Ethnomathematics as an issue on educational research
"Ethnomathematics as an issue on educational
research"
1.
Introduction
Ethnography
is a study at firsthand about what about people do and say in particular
context. Most researcher collect data though participant observation and
open-ended interviews, also from various document to understand and explain the
participant's perspectives, activities and behaviors. In other word ethnography
originally came from anthropology with aims to analyze human's way of life(or
culture) holistically, Relativistically
and comparatively. Ethno-mathematics refers
the form of mathematics that varies as consequence of being emended in cultural
activities whose purpose in the other ten doing mathematics. The mathematics
idea such as measurement, counting, classifying, etc are created from the
cultural activities of people which can be in the different nature in different
cultural base. The term ethno-mathematics
is used to express the relationship between culture and mathematics. The term
requires a dynamic terpretation because it describes concepts that are themselves
neither rigid nor singular-namely, ethno and mathematics. The term ethno
describes "all of the ingredients that make up the cultural identity of a
group: language, codes, values, jargon, beliefs, food and dress, habits, and
physical traits." Mathematics expresses a "broad view of mathematics
which includes herring, arithmetic, classifying, ordering, inferring, and
modeling".
Nepal
is multicultural society so mathematical knowledge is also generating from
different way as they use in daily life.
But great effort is also need to formulate a concept of
"mathematics for all" and final aims of this teaching as regards
conception of individual; society as well as cultural prospective. Such a
teacher should teach whole class and apply student as they like as their
culture. So here reformation demands serious answer to two basic question
"why mathematics for all"? And "which mathematics for all"?
Nepal is developing country here lack of resource of staff, science and
technology and many more. How to people understanding mathematics? Which
culture student will came from this class room? In this essay I mention
development of ethno-mathematics, relation between teacher and student as ethno-mathematics
and major issue of ethno-mathematics as research prospective.
2.
How can Ethnomathematics help children in schools?
Many
educators may be unfamiliar with the term, yet a basic understanding of it
allows teachers to expand their mathematical perceptions and more effectively
instruct their students. Teachers and the public in general do not commonly say
that mathematics and culture are connected. When teachers do acknowledge a
connection, often they engage their students in multicultural activities merely
as a curiosity. Such activities usually refer to a culture's past and to
cultures that are very remote from that of the children in the class. This
situation occurs because teachers may not understand how culture relates to
children and their learning. An important component of mathematics education
today should be to reaffirm, and in some instances to restore, the cultural
dignity of children. Although multicultural mathematics activities are
important, they should not be our final goal. As our students experience
multicultural mathematical activities that reflect the knowledge and behaviors
of people from diverse cultural environments, they not only may learn to value
the mathematics but, just as important, may develop a greater respect for those
who are different from themselves.
To
acquire these skills while maintaining cultural dignity and to be prepared for
full participation in society require more than what is offered in a
traditional curriculum. Much of today's curriculum is so disconnected from the
child's reality that it is impossible for the child to be a full participant in
it. The mathematics in many classrooms has practically nothing to do with the
world that the children are experiencing. Just as literacy has come to mean
much more than reading and writing, mathematics must also be thought of as more
than, and indeed different from, counting, calculating, sorting, or comparing.
Today's
children are living in a civilization that is dominated by mathematically based
technology and unprecedented means of communication. Much of the content of
current mathematics programs does little to help students learn the information
and skills necessary to function successfully in this new world. It is
important to recognize that students and parents have a real expectation that
school will improve opportunities for employment. This requirement means that
educators must understand the evolution of the job market. The goal of
mathematics education should be to foster students' ability to successfully use
modern technology to solve problems and communicate their thinking and answers
as they gain an awareness of the capabilities and limitations of technological
instruments.
We
can help students realize their full mathematical potential by acknowledging
the importance of culture to the identity of the child and how culture affects
how children think and learn. We must teach children to value diversity in the
mathematics classroom and to understand both the influence that culture has on
mathematics and how this influence results in different ways in which
mathematics is used and communicated. We gain such an understanding through the
study of ethnomathematics.
Ethnomathematics
encourages us to witness and struggle to understand how mathematics continues
to be culturally adapted and used by people around the planet and throughout
time. Traditionally in mathematics classrooms, the relevance of culture has
been strangely absent from the content and instruction. The result is that many
students and teachers unquestioningly believe that no connection exists between
mathematics and culture. Failing to consider other possibilities, they believe
that mathematics is a cultural, a discipline without cultural significance.
This
a cultural mathematical perspective is reflected during instruction in several
ways. First, in many classrooms, students are not permitted to construct a
personal understanding of the mathematics that is presented.
The values, traditions, beliefs, language, and
habits reflective of the culture of the students are ignored. In such
situations, the ways that children might invent personally meaningful
conceptualizations are not respected. Children are expected to assimilate
prescribed procedures by rote without necessarily gaining a deeper and
conceptually significant understanding of the mathematics that they are studying.
This
style of instruction unfortunately restricts learning to the length of time
that students accurately remember the procedures. An application of the
learning is also often context specific and poorly generalized because it is
limited to the types of problems practiced when the procedures were taught.
Students should be encouraged to construct personal mathematical understandings
and be able to explain their work. When cultural characteristics of the
children's invention, experience, and application of mathematics are realized
and respected, these students more closely resemble the budding mathematicians
we desire.
An
acultural mathematical curriculum also distorts the facts that children learn
about how mathematics has evolved and who has contributed to this evolution.
The historical contributions that are described are all too often Eurocentric,
paying homage to the fair-skinned Greeks as the purveyors of most of our
significant mathematical knowledge. Children are seldom taught that several of
the ancient Greek mathematicians, for instance, Pythagoras and Thales, the
legendary founder of Greek mathematics, traveled and studied in such places as
India and northern Africa, where they acquired much of their mathematical
knowledge. Students know little of the mathematical inventions or applications
of such ancient non-European people as the Egyptians, the Babylonians, the
Maya, and the Incas, to name but a few, because they have often not been taught
that many cultures have contributed to the development of mathematics, cultures
with members who were certainly intelligent, resourceful, and creative.
3. Dealing with cultural diversity
in the classroom
Ethnomathematics
applied in education had a Brazilian origin, but it eventually became common
practice all over the world. It has been extended from an exotic interpretation
to a way of intercultural learning that is applicable within any learning
context. Dealing with cultural diversity in the classroom is the universal context
within which each specific context has its place.
The
meaning of the ethno concept has been extended throughout its evolution. It has
been viewed as an ethnical group, a national group, a racial group, a professional
group, a group with a philosophical or ideological basis, a socio-cultural
group and a group that is based on gender or sexual identity (Powell 2002,
p.19). This list could still be completed but since lists will always be
deficient, all the more because some distinctions are relevant only in a
specific context, we use the all-embracing concept of cultural diversity. With
respect to the field of mathematics, and in line with Bishop’s (2002)
consideration on mathematics as human and cultural knowledge, there appears to
be a change in the meaning of ethnomathematics as diversity within mathematics
and within mathematical practices. This view enables us to see the comparative
culture studies regarding mathematics that describe the different mathematical
practices, not only as revealing the diversity of mathematical practices but
also to emphasize the complexity of each system. In addition there is interest
in the way that these mathematical practices arise and how they are used in the
everyday life of people who live and survive within a well-defined
socio-cultural and historical context. Consequently there has to be a
translation of this study to mathematics education where the teacher is challenged
to introduce the cultural diversity of pupil’s mathematical practices in the
curriculum since pupils also use mathematical practices in their everyday life.
4. Ethnomathematics is every class
Room.
The
extended notion ethnomathematics as dealing with pupils’ everyday mathematical
practices has equality of all pupils as its main objective. Ethnomathematics
becomes a philosophy of mathematics education where mathematical literacy is a
basic right of all pupils. The teaching process tries to reach all pupils and
tries to involve them in the learning process of mathematics, irrespective of
their cultural diversity. All pupils are equal. This notion of mathematics for
everyone fits in with the ethical concept of pedagogic optimism that is
connected with the theory of egalitarianism. By extending the notion
ethnomathematics to cultural diversity and mathematics education, the
distinction between mathematics and ethnomathematics seems to disappear. Hence
the critical question can be raised whether the achievements of
ethnomathematics will not become lost then. On the contrary the distinction between
ethnomathematics and mathematics can only disappear by acknowledging and
implementing the ethnomathematics’ achievements in the mathematics education.
The issue on the distinction between ethnomathematics and mathematics has been
raised before within the theory development of ethnomathematics. Being critical
on the dominant Western mathematics was the basis out of which ethnomathematics
has developed and now the time is right to raise the critical questions also
internally, within the field of ethnomathematics itself. What exactly
distinguishes ethnomathematics from mathematics?
UNESCO
believes that education is key to social and economic development. We work for
a sustainable world with just societies that value knowledge, promote a culture
of peace, celebrate diversity and defend human rights, achieved by providing
education for all. The mission of the UNESCO Education Sector is to provide
international leadership for creating learning societies with educational
opportunities for all populations; provide expertise and foster partnerships to
strengthen national educational leadership and the capacity of countries to offer
quality education for all. (UNESCO 1948)
Taking
into account these general stipulations we have to conclude that the explicit
values of the general education objective connect to the values of equal
chances for all pupils which are central within ethnomathematics. Consequently
the expansion of ethnomathematics as a way of teaching mathematics which takes
the diversity of pupils’ mathematical practices into account can be justified.
There is a kind of inequality in every group and the real art is to learn to
detect the skins of inequality and the skins of cultural diversity. Instead of
a depreciation of the concept ‘ethnomathematics’ this extended notion could
mean a surplus value in situations where heterogeneity and cultural diversity
are less conspicuous.
Within
ethnomathematics education two aspects are highlighted. First there is the
curriculum’s content. Often this is the first step when implementing
ethnomathematics. Besides the mathematics that can be found in the traditional
curriculum, there will now be additional space to be introduced to more exotic
or traditional mathematics practices. Powell & Frankenstein (1997) also
emphasize this aspect in their definition of the enrichment of a curriculum
through ethnomathematics. Stressing
other mathematical practices offers the opportunity to gain a better perception
in the own mathematical practice and its role and place in society (D’Ambrosio
2007a). It also offers the opportunity to philosophize and critically reflect
on the own mathematical practice. In language teaching it goes without saying
that it is better to learn more than one language. It broadens the outlook on
the world and offers a better adaptation to dealing with other people in this
globalized world. Knowledge of several languages is undoubtedly an advantage
and besides it broadens the knowledge of the mother tongue. This comparison
could even be extended to the mathematics education where knowledge of
mathematical practices of several cultural contexts and throughout time proves
to be advantageous.
5. Ethnomathematics is Human Right
D’Ambrosio,
who is the mathematician and educationist of the mathematics on which,
ethnomathematics is based, situates mathematics education within a social,
cultural and historical context. He can also be considered the first to
explicitly link mathematics education and politics. Mathematics education is a
lever for the development of the individual, national and global well-being
(D’Ambrosio 2007a, 2007b). In other words the teaching and learning of
mathematics is a mathematical practice with obviously a political grounding.
D’Ambrosio advances the political proposition that mathematics education should
be accessible to all pupils and not only to the privileged few. D’Ambrosio
develops three concepts to focus on in a new curriculum regarding the usage of
the international (UNESCO) emancipatory objectives - literacy, matheracy and
technoracy.
Literacy
has to do with communicative values and it is an opportunity to contain and use
information. Here both spoken and written language is concerned but so are
symbols and meanings, codes and numbers. Mathematical literacy is undoubtedly a
part of it. Matheracy is a tool that offers the chance to deduce, to develop
hypotheses and to draw conclusions from data. These are the base points for an
analytical and scientific attitude. Finally there is Technoracy which offers
the opportunity to become familiar with technology. This does not imply that
every pupil should or even could get an understanding of the technological
developments. This elementary form of education needs to guarantee that every
user of a technology should get to know at least the basic principles, the
possibilities and the risks in order to deal with this technology in a sensible
way or deal not at all with it. With these three forms of elementary education,
which can be developed throughout the ethnomathematics research program, D’Ambrosio
wants to meet the Universal Declaration of the Human Rights that relate to the
right to education and the right to the benefits of the scientific
developments.
6. Gestation of new concepts
Various
concepts have been proposed to provide a contract between ethnomathematics and
the academic school mathematics which had been transplanted into the school
system of developing nations. These are Indigenous Mathematics, Socio
Mathematics, Informal Mathematics, Mathematics in the socio-cultural
environment, Spontaneous Mathematics, Oral Mathematics, Oppressed mathematics,
Non-standard mathematics, Hidden Mathematics, Flock mathematics, People
mathematics, Mathematics codified, Implicit and Non-professional mathematics.
The concept associate with these term were
provisional. They arose in the context of indigenous 'Third world' thinking and
later found their expression in the other counties. The various concept
illuminated by the aforementioned provisional concept have been gradually
united under the more general common denominator of ethnomathematics.
7.
Criticisms and Contradictions on the Educational Implication of Ethnomathematics.
Ethnomathematics
carries with it a critique on school. D’Ambrosio (2003), for instance, compares
current school with a factory, where people are components of big machinery
that aims uniformity. In school, as mentioned by Rowlands and Carson (2002,
2004), we are introduced to a certain society. And if we are delighted with our
current society, as apparently is the case of Rowlands, Carson, Horsthemke and
Schäfer, then we must prepare students the best we can to be full members of
that society.
But
part of the studies in ethnomathematics does not share this optimistic view on
current society. Society should be problematized, and not taken for granted,
especially when we are aware of the economical politics based on market
priorities, and all the ideologies that
fuel our way of living (like the liberal view on mankind). What does it mean to
educate people to be participative, active authors in a more and more merchandized
society? Do we all want “schooling to serve the needs of industry and
commerce?” (Rowlands & Carson, 2002, p. 85).
Hence,
a problematization of society, and the role of school in society is, in our
opinion, a priority in a research program like ethnomathematics. But that is
far from happening. For instance, and to
speak to one of the criticisms made by Rowlands, Carson, Horsthemke and Schäfer
regarding the use of ethnomathematical knowledge in regular schools, we can
identify a contradiction on how ethnomathematicians understand this pedagogical
implications. On the one hand, as mentioned before, some researchers defend the
idea of using students’ ethnomathematical knowledge to construct a bridge for
the learning of formal mathematics. But, on the other hand, researchers like
Knijnik (2006) clearly said that: it’s not a matter of establish connections
between school mathematics and mathematics as it is used by social groups, with
the purpose of achieving a better learning of school mathematics. (p. 228)
Behind these two postures, is the way researchers understand the role of
mathematics and school in our society. The problem with the first one,
characterized by the “bridge metaphor”, is the reinforcement of the hegemony of
school mathematics because the ‘other’ is valorised only as a way to achieve
the true knowledge.
Thus,
it contradicts the critique that ethnomathematics makes to the hegemony of
academic mathematics. The same problem identified by the critics regarding the
valorisation of background instead of the foreground, is also raised by Knijnik
(2006), Monteiro (2006) and Duarte (2006). These authors raise questions about
the usually folkloric way ethnomathematical ideas appear in the curriculum.
According to them, the use of local knowledge as a curiosity to start the
learning of school mathematics could be the cause of social inequalities, as is
mentioned by the critics. But to truly contemplate ethnomathematical ideas in
the curriculum is no less problematic. If we focus on a regular school, and
take into account its role preparing students to a market orientated society,
with all the pressure to learn the mathematics of the standard curriculum that
will be essential to students’ approval in the high stakes tests, we can ask
ourselves if there is a place for ethnomathematical knowledge (or other local,
non scholar knowledge)? Our opinion, according to our review on
ethnomathematical research in Brazil, is that those educational implications
of ethnomathematics (in a regular
school) ended up being phagocytised by a school that, as Rowlands, Carson,
Horsthemke and Schäfer would agree, is worried with the uniformization of
knowledge. In that sense, we agree with them and also with Skovsmose and Vithal
when they say that focussing the learning of mathematics in students’ local
knowledge could be a factor for social exclusion. But the problem is not just
in ethnomathematics, but in school itself. Monteiro (2006), a very well
renowned ethnomathematicians makes the definitive question: “Is it possible to
developing ethnomathematical work in the current school model?” (p. 437).
Hence,
it is not just the valorisation of students’ background that should be dealt
with care, but also the valorisation of students’ foreground. Although we
realise the importance of students having the opportunity for emancipation, and
for full participation in a technological world (that is also a capitalist
world based on a liberal idea of economy that stress the individual above the social),
we should criticize ideologically loaded ideas about society. Preparing
students to become participants in a society is also preparing them to assume
critical points of view about society, different ways of thinking, acting and
doing mathematics. Using the words of D’Ambrosio, we need to emancipate
students by learning academic mathematics, but also by reinforcing its roots.
If we analyse the role of school in modern societies, this is obviously a
paradox.
Critical
mathematics education and ethnomathematics, as mentioned by Skovsmose &
Vithal (1997), have common concerns. Both developed a critique of the way
mathematics is usually understood as one of the biggest achievements of
mankind, and the intrinsic resonance (seen as something inherently good) that
feeds its education. But in the struggle for a better mathematics education,
they should take care when suggesting pedagogical proposals to be implemented
in a problematic school. Taking school for granted is the best way to
trivializing critical and ethnomathematical ideas.
8. Conclusion
A
definition is proposed for ethnomathematics as the study of mathematical
practices within context. Four types of ethnomathematical activity are
identified: descriptive, archaeological, mathematising, and analytical
activity. The definition also gives rise to a categorisation of
ethnomathematical work along three dimensions: the closeness to conventional
mathematics; the historical time; and the type of host culture. The mechanisms
of interaction between mathematical practices are identified, and the
imperialistic growth of mathematics is explained. In this paper will be There
are ethomathematicians who work within their own culture, however the
ethnomathematical part of their work is the interpretation of their own culture
(or of parts they wish to call mathematical) in a very way which is
understandable to those outside the culture. Such activity is still dependent
in a theoretical way on some concept of mathematics – a concept that, in its
international sense, is not internal to any one culture. In This paper I can
Include How can ethnomathematics help to understand mathematics knowledge.
Mathematics is cultural process. Nepal is multicultural society so
ethnomathematics help the encouraging the mathematics knowledge. Cultural diversity is commonplace in
education around the world. It has profound influence on learning and teaching.
Such a rich diversity between cultures, and therefore within mathematics as
whole can considerably enrich of quality of mathematical activities in
different classrooms around the world. The developing countries like as Nepal
that have wealth ethnomathematics in their cultures contribute toward this goal
for math for all. Mathematics learning is a socially-referenced activity in
several related ways. It involves students learning a particular set of
culturally determined ideas such that entomathematics is Human right. Cultures
can be understood as knowledge, beliefs and conceptions, in this case, about
particular mathematical situations so commutation of culture can adjust in
every classroom.
Reference
Pandit, R.P. (2011) Recent Trends in mathematics
Education. Kathmandu:
Indira Pandit
Chertri,
D.B. (2067) Studies in Mathematics
Education: Sunlight Publication.
Nayabazar, Kritipur, Nepal
Upreti, Sahadev
(2011) Ternds in Mathematics
Education, Gyankunja Prakashan
, Kritipur, Kathmandu
http:/
etnomatematica.org/articulos/Ambrosio1.pdf
en.wikipedia.org/wiki/Ethnomathematic
D'Ambrosio
U. (2006) Ethnomathematics: Link Between traditions and
Modernity Rotterdam,
The Netherlands: Sense
Hersh,
R. (1997), What is Mathematics Really? NY: Oxford University Press.
Hersh,
R (Ed) (2006) 18 unconventional essays on the nature of mathematics. NY: Springer.
D’Ambrosio, U.
(2004). Posfácio. In Ribeiro, J., Domite, M & Ferreira, R. [orgs],Etnomatemática: papel, valor
e significado. São Paulo: Zouk.
Comments
Post a Comment