Gloria Gilmer, ISGEm Chair
Milwaukee, WI USA
13100 Campinas, SP BRASIL
Gilbert J. Cuevas
Coral Gables, FL USA
Patrick (Rick) Scott
Albuquerque, NM USA
A business meeting of ISGEm will be held on Tuesday, April 7, 1987 at the Annual Meeting of the National Council of Teachers of Mathematics (NCTM) in Anaheim, California. The meeting will be in Room XXX of the Convention Center from 3:00 to 5:00 PM. All persons interested in Ethnomathematics are encouraged to attend.
Another important activity at the Anaheim meeting will be a Research Section on Ethnomathematics on Friday, April 10, from 10:00 to 11:00 AM in the Orange Room of the Convention Center. Gloria Gilmer, ISGEm Chair, will be presiding. Ubiratan D'Ambrosio of UNICAMP in Brazil will speak on "Socio- Cultural Bases of Mathematics Education: Research Status Worldwide." Marilyn Frankenstein of U-Mass, Boston, will make a presentation on "Teaching Mathematics in a More Useful Way to Public and Community Service Workers."
"Have You Seen" is a feature of the ISGEm Newsletter in which works related to Ethnomathematics can be reviewed. We encourage all those interested to contribute to this column. Contributions can be sent to:
Rick Scott, Editor
College of Education
University of New Mexico
Albuquerque, NM 87131 USA
On Culture, Geometrical Thinking and Mathematics Education by Paulus Gerdes in Cultural Dynamics, Vol. 2, 1987.
In analyzing some of the social and cultural aspects of Mathematics Education in Third World countries Professor Gerdes of Eduardo Mondlane University in Mozambique quoted many ideas of Ubiritam D'Ambrosio. He stressed that formal school Mathematics is a common "barrier to social access" and that there often exists a "psychological blockage" between "learned materacy" and "spontaneous matheracy". He also referenced the work of Gay and Cole, and others, on the necessity of incorporating indigenous Mathematics (Ethnomathematics) into the curriculum, and suggested that thus a "cultural-mathematical-reaffirmation" and a resulting regaining of "cultural confidence" is possible in Third World countries.
He then provided examples of the kinds of methodology that can be used in Mathematics teacher education to uncover mathematical traditions that may be "hidden" or "frozen". The examples are from Mozambique culture:
Studying alternate axiomatic constructions of Euclidean geometry based on how houses are built.
An alternate construction of regular polygons by considering how artisans weave funnels.
Rediscovering the Theorem of Pytha goras by studying the technique used in weaving square buttons.
A consideration of traditional fishtraps leading to alternate circular functions, soccer balls and (semi) regular polyhedra.
Socio-Cultural Bases for Mathematics Educaction by Ubiratan D'Ambrosio, Campinas, Brazil: UNICAMP, 1985.
This small, powerful book is a back- ground paper for the plenary address given at the 5th International Con- gress of Mathematics Education. In it D'Ambrosio presents "the texture of what might be called Mathematics Education with a special emphasis on its social role."
Chapter 1 considers the issue of creativity and culture. D'Ambrosio reviews many conceptions of creativity and stresses the difficulty of arriving at a satisfactory definition. He indi- cates that on the one hand creativity demands that "we transgress limits or extend existing limits" while at the same time it "depends on some form of acceptance, of legitimation." The creative individual must somehow become immersed in the reality of the socio/ cultural/ natural environment, reflect on that reality, and then choose a course of action (a continuous cycle of individual, reality, action). The consideration of creativity leads to a look at the relationship between power and knowledge, particularly as it has concerned the relationship between countries of the Western World and those of the Third World. From there the discussion enters into a comparison of formal and nonformal education. D'Ambrosio suggests that nonformal education might do much to enhance creativity by substituting a teacher with an "unemotional and uncensorious" piece of equipment, as well as removing the "tensions caused by the evaluation process."
In Chapter 2, "Mathematics as a Cultural System: Literacy and 'Matheracy'" the point made by Wilder that all cultural groups develop their own Mathematics is stressed. D'Ambrosio uses the term introduced by Kawaguchi, "matheracy", to describe the "use of numbers, of quanti-ties, the capability of qualifying and quatifying and some pattern of infer- ence." "Unmatheracy is very rare, al- most as rare as incapability of language communication." However, D'Ambrosio suggests that the "spontaneous mathe- racy" that is so common among the unschooled is often eliminated by the "learned matheracy" of the school. The distinct, formal approaches to mathe- matics presented in schools create a "psychological blockage" between the different modes of mathematical thought that on the one hand degrades the value of that which is "spontaneous" while at the same time it impedes the acquisition of that which would be "learned" in school. The increasing technological presence in Third World countries demands improved mathematical compe- tence, but spontaneous abilities are "downgraded, repressed and forgotten." D'Ambrosio is led to the conclusion that the student becomes alienated from his reality, and thus the possiblity for creativity through reflection and action on that reality is severely curtailed.
"The Changing Mood of Students and a New Role for Teachers" are explored in Chap-ter 3. D'Ambrosio focuses on secondary school students in Third World countries who he says are a privileged group in society with a growing level of politicization, social concern and commitment to change. The introduction of a diversified curriculum in a rapidly expanded system has led to the hiring of many unqualified teachers. Almost all teachers appear to be unprepared to teach "practical mathematics" or "useful mathematics". Some countries are thus reverting to a system based on the "academic model, with optional professional training". Although D'Ambrosio assures us that prediction of what will happen at the secondary level is very difficult, "the updating of teachers in Mathematics for the secondary level requires three components which have been practically disregarded in traditional training: modelling, interdisciplinarity and social studies of mathematics." He defines the Social Studies of Mathematics" as "social history, philosophy, and a critical appreciation of the role of mathematics in development."
Chapter 4 deals with "Schooling and Out-of-School Mathematical Experience: Ethnomathematics." D'Ambrosio suggests that elementary education in the future will focus on calculating (with calculators!), reading, writing and information retrieving and simulating." Although this means that differently prepared adolescents will be entering secondary schools, strong conservative forces at that level will be calling for still more "back to the basics" to pre- pare students to pass university entrance examinations. He pleads that conservative views of Mathematics must be broken up. Ethnomathematics is a part of the reality of many Third World students. It therefore must be incorporated into the curriculum if the increasingly important formal Mathematics is also to be learned.
In Chapter 5, "Curriculum Development and Research Priorities," D'Ambrosio interprets "curriculum as the strategy for educational action." He urges anthropological research in mathematics to serve as "the underlying ground upon which we will develop curriculum." He characterizes the distinction between pure and applied Mathematics as "highly artificial and ideologically dangerous" in Third World countries." He points to a few innovative projects at the elementary level that combine "theory" with "doing" in "the construction of kites, the construction of scale models of houses, cars, etc..." Even less such work is being done at the secondary level where the emphasis is on passing university entrance examinations. He insists that "more effective efforts must be concentrated at the graduate level, to prepare trainers of teachers." "Regrettably, we notice that the less developed the country, the more formal and theoretical is its mathematics teaching." He sees hope in efforts with Ethnomathematics. "But there is much ground before the pedagogization of ethnomathmatics takes place. And even before ethnomathematics becomes recognized as valid mathematics."
Chapter 6 contains "A Brief Review of Projects and Research." D'Ambrosio points to The Journal of Undergraduate Mathematics and its Applications and The Bulletin of the Institute of Mathematics and its Applications as good sources of situations that have to do with the environmental issues in Mathematics Education. Among the promising research project he mentions are those being carried out by the Interdisciplinary Center for Research in Experimental and Mathematical Psychology in Argentina, the Interdisciplinary Center for the Improvement of Science Education in Brazil, the Experimental Project in Bilingual Education in Peru, and the work being done in the Faculty of Education's Department of Mathematics in Mozambique.
The book ends with an extensive bibliography for those interested in pursuing the socio-cultural bases for Mathematics Education.
The VII Inter-American Conference on Mathematics Education (VII IACME) will be held in Santo Domingo, the Dominican Republic, from July 12-16, 1987, at the Universidad Católica Madre y Maestra.
Throughout the VII IACME, plenary sessions and panel discussions will be held. Work and discussion groups will be organized to study certain issues of mathematics teaching relevant to the American continent, with emphasis on the particular difficulties of each level. There will also be poster sessions and displays of materials related to mathematics teaching.
The official languages of the Conference will be Spanish, English and Portuguese. The papers will be mainly presented in Spanish and English.
During VII IACME, three plenary sessions will be given by internationally known
specialists in the field of mathematics education.
Four panel discussions will be held on the following topics:
A. Integration of the sociocultural context in mathematics teaching.
B. How to develop problem solving skills in students.
C. Innovational uses of calculators and computers in mathematics teaching in Latin America.
D. How to improve geometry teaching in elementary and secondary schools.
For further information write:
Centro de Investigaciones
Universidad Católica Madre y Maestra
Apartado Postal 822
Santiago de los Caballeros
The Sixth International Congress on Mathematics Education will held from July 27 to August 3, 1988 in Budapest, Hungary. For information you can write to:
Secretary of the Organizing Committee:
ICME 6 Arrangements
Janos Bolyai Math Society
Budapest, POB 240, H-1368