Introduction
The authors of
this book first met in Brazil in 1998. One, a visiting Fulbright scholar
at the Pontifícia Universidade Católica de Campinas from California
State University in Sacramento; and the other, a Brazilian mathematics teacher
working in both a public high and middle school in Amparo in the state of
São Paulo, Brazil. The idea of this book emerged over long walks on
Brazilian beaches, numerous beers and late night conversations as the visiting
professor asked countless questions as he learned about the challenges of
mathematics education in Brazilian public schools, and the complications and
joy of a population learning about democracy. After numerous, often heated
discussions, the idea of putting this book together went from a dream to its
reality.
It is with the
many new or emerging economies entering the world stage, that many academics
have only begun to recognize the important contribution to mathematics and
science of peoples whose traditions can best be described as "non-western"
or "non-European". The study of the mathematics, and the accompanying problem
solving traditions, as developed and used by underrepresented minorities,
their non-academic uses of mathematics, often linked to numerous ancient
ways, has allowed many people to think "outside the box" as it were. It is
our hope that this book may add to the growing chorus proclaiming this interesting
phenomenon. One song just beginning to be sung, is that of ethnomathematics.
A principal goal of this book is to demonstrate that an ethnomathematical
perspective has a place as an emerging academic field of study. Ethnomathematics
offers a unique perspective to mathematicians and cultural anthropologists
alike.
There are researchers
in over twenty countries investigating the ideas as first presented by Ubiratan
D'Ambrosio of São Paulo. Much has been written about the ethnomathematical
ideas as presented by Brazil's foremost pedagogue since Paulo Freire. Over
the fifteen years since Professor D'Ambrosio outlined his idea initial thoughts
in Australia, very little has been written about the pedagogical implications
and various methods of discovering ethnomathematical data. The growing interest
and enthusiasm in this theory has fundamentally transformed the thinking of
those interested in the area of mathematics as influenced by issues of access,
equity, culture and history (Frankenstein and Powell, 1997). This transformation
is the cause for many of us to ask how we might apply this idea to our daily
lives, and teaching / learning environments.
We have observed
as schooling in both countries moves towards more accountability and testing
, that there is a need for the development of practical links between the
academic mathematics, (school and university) and the mathematics of the daily,
out of school / non-academic environment. We seek here to describe a way
in which practitioners, researchers and mathematicians alike might consider
the application of as, Ubiratan D'Ambrosio calls an "ethnomathematical pedagogical
program" to the uncovering of new forms of knowledge. It is a principal goal
of this book to assist the reader in unearthing his or her own ethnomathematical
activities. We wish to share a method that we have found useful, indeed successful
in both in São Paulo and California.
Chapter one seeks
to introduce the reader to various definitions of ethnomathematics. Chapter
two describes the process of mathematical modeling. Chapter three seeks to
outline a method we have found useful in applying mathematical modeling. Chapters
four and five illustrate numerous methods and further examples including important
connections to National Council of Teachers of Mathematics Standards. Finally
the authors seek to demonstrate the application of ethnomathematics/mathematical
modeling as organized by the transversal themes as outlined by Brazilian Ministry
of Education and Sports:
In Chapter 6
we have described some favorable / unfavorable arguments related to mathematical
modeling especially those related to students, teachers, curriculum &
pedagogy.
A further objective
for Ethnomathematics as Pedagogical Action is to encourage the reader
to develop a sense of world citizenship in all their children. To achieve
this objective, the authors of this book believe that the teaching of mathematics
must respect regional and cultural diversity. We offer here a model that will
enable children access to good mathematics by using relevant cultural resources
in order for them to fully participate in their society. In this way, our
proposal seeks to introduce the reader to goals that can help their students
to confront the real world as Paulo Freire says as "fully participant citizens".
To do this, students must be able to reflect on and develop their own opinions
and theories, while respecting those of others.
It is our hope
that this book will be useful in supporting pedagogical discussions in classes
and schools, to elaborate mathematical projects, and to plan classes and lessons.
We hope as well that this book will assist the reader to reflect on ethnomathematical
ideas as pedagogical action, and above all to assist their students in gaining
the tools they so desperately need to become fully participant citizens in
the next century.
Daniel Clark
Orey
Milton Rosa
Sacramento, California
Fall 2002