Book Review: Ethnomathematics: A Multicultural View of Mathematical Ideas, by Marcia Ascher,"Humanistic Mathematics Network Journal: Iss. 14, Article 13.Available at: http://scholarship.claremont.edu/hmnj/vol1/iss14/13Book Review: Ethnomathematics: AMulticultural View of MathematicalIdeas, by Marcia AscherBernadette Berken51. Norbe~ CollegeDe Pee , WI 54175Etlmomathematics:A MuIt icul tural View of Mathemati-cal Ideas. Marcia Asche r. Brooks/Cole Publishing,Co.: Pacific Grove, 1991. 203 pp, ISBN 0-534·14880-8.Ma rcia Ascher ' s book Ethnomathemat ics: AM ulticultural ViewofMathematiCilI Ideas is a superb trea-tise on mathematics from a multicultural point ofview. The text focu ses on a diverse collection of math-ematical ideas and ap plications. Ins tead of limitingthe scope of her text to the usual Eurocentric discus-sion, Ms. Ascher introduces the reader to the math-ematical ideas of peoples who have generally beenexcluded from d iscussions of mathematics and thedevelopment / history of mathematics. These peopleare the ones who live in trad itional or small-scale cul-tures, the ind igenous peoples wh o live in places thatwere "d iscovered" and colonized by Europeans andinclude such d iverse groups as the Iniut, Na vajo, andIroquois of North America; the Incas of South America;the Malekula, WarJp iri, Maori and Caroline Islandersof Oceania; and the Tshokwe , Bushoong and Kpelleof Africa.In her introd uction , Ms. Ascher sets the stage for hertext. This introductory discussion acknowledges that"there is no sing le linear path along which culturesprogress, with some ahead and others behind," thatmathem atics has no genera lly accep ted def initionsand that most definitions of ma thematics are basedsolely on Western expe rience. Nevertheless, Ascheris qu ick to point out tha t although a pa rticu lar cu l-ture ma y not classify an idea as "mathematics," trad i-tional cu ltures most de finitely express mathematicalideas in contexts that we westerners might call art,naviga tion, religion, record keeping, game playing,or kin relationships. In ad d ition, Ms.Ascher acknowl-edges that as one views the mathema tical ideas of oth-ers in their cu ltu ral context, one is limited by his orher own cul tura l and mathematical frameworks. Fol-lowing this importan t introduction, Ms.Ascher guidesthe reader on an exciting joumey that explores nu-merous mat hematical ideas in a variety of culturalcontexts.Chapter 1 focuses on the concept of numbers and thewords, symbols, and understanding associated withthem. The sets of number words of several culturesare examined and the pattems and arithmetic rela-tionships are described. The importance of langu ageand its relationship to number words is emphasizedand Ascher includes a clear and informative d iscus-sion of num era l classifiers. She devotes a substantiveportion of this chapter to a discussion of the Incas andthe organizati on and use of qu ipus within their cu l-ture.Graph theory is the focus of Chapter 2. It is here thatAscher examines the san d tracings of the Bushoongand Tsho kwe in Afr ica, and th e drawi ngs of theMalekula of the South Pacific. She clearly establishesthe fact that many differen t peoples have ponderedsimilar mathematical problems relating to Eulerianpaths and provides an excellent background discus-sion of the Bushoong, Tshokwe and Malekulan cul-tures as she exp lores graph theory ideas within therespective cultures.In Chapter 3, Ascher explores the important math-ematical idea of relations or the specified propertiesthat link pa irs of objects. She d oes this by examiningthe logicof kin relations . The native peoples of north-ern Australia (the WarlpirD a grou p with a parti cu-larly comp lexkin system provide an excellent examplethat forms the basis for this discuss ion which drawsupon ideas from group theory.Games of strategy and chance and the logic of puzzlesprovide the basis for Chapter 4. Since every gamecan be seen as an expression of a pa rticu lar cultu re,Ascher is careful to identify not just the rules of thegame but also the simple objects used for it, the timesand places for ap propriate playing of the game, theHumanisticMathematicsNetwork Journal #14social settings, the level of concentration, the systemsof rewards and all the other important aspects thatmake up the game. She includes an analysis of theAmerican Indi an game of Dish that is clearly rootedin the area of probab ility. This chapter also providesan excellent discussion of the Maori game of strategyknow n as Mu torcre. Starting with a simpler version,Ascher leads the reader not only to an understandingof how to play Mu torere but also to a basic under-standing of the mat he matics connected with thisgame. Acollection of river crossing puzzles from vari-ous cultures and the logic behind their solutions pro-vide the final area of focus for this chap ter.The organization and modeling of space and timeprovides the content for Chapter 5. Because notionsof time and space are so ba sic to the way we perceive,st ruc ture, and interpret our experiences, it is some-times hard to understand or visualize the space-timeideas of other cultures . Nevertheless, Ascher success-fully bridges this po ten tial difficulty by her choice ofexamp les. She includes apt discussions on the dy-namic universe of the Navajo, the unique process andchange dimension of the space-time concerns of thelniut, and the navigational processes of the CarolineIslanders.Spatial configuration is the basis of Chap ter 6 whichfocuses part icularly on symmetric strip decora tions .Ascher includes an introductory d iscuss ion ofisometries, symmetry, and symmetry groups and de-scribes and utilizes a four character naming schemefor the possible strip patterns. (This scheme wa s de-veloped by Russian crys tallographers and is now ac-cepted as the interna tional standard.) A discussion ofperfect colorin g is also included in this chapter. Rafterpa tterns of the Maori and str ip patterns found on Incapottery provide bea utifu l and illus tra tive examplesfor the discussion of strip patterns in this chapter.The final chapter of the boo k affords Marcia Ascheran opportuni ty to weave together the ma thematicalideas and phi losophies that are the basis for her boo k.She connects these ideas and issues to mathema ticseduca tion, emphasizing the need for a redefinition ofthe boundaries of mathem atics, and a revision of ourphilosophy and history of ma thematics.This out standing book is a clearly written text that iswell-suited for the college undergraduate level. Thediverse collection of ma the ma tical ideas in their cul-tural context provides a challenging yet very interest-ing array of mathematical topics. Ascher providesextensive notes with appropriate references whichafford the reader additional sources for reading andscholarship. Marcia Ascher's book Ethnomathematics:A Multicultural View ofMathematical Ideas is a rare gemof a book. Read it!PsychosisLee GoldsteinNooscop ic insociabilityCan drive the human intelligence of an incognizable numinosity,Thenceforw ard, to the equations of the sphere,Whi le this programmatic transpositionCan also beget, through the unconscious, an incipient eidosThat splits the per sonalAnd abets an insurgence of psychical energiesUnto the hallucinatory;That is seeming or chaotic.nooscopic: pertaining to the examina tion of the mindHumanistic Mathematics Network Journal #14 41

Book Review: Ethnomathematics: A Multicultural View of Mathematical Ideas, by Marcia Ascher

Bernadette Berken

Crossref

Ethnomathematics: A Multicultural View of Mathematical Ideas, by Marcia Ascher

Keck Graduate Institute

Humanistic Mathematics Network Journal
Issue 14 Article 13
11-1-1996
Book Review: Ethnomathematics: A Multicultural
View of Mathematical Ideas, by Marcia Ascher
Bernadette Anne Berken
St. Norbert College
Follow this and additional works at: http://scholarship.claremont.edu/hmnj
Part of the Mathematics Commons, and the Music Commons
This Book Review is brought to you for free and open access by the Journals at Claremont at Scholarship @ Claremont. It has been accepted for
inclusion in Humanistic Mathematics Network Journal by an authorized administrator of Scholarship @ Claremont. For more information, please
contact scholarship@cuc.claremont.edu.
Recommended Citation
Berken, Bernadette Anne (1996) "Book Review: Ethnomathematics: A Multicultural View of Mathematical Ideas, by Marcia Ascher,"
Humanistic Mathematics Network Journal: Iss. 14, Article 13.
Available at: http://scholarship.claremont.edu/hmnj/vol1/iss14/13
Book Review: Ethnomathematics: AMulticultural View of Mathematical
Ideas, by Marcia Ascher
Bernadette Berken
51. Norbe~ College
De Pee , WI 54175
Etlmomathematics:A MuIt icul tural View of Mathemati-
cal Ideas. Marcia Asche r. Brooks/Cole Publishing,
Co.: Pacific Grove, 1991. 203 pp, ISBN 0-534·14880-8.
Ma rcia Ascher ' s book Ethnomathemat ics: A
M ulticultural ViewofMathematiCilI Ideas is a superb trea-
tise on mathematics from a multicultural point of
view. The text focu ses on a diverse collection of math-
ematical ideas and ap plications. Ins tead of limiting
the scope of her text to the usual Eurocentric discus-
sion, Ms. Ascher introduces the reader to the math-
ematical ideas of peoples who have generally been
excluded from d iscussions of mathematics and the
development / history of mathematics. These people
are the ones who live in trad itional or small-scale cul-
tures, the ind igenous peoples wh o live in places that
were "d iscovered" and colonized by Europeans and
include such d iverse groups as the Iniut, Na vajo, and
Iroquois of North America; the Incas of South America;
the Malekula, WarJp iri, Maori and Caroline Islanders
of Oceania; and the Tshokwe , Bushoong and Kpelle
of Africa.
In her introd uction , Ms. Ascher sets the stage for her
text. This introductory discussion acknowledges that
"there is no sing le linear path along which cultures
progress, with some ahead and others behind," that
mathem atics has no genera lly accep ted def initions
and that most definitions of ma thematics are based
solely on Western expe rience. Nevertheless, Ascher
is qu ick to point out tha t although a pa rticu lar cu l-
ture ma y not classify an idea as "mathematics," trad i-
tional cu ltures most de finitely express mathematical
ideas in contexts that we westerners might call art,
naviga tion, religion, record keeping, game playing,
or kin relationships. In ad d ition, Ms.Ascher acknowl-
edges that as one views the mathema tical ideas of oth-
ers in their cu ltu ral context, one is limited by his or
her own cul tura l and mathematical frameworks. Fol-
lowing this importan t introduction, Ms.Ascher guides
the reader on an exciting joumey that explores nu-
merous mat hematical ideas in a variety of cultural
contexts.
Chapter 1 focuses on the concept of numbers and the
words, symbols, and understanding associated with
them. The sets of number words of several cultures
are examined and the pattems and arithmetic rela-
tionships are described. The importance of langu age
and its relationship to number words is emphasized
and Ascher includes a clear and informative d iscus-
sion of num era l classifiers. She devotes a substantive
portion of this chapter to a discussion of the Incas and
the organizati on and use of qu ipus within their cu l-
ture.
Graph theory is the focus of Chapter 2. It is here that
Ascher examines the san d tracings of the Bushoong
and Tsho kwe in Afr ica, and th e drawi ngs of the
Malekula of the South Pacific. She clearly establishes
the fact that many differen t peoples have pondered
similar mathematical problems relating to Eulerian
paths and provides an excellent background discus-
sion of the Bushoong, Tshokwe and Malekulan cul-
tures as she exp lores graph theory ideas within the
respective cultures.
In Chapter 3, Ascher explores the important math-
ematical idea of relations or the specified properties
that link pa irs of objects. She d oes this by examining
the logicof kin relations . The native peoples of north-
ern Australia (the WarlpirD a grou p with a parti cu-
larly comp lexkin system provide an excellent example
that forms the basis for this discuss ion which draws
upon ideas from group theory.
Games of strategy and chance and the logic of puzzles
provide the basis for Chapter 4. Since every game
can be seen as an expression of a pa rticu lar cultu re,
Ascher is careful to identify not just the rules of the
game but also the simple objects used for it, the times
and places for ap propriate playing of the game, the
HumanisticMathematicsNetwork Journal #14
social settings, the level of concentration, the systems
of rewards and all the other important aspects that
make up the game. She includes an analysis of the
American Indi an game of Dish that is clearly rooted
in the area of probab ility. This chapter also provides
an excellent discussion of the Maori game of strategy
know n as Mu torcre. Starting with a simpler version,
Ascher leads the reader not only to an understanding
of how to play Mu torere but also to a basic under-
standing of the mat he matics connected with this
game. Acollection of river crossing puzzles from vari-
ous cultures and the logic behind their solutions pro-
vide the final area of focus for this chap ter.
The organization and modeling of space and time
provides the content for Chapter 5. Because notions
of time and space are so ba sic to the way we perceive,
st ruc ture, and interpret our experiences, it is some-
times hard to understand or visualize the space-time
ideas of other cultures . Nevertheless, Ascher success-
fully bridges this po ten tial difficulty by her choice of
examp les. She includes apt discussions on the dy-
namic universe of the Navajo, the unique process and
change dimension of the space-time concerns of the
lniut, and the navigational processes of the Caroline
Islanders.
Spatial configuration is the basis of Chap ter 6 which
focuses part icularly on symmetric strip decora tions .
Ascher includes an introductory d iscuss ion of
isometries, symmetry, and symmetry groups and de-
scribes and utilizes a four character naming scheme
for the possible strip patterns. (This scheme wa s de-
veloped by Russian crys tallographers and is now ac-
cepted as the interna tional standard.) A discussion of
perfect colorin g is also included in this chapter. Rafter
pa tterns of the Maori and str ip patterns found on Inca
pottery provide bea utifu l and illus tra tive examples
for the discussion of strip patterns in this chapter.
The final chapter of the boo k affords Marcia Ascher
an opportuni ty to weave together the ma thematical
ideas and phi losophies that are the basis for her boo k.
She connects these ideas and issues to mathema tics
educa tion, emphasizing the need for a redefinition of
the boundaries of mathem atics, and a revision of our
philosophy and history of ma thematics.
This out standing book is a clearly written text that is
well-suited for the college undergraduate level. The
diverse collection of ma the ma tical ideas in their cul-
tural context provides a challenging yet very interest-
ing array of mathematical topics. Ascher provides
extensive notes with appropriate references which
afford the reader additional sources for reading and
scholarship. Marcia Ascher's book Ethnomathematics:
A Multicultural View ofMathematical Ideas is a rare gem
of a book. Read it!
Psychosis
Lee Goldstein
Nooscop ic insociability
Can drive the human intelligence of an incognizable numinosity,
Thenceforw ard, to the equations of the sphere,
Whi le this programmatic transposition
Can also beget, through the unconscious, an incipient eidos
That splits the per sonal
And abets an insurgence of psychical energies
Unto the hallucinatory;
That is seeming or chaotic.
nooscopic: pertaining to the examina tion of the mind
Humanistic Mathematics Network Journal #14 41


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