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 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?

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