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Ethnomodeling: A Pedagogical Action for
the Ethnomathematics Program
Dr. Milton Rosa
Encina P.H.S.
San Juan U.S.D.
Dr. Daniel C. Orey
California State University,
Sacramento
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Introduction
Our work involves the
consideration of
mathematics as:
• An expression of human
development, culture, and
language.
• An integral part of the
cultural heritage of
humankind.
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Introduction
Mathematical reasoning is influenced by the vast diversity of human characteristics such as culture, languages, religions, morals, and environmental, economical, social, and political activities.
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Introduction
Each cultural group has its own way of doing mathematics, especially in the way that they quantified and used numbers, geometric forms and relationships, measured or classified objects in their own environment.
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Introduction
• Each cultural group has
developed its own way to
mathematize their own
realities.
• Mathematization is a process
in which individuals from
different cultural groups come
up with different mathematical
tools that can help them to
solve specific problems
located in the context of their
real-life situation.
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Introduction
Disrespect of and refusal to
acknowledge a cultural
identity by some educators,
scientists, and mathematicians
puts all processes of
understanding and
comprehension of many non-
Western cultural systems at
risk (D’Ambrosio, 1985, Zaslavsky, 1996).
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Introduction
A search for new methodological
approaches is necessary to record
historical forms of mathematical
ideas that occur in different cultural
contexts.
It is necessary to search for
mathematical ethnomodels that can
translate our deepening
understanding of both real world
situations and diverse cultural
contexts.
Ethnomathematics
Ethnomathematics can be understood as the region of
intersection between cultural anthropology and academic
mathematics that utilizes mathematical modeling to
solve problems taken from reality (D’Ambrosio, 1990;
Rosa e Orey, 2007).
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Ethnomathematics and Modeling
• Ethnomathematics that uses the manipulations of models of reality (ethnomodels) and modeling as a strategy of mathematical education uses the codifications provided by others in place of formal language of academic mathematics (Rosa & Orey, 2007).
• Mathematical modeling is a methodology that is closer to an ethnomathematics program (D’Ambrosio, 1993; Bassanezi (2002)
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Investigations in modeling have been found to be useful in the translation of ethnomathematical contexts in order to document and study the mathematical ideas and practices found in diverse traditions (Caldeira, 2007; Ferreira, 2004; Monteiro, 2004; Rios, 2000; Rosa & Orey, 2003).
It has becoming an important tool used to describe and solve problems arising from specific systems such as cultural, economical, political, social, environmental, which brings with it numerous advantages to mathematics learning (Barbosa, 1997; Bassanezzi, 2002; Biembengut, 1999; Cross & Moscardini, 1985; Hodgson & Harpster, 1997; Orey, 2000, Rosa, 2000).
Ethnomathematics and Modeling
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Ethnomodeling
Ethnomodeling is a process of elaboration of problems and questions growing from real situations that form an image or sense of an idealized version of the mathema.
Ethnomodeling essentially forms a critical analysis of the generation and production of knowledge (creativity), and forms an intellectual process for its production, the social mechanisms of institutionalization of knowledge (academics), and its transmission (education).
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Ethnomodeling
By analyzing the role of ethnomodels in reality as a whole, this holistic context allows those engaged in the ethnomodeling process to study systems taken from the reality of diverse cultural groups in which there is an equal effort made by these groups to create an understanding of all components of the system as well as the interrelationships among them (D’Ambrosio, 1993; Bassanezi, 2002; Rosa & Orey, 2003).
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Ethnomodeling
The use of ethnomodeling as pedagogical action for an ethnomathematics program values the previous knowledge of the community by developing students’ capacity to assess the process of elaborating a mathematical model (ethnomodel) in its different applications and contexts by having started with the social context, reality and interests of the students and not by enforcing a set of external values and curriculum without context or meaning for the learner (Bassanezi, 2002).
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Ethnomodeling studies
the mathematical ideas
and procedures
elaborated by different
cultural groups.
It involves the
mathematical practices
that are present in
diverse situations in the
daily lives of members
of these diverse groups.
Ethnomodeling
This interpretation is
based on D’Ambrosio’s
(1990) trinomial:
Ethnomodeling
It is necessary for school curriculum, to
translate the interpretations and contributions
of ethnomathematical knowledge into
systemized mathematics through
ethnomodeling because students will be able to
analyze the connection between both
traditional and non-traditional learning
settings.
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Ethnomodeling
By using ethnomodeling, teaching
is much more than the transferance
of knowledge because teaching
becomes an activity that
introduces the creation of
knowledge (Freire, 1998).
This approach in mathematics
education is the antithesis of
turning students into containers to
be filled with information (Freire,
1970).
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The Mayan Example
(Rosa & Orey, 2007)
Decoding Messages Using the Sacred Mayan Mat Pattern
(Mexico and Guatemala)
The Sioux Example
(Orey, 2000)
The Tipi of the
Sioux
(United States)
Tripodal versus
quadripodal
Foundations
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The Sioux Example
(Orey, 2000)
The Geometry of the Base
of the Tipi
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The Freedom Quilt Example
(Rosa & Orey, 2009)
Shoofly told them to dress
up in cotton… Slaves knew
that Shoofly was someone to
be trusted or was someone
among friends or a friendly
guide who is nearby and
could help them to runaway.
(United States and Brazil?)
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The Freedom Quilt Example
(Rosa & Orey, 2009)
Modeling the Shoo Fly Quilt
Block: Reflection over the line y =
-x
When a point is reflected over the
line y = -x, the x the y coordinates
change place and they are negated.
The mapping for this reflection is
P(x, y) P'(-y,-x). In so doing the
coordinates of the image of the
three points are A(9,3)A'(3,9),
B(-3,-9)B'(-9,-3), and
C(3,3)C'(-3,-3)
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The Wall Example
(Rosa & Orey, 2010)
Modeling the Wall
Catenaries or Parabolas?
(Ouro Preto, Minas
Gerais, Brasil)
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The Wall Example
(Rosa & Orey, 2010)
After examining the data
collected when we
measured various curves on
the wall and trying to fit
them to the exponential,
quadratic, and catenary
functions through
mathematical models we
came to the conclusion that
the curves on the wall
approximate to the
catenary curve.23
The California State University Sacramento
Math Trail
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Ethnomodeling: A Controversial Issue
Água e Óleo: Etnomatemática e Modelagem?
[Water and Oil: Ethnomathematics and
Modeling] (Scandiuzzi, 2002, BOLEMA)
Vinho e Queijo: Etnomatemática e
Modelagem! [Wine and Cheese:
Ethnomathematics and Modeling! (Rosa &
Orey, 2003, BOLEMA)
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Ethnomodeling: A Controversial Issue
Modelagem Matemática e Etnomatemática no Contexto
da Educaçào Matemática: Aspectos Filosóficos e
Epistemológicos [Mathematical Modeling and
Ethnomathematics in the Context of Mathematics
Education: Philosophical and Epistemological Aspects
(Klüber, 2007).
Coming Soon…
Alho e Sal: Etnomatemática com Modelagem [Garlic and
Salt: Ethnomathematics with Modeling] (Rosa e Orey,
2010)
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Final Considerations
We would like to broaden the
discussion of possibilities for
the inclusion of ethnomodeling
as pedagogical action for the
ethnomathematics program,
which respects the social and
cultural diversity of all people
in order to guarantee the
development of understanding
our differences through
dialogue and respect.
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See you next time!
Até uma próxima vez!
Thank you!
Obrigado!
¡Gracias!
Merci!
Dhanyabaad!
Toda Raba!
Baie Dankie!
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