International Study Group on Ethnomathematics
Volume 14 Number
1 January
2003
Hello Pedro,
My name is Tod Shockey and I've been trying to help edit the newsletter
for the past year. Here are a few items that I have accumulated for the
newsletter that you might consider including. If I can offer any assistance
please let me know.
Cheers,
Tod
Tod L Shockey, Ph.D.
Assistant Professor
Department of Computer Science, Mathematics & Statistics
Email de 21/10/02
Book Review by Claudia Zaslavsky
Bazin, Maurice, Modesto Tamez, and the Exploratorium Teacher Institutue.
Math
and Science Across Cultures; Activities and Investigations from the
Exploratorium. New York: The New Press, 2002. Pb, 192 pp, $19.95.
1-56584-541-2.
This
collection of fourteen inquiry-based activities was developed by the staff of
the famed San Francisco Exploratorium, working with teachers and students over
a period of several years. Subjects include ancient Egyptian numeration, the
quipus of the Inca, a game of solitaire from Madagascar, Maya numeration and
calendars, patterns in basket weaving of many cultures, and much more. During a
visit to the United States, Paulus Gerdes created the activity dealing with
African sona sand drawings.
Mathematical concepts are developed clearly in both the math and science
activities.
Each of these
“hands-on and minds-on” activities is carefully designed to engage the students
in discovery and encourage creativity. Symbols placed at strategic places
suggest that the student stop reading and try an experiment or investigation.
Each chapter is self-contained and can be used independently. Teachers of
middle and secondary classes, of inservice courses, and of liberal arts college
courses, will find this a valuable collection.
_______________________
Ethnomathematics
Place in Teacher Preparation Programs
By: Amy Dyal - Graduate student at the
University of Florida.
I was a first semester graduate student at the
University of Florida, before I was ever introduced to the idea of Ethnomathematics. I decided to enroll in a Multicultural
Mathematics course that introduced the idea of connecting math to the student’s
culture.
There were two main components to this class: activities and core course
component presentations. First, the activities introduced me to
ethnomathematics and sparked my curiosity.
The activities were lesson plans or activities that involved mathematics
and were developed based on one of five regions: Africa, Asia, Europe, North
America, and Central and South America.
The activities identified the various ways people used mathematics in
their day-to-day activities, such as sewing and/or quilting, games, trade,
building construction, calendars and time, etc. Secondly, the presentations
gave me more information on ethnomathematics, including background on what it
is, why we should use this method in the classroom, groups or individuals
related to invention of ethnomathematics, etc.
For the presentations we were divided into groups of two and assigned a
topic to present to the class. My
partner and I received “ethnomathematics,” and up until this point we had only
discussed multicultural education and had never been introduced to the term
ethnomathematics. However, we quickly
learned they were closely related. We
researched the topic a lot for our presentation, but my curiousity did not stop
there. Afterwards, I still continued to
research the topic because it seemed like a great approach to teaching
mathematics.
As a child, I was often intimidated by
mathematics because it seemed so abstract and/or distant from my everyday
life. As a child, you wanted and
possibly even need to make personal connections to truly understand the
idea. While I always received good
grades in mathematics, I never truly understood the ideas presented to me, I
simply did the algorithms and procedures given to me by the textbook or the
teacher. However, this only led to a superficial understanding of the material
and I was unable to apply those concepts into other situations. Often I would
have to be re-taught those same procedures in later mathematics classes.
However, if I would have been taught using ethnomathematics, I feel things
would have been better or easier for me. I would have greatly benefited from
the connections between math and my day-to-day life. Mathematics can be found
in sewing, calendars, architecture, trade, and many other things that I
willingly participate in without even realizing the mathematics that is
involved. Participating in explorations, as an elementary student like those in
my multicultural mathematics class, would of allowed me to build
self-confidence in mathematics, realize that it can be “conquered” and that I
can be successful in mathematics.
Not only did these explorations, presentations,
and individual research I did make me think about my mathematics as a young
student, but it also made me think critically about my previous mathematics
methods course. Why had I not been
introduced ethnomathematics before?
Creating a personal connection for students is a central component of
all my other methods courses. Why are
teacher preparation courses in mathematics behind, when mathematics is a
subject that most often alienates or intimidates students?
Ethnomathematics has so many positive benefits
for students. First, as stated before,
it creates a personal connection that other teaching styles or methods simply
do not provide. Students, especially at
the elementary school level, need to see the material they are learning is useful
in their everyday lives. They need to
see the value of learning the material presented to them. Students will be more interested and engaged
in activities they feel benefit them in some way. Secondly, it allows students to develop a sense of pride in their
culture. When students see contributions their culture has made to mathematics,
no matter how big or small, they will develop a sense of pride about who they
are and where they come from. This
pride will transfer over into self-confidence and will help them to take risks
that they were unwilling to take before.
Also, students acquire self-confidence by realizing they have been using
mathematics, without even knowing it, in many of their daily activities. Ethnomathematics also helps to foster
tolerance and acceptance among the children because they learn that each
culture is valuable. As you can see,
helping the students to create a personal connection with the mathematical
material will affect so many aspects of that child’s life.
As a student of mathematics, I was able to
experience the positive benefits of ethnomathematics firsthand. I am extremely disappointed that I had not
been introduced to this method, or teaching approach, before graduate school.
Ethnomathematics should be part of all teacher preparation courses. There are many future teachers who did not
attend graduate school or who decide to enroll in another math methods course
and as a result they missed the opportunity to learn about
ethnomathematics. I have several
friends who just graduated from another university, and I asked them if they
had ever heard of ethnomathematics. Unfortunately, they all answered no. As a
result, their students will not be receiving this type of instruction. I
believe learning about and implementing ethnomathematics in the their future curriculum
will allow their students to truly understand mathematical content and make
them all want to become life-long mathematicians.
Contact: amydyal@yahoo.com
Check out www.webCT.com/math,
and then click on Math Medley to hear a radio talk show with guest Gloria
Gilmer. Math Medley is a weekly call-in talk radio show, hosted by Pat
Kenschaft from the Department of Mathematical Sciences at Montclair State
University. Each show features an interview with a guest discussing a topic
with an underlying theme of mathematics such as education, parenting, equity,
or the environment.
__________________________
Hello Pedro,
Here is one more site to consider for the newsletter, this was submitted
by Marcia Ascher.
http://redescolar.ilce.edu.mx/redescolar/act_permanentes/mate/kolam01.htm
__________________________
Dom Pepe -
Eduardo asked me to do a write up for HPM, you can use it if you wnat
for the next newsletter.here it is:
http://www.csus.edu/indiv/o/oreyd/hpm.html
__________________________
II
CIEM: Report on the International Congress on Ethnomathematics in Ouro Preto, Brazil.
5-7 August 2002
Ouro Preto, Brazil
History
and Pedagogy of Mathematics Newsletter
The 2nd International Congress on
Ethnomathematics (II CIEM) met 5-7 August
2002. Ouro Preto, Brazil Over 300 participants from 19 countries came
from; South Africa, Germany, Brazil,
Canada, Denmark, Spain, United States, Greece,
Guatemala, India, Italy, Japan, Mexico, Mozambique, New Zealand, Peru,
Portugal, United Kingdom and Zimbabwe.
The conference began with a moving tribute to Paulo Freire: entitled:
“Paulo Freire´s Contribution to the Epistemology of Ethnomathematics”. During
the conference four lectures were given:
Terezinha Rios spoke about the
“Philosophy of Education and
Ethnomathematics Perspectives”; .Emmanuel Lizcano talked was titled “The
Mathematics of the European Tribe: A
Case Study; Prof. Eduardo Sebastiani shared his experience with
Ethnomathematics in national Perspective of Brazil. The conference ended with a moving lecture given by Ubiratan D’Ambrosio entitled
“Ethnomathematics an Overview”. The
conference was organized as well around
6 Round Tables:
1- Ethnomathematics and
Indigenous: Coordinated by: Bill Barton, New
Zealand:
2- Ethnomathematics and
Rural Education: Coordinated by: Gelsa
Knijnik, Brazil
3- Ethnomathematics and its
Theory: Coordinated by: Maria do Carmo Domite, Brazil
4- Ethnomathematics
Urban Education: Coordinated by: Arthur Powell, United States;
5- Ethnomathematics and
Teaching Qualification: Coordinated by: Lawrence Shirley, United States;
6- Ethnomathematics
through History: Coordinated by: Franco Favilli, Italy
Two poster sessions allowed over 90 posters to
be presented and discussed by conference participants. The posters showed the
real diversity found in the emerging
field of ethnomathematics. II CIEM
also added a new activity, the presentation of
the 1st Ubiratan D’Ambrosio Prize which was awarded for the most
significant work in ethnomathematics. The award was given for work in:
• Teacher Education: Helena Dória de Oliveira
• Rural Education: Franco Favilli, Laura Maffei and Irene Venturi
• Indigenous Education: Ieda Maria Giogo
• Urban Education: Josinalva Menezes, Simone da Silva and Rosália da Silva
• History /Epistemology: Roseli Correa, Caroline dos Passos and Dirceu dos Santos.
The III International Congress on
Ethnomathematics will take place in Auckland, New Zealand in 2006. For further information related to future
ethnomathematics activities we invite the
reader to go to: ISGEm International Study Group on Ethnomathematics (http://www.rpi.edu/%7Eeglash/isgem.htm).
For more information and a copy of the
CD Rom, contact Prof. Eduardo Sebastiani at: sebastiani@uol.com.br.
Daniel Clark Orey -
California State University, Sacramento - http://www.csus.edu/indiv/o/oreyd/
__________________________
Hello Pedro,
That last ISGEm newsletter was January 2002, Volume 16, Number 3.
Thanks,
Tod
__________________________
Etnomatemática e
hortaliças: caminhos facilitadores da vida cotidiana dos horticultores
Francisco de A. Bandeira
Bernadete B. Morey
Gramorezinho, comunidade
situada no litoral norte da cidade de Natal (RN), originou-se na década de 50
quando um grande número de famílias, fugindo da seca, emigrou do interior do
estado. Hoje conta com 300 famílias que vivem da cultura de hortaliças (alface,
coentro, cebolinha e pimentão). Na comunidade há duas escolas municipais do ensino
fundamental. Não há transporte coletivo, posto médico e nem posto policial. As
ruas não são calçadas e não dispõem de saneamento básico.
A produção de hortaliças
em Gramorezinho é caracterizada por pequenas propriedades familiares nas quais
trabalham no máximo quatro pessoas de uma família. Quase não se emprega mão de
obra assalariada.
As propriedades são
hortas irrigadas com água da Lagoa de Gramoré, adubadas com adubo comprado do
aviário, contendo no máximo 90 leiras de 20 metros de comprimento por 2 metros
de largura.
Os horticultores
trabalham na horta todos os dias, desde o nascer ao pôr do sol, o que em Natal
habitualmente acontece às cinco horas da manhã e às seis horas da tarde. A
única exceção é aos domingos, dia em que eles vão para casa descansar depois da
irrigação da horta pela manhã.
Detectamos práticas
específicas elaboradas pelos agricultores que já foram incorporadas na sua
rotina de trabalho. Tais práticas se revelam tanto na etapa da produção como na
etapa da comercialização das hortaliças. Das práticas da etapa de produção
observamos o “par de cinco”, a utilização de medidas não oficiais de
comprimento e volume, contagem de tempo pelos processos naturais, etc.
O “par de cinco”. As hortaliças, à medida que vão
sendo colhidas, são amontoadas no chão, dentro da leira, em grupos de cinco
unidades (cinco pés de alface, cinco molhos de coentro, cinco molhos de
cebolinha), o “par de cinco”. Depois de ter uma determinada quantidade de
hortaliça colhida, o horticultor toma um saco de farinha de trigo aberto e vai
passando para ali as hortaliças, contabilizando a quantidade de “par de cinco”.
Havendo, numa trouxa, duzentos molhos de coentro, o horticultor os contabiliza
como quarenta “par de cinco”. Pode-se ver aí um instrumento facilitar da
atividade do horticultor, onde agrupamentos de cinco aparece como uma base
auxiliar do sistema de base dez.
Medidas não oficiais. As medidas oficiais (centímetro,
metro) são utilizadas em ocasiões como na construção de leiras, o que é feito
raramente. Já nas atividades diárias, se utilizam medidas não oficiais como o
palmo, ou mesmo o pé, como na horta de seu Edvaldo. Tanto o palmo como o pé são
utilizados no momento do plantio das hortaliças (no espaçamento entre as mudas
de alface, cebolinha e pimentão, na distância entre as covas de coentro). Na
medição do adubo, seja na etapa da comercialização ou na adubação das leiras,
comumente se usam latas, carrinhos de mão e outras medidas informais como
subdivisões do metro cúbico.
O controle de adubação
das hortaliças é feito observando o tamanho e/ou aparência das mesmas. Esse
procedimento de observar o tamanho e/ou aparência das hortaliças para, em
seguida, aplicar a adubação necessária, ocorre também com o período da
colheita, ou seja, os horticultores não registram a data que as hortaliças
devam ser colhidas. Aqui podemos ver uma noção de tempo intrinsecamente ligada
aos processos que decorrem na natureza. O tempo é quantificado pelos processos
que vão surgindo: germinação, crescimento
das plantas, cor das folhas, etc.
À etapa de
comercialização nós relacionamos procedimentos tais como: cálculo do custo de
produção das hortaliças, cálculo do preço de venda, avaliação do lucro obtido.
Os horticultores
mencionaram como custo de produção das hortaliças, em sua maioria, apenas as
despesas com adubo e sementes de coentro. De fato, pouquíssimos horticultores
utilizam mão de obra assalariada, mas gastos com energia elétrica (para a bomba
d’água), impostos, utensílios com pás, enxadas, foram mencionados apenas por um dos entrevistados.
O preço de venda das
hortaliças depende de vários fatores tais como, a época do ano (inverno ou
verão), presença ou não de chuvas e oferta ou não de hortaliças de outras
regiões do interior do Rio Grande do Norte, fatores estes sobre as quais o
horticultor não tem controle. Resta-lhes apenas estabelecer uma
proporcionalidade no plantio de hortaliças de acordo com a demanda (mais
coentro, menos alface, etc.).
Para os horticultores, o
lucro está associado à quantidade de hortaliças vendidas e à localização das
feiras. Eles não têm idéia precisa do ganho que auferem de sua atividade.
Conforme nos relatou José Vieira, em 01/02/01, “não tenho base mais ou menos
não, porque não tem um canto de controle. As vez dá mais, as vez dá menos”.
As práticas relacionadas
com a produção das hortaliças nos pareceram eficazes e nelas percebemos a
intenção de FACILITAR o trabalho diário dos horticultores;
Algumas das práticas
relacionadas com a comercialização das hortaliças nos pareceram DESVANTAJOSAS
para os horticultores e merecem uma investigação mais cuidadosa. Tal
investigação nos ajudaria a esclarecer se, de fato, a falta de um instrumento
de contabilidade e administração de sua atividade está levando os agricultores
a ter seu ganho minimizado. Caso isto se confirme, seria o caso de propor-lhes
algum tipo de ação conjunta que os ajudasse na administração dos aspectos
econômicos de sua horticultura.
______________________
______________________
______________________