California State University, Sacramento
Department of Teacher Education
Title:
From Reality to Mathematical Modeling: A Proposal for Using Ethnomathematical
Knowledge
Type:
M.A. Thesis in Education – Curriculum and Instruction – Mathematics
Author:
Rosa, Milton
Committee
Chair:
Dr. Daniel C.Orey
Department
Chair:
Dr. Edward Arnsdorf
Fall 2000
Abstract
Statement of
Problem
Based
on review of the literature, there is a need for curriculum reform in mathematics.The
literature supports the view that ethnomathematics and mathematical modeling
can provide tolls needed to move the curriculum reform forward.New
concepts for mathematics curriculum call for the use of different methodologies
and strategies to ascertain students’ development in mathematical thinking
and understanding.Additionally,
mathematics curriculum reform would benefit students by introducing a curriculum
that demonstrates the evolving nature of mathematics and its connections
with real-world problems.It is important
to apply ethnomathematics as pedagogical action and mathematical modeling
as methodology to understand that mathematics provides mathematical models
to explain real-life situations.It
is the purpose of this study to investigate the importance of ethnomathematics
and mathematical modeling in the mathematics curriculum in elementary,
middle and high schools.
Problems of the Study
No
specific guidelines are offered concerning the extend to which the curriculum
should be influenced by ethnomathematics and mathematical modeling.At
a time when even modest reform efforts are being attacked, it is especially
important that research made in this field answer fundamental questions
such as:
-
How
extensively can teachers include ethnomathematics and mathematical modeling
in the curriculum and be assured that their students are learning the mathematics
that they will be held accountable for on standardized examinations?
·How
much of the traditional mathematics curriculum can be supplanted by the
study of ethnomathematics and mathematical modeling?
·What
ways do the use of ethnomathematics and mathematical modeling benefit students?
-
What
ways do the use of ethnomathematics and mathematical modeling affect the
teacher?
Sources of
Data
The
information was gathered through a review of related literature gleaned
from both library and internet resources.Books,
thesis and articles were analyzed according to literature in support of
the infusion of ethnomathematics and mathematical modeling into the mathematics
curriculum.Ethnomathematics
as pedagogical action, mathematical modeling as methodology, and mathematical
models as strategies are a relatively recent phenomenon.The
author also utilized as literature non-English books and non-English journal
articles gleaned from various sources in
the archives at Pontifícia Universidade Católica de Campinas
(PUCC) in Campinas, São Paulo, Brazil.
Definitions
·Ethnomathematicsshould
be understood in a broader sense: the prefix ethno is today accepted
as a very broad term that refers to the social-cultural context, and therefore
includes as language, jargon, and codes of behavior, myths, and symbols.The
derivation mathema means to explain, to know, to understand, and to do
activities such as ciphering, measuring, classifying, ordering, inferring,
and modeling.The suffix tics is
derived from techne, and has the same root as art and technique (D’Ambrosio,
1985, 1990).
·Mathematical
Modeling
as defined by Bassanezi (1990, 1994) uses mathematics as a language for
understanding, simplification and resolution of real world problems and
activities. Data gleaned from these studies are used to make forecasts
and modifications pertaining to the objects initially studied.Mathematical
Modeling can also be interpreted as a dynamic process used to understand
a problem or situation of interest in Physics, Chemistry, Biology, or any
other field of the human knowledge.
Conclusions
Reached
In addition
to teaching students just techniques and tools to solve mathematical problems,
one of the most important objectives in teaching mathematics should be
the development of a mathematical capacity in students.All
students need to learn more than mere basic mathematical algorithms.They
need to extend their understanding to include how mathematics connects
to other disciplines, to problems in society and the environment, and how
diverse people around the world use it.Concepts
related to ethnomathematics and mathematical modeling has been investigated
to help students and teachers to discover the relationship between mathematics,
real-world and daily life.The literature
demonstrates that ethnomathematics and mathematical modeling encourages
the development of a learning environment that allows for the contribution
of mathematical learning in the context of its relationship with other
areas of human understanding.The
development of this form of understanding and problem solving gives mathematics
a large area to explore for learners, researchers, educators and teachers.Ethnomathematics
and mathematical modeling create a learning environment that senses the
applicability and practicality in concrete situations.This
assists students to resolve day-to-day problems that are diagnosed and
elaborated during the process of doing research.Ethnomathematics
and mathematical modeling amplify the knowledge of the subject being studied
and help students to understand, explain and reflect upon their own reality.
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Milton
Rosa
Brazilian
Exchange Mathematics teacher at Encina High School
Mathematics
Department
1400
Bell Street, Sacramento, CA 95825
M.A.
Education - Curriculum and Instruction - Mathematics