Chapter 7 - Pedagogical Trends in Ethnomathematics as Pedagogical Action
In educational terms, the Ethnomathematics as Pedagogical Action includes
mathematical modeling as a teaching-learning methodology. It has an aspect
of practical pedagogy that has not been applied widely to date. The real
effectiveness Ethnomathematics as Pedagogical Action has been demonstrated
in just a few isolated programs in a few countries – most notably Brazil.
With relation to education in general, it can be observed that the biggest
difficulty in adopting a methodology such as this is the barrier created
by traditional educational philosophies and the accompanying institutions.
Whereas in modern educational philosophies the object of study is clear and
obeys a predictable series of prerequisite stages, where teachers and students
can accurately anticipate the results foreseen in the end process or goal.
An obstacle hindering the success of ethnomathematics is the lack of documented
data supporting the practical applications in mathematics programs in schools.
The required time to work with mathematical content and the time needed to
develop a program in accordance with the practicalities of school regulations
are extremely problematic for even the most flexible of curriculum options.
This is extremely serious in many countries where the push is toward testing,
standards and accountability. However, the biggest impediment to implementing
Ethnomathematics as Pedagogical Action seems to be the bureaucratic needs
of the school that must be rigorously followed and that cannot regard the
constructive stages for the acquisition of knowledge of students.
Despite these obstacles, it can be argued here that a need exists for continued
investigations related to the advantages of implementing Ethnomathematics
as Pedagogical Action and for the use of mathematical modeling as a basic
instructional methodology. Therefore through these processes we are better
able to give meaning to mathematics, to life experiences, and to the further
illumination of concepts related to citizenship and to connect mathematics
to important interdisciplinary connections.
Mathematics, physics, chemistry, biology and other disciplines contribute
to the study of subjects like citizenship, health and the environment. However,
to make these practical is a great challenge, therefore those programs in
these disciplines are not complete themes they are, by their very nature,
interdisciplinary (D'Ambrosio, 1999) .
With relation to the practical teaching aspects of mathematical modeling,
some difficulties can be characterized by lack of experience, anxiety and
the unreliability caused by being unfamiliar with the process in general.
The fact that modeling leaves the authority to the learning process itself
is also cause for some concern by many teachers. The general lack of support
and time for interdisciplinary study is also a great impediment. The
lack of time for the preparation of participatory lessons in accordance with
the bureaucratic reality of each subject is also a concern.
With all these difficulties in mind, the teachers many times do not always
integrate the mathematics involved in the activity with other areas of knowledge.
Often, a superficial form of integration is allowed. They may not have the
ability to develop all the content areas necessary with the problem their
students are working on. In this way, the practical distanciamento of the
pedagogical one in vigor in the schools with the desire of active participation
of the teachers in this process of learning is provoked.
This necessitates a new form of literacy; one that moves from a limited “Three
R’s” view, to that which involves the tools that emphasize and active research
methods. The tools needed are closer to an ability to search, sort, create
and report new forms of information (Norton, 19xx), and away from the traditional
basics, which are embedded in these processes. D’Ambrosio calls for a similar
move away from the three R’s towards what he calls a “trivium for a new era”.
It is a three-step process involving:
Literacy
Numeracy
Technocracy
1/5/00 xxx 1/5/00
Many mathematical educators are not motivated, seem disinterested, lack creativity,
many times with an inadequate formation and if support consequently in the
textbooks that almost always are entailed of the partner-politician-cultural
context ampler than the teachers and pupils are lived deeply by.
However, we mainly evidence that the problems most serious are structural,
in consequences of the situation partner-economic-politics that many countries
in the world cross and whose effect we are sentirndo in the classrooms. However,
we cannot eliminate these problems if not make a deeper questioning on what
it originated them. In many countries the lack of resources for the education
is very frequent and in this context, the figure of the professor is very
important, therefore using itself of its creativity of educator and over
all with its solidarity, it it can collaborate for the solution of these
problems.
In this program, substantial changes happen in the position of the professor,
therefore its motivation is sharpened and activated and it starts to perceive
the Real meaning of the content that is considering. They also start to believe
that they have conditions to create new problems, different, significant,
challenging and interesting.
Thus, we do not have in accomodating them and we have that to try a way to
be able to act inside of this reality in the direction to help our pupils
in the learning and the understanding of world. With the use of the Mathematical
Modeling, we intend to supply to the teachers conditions so that they can
change the concept of educative practical its, freeing them of some myths
with relation to the severity of the mathematics education , with the
valuation of the mathematical conceptual knowledge in the global context
and also of its power of performance in practical situations.
Participating of the Ethnomathematics Program and the Methodology of the
Mathematical Modeling, the professor obtains to dinamizar its intellectual
development; he will have a permanent learning through the exchange of experiences
with pupils and the community; he characterizes yourself as a orienting and
mediating professor of the learning process and constantly keeps a relationship
of complicity with the pupils; therefore they discover together a dynamics
adjusted for one better agreement and understanding of the mathematical contents.
With relation to the pupil, this methodology also implies in a change of
position in classroom and in the first contacts it must be left clearly as
it is the functioning of this process. The difficulties found for the pupils
with relation to the modeling, in a general way are the difficulties in working
in group, interpreting and to assimilate simultaneously diverse questions
and contents and associates to others you discipline.
The great majority of the pupils does not possess the research and study
habit having little experience to formulate questions; facts that are essential
so that if it develops the modeling.
But, the fact that more in the flame the attention is the custom that the
pupils possess in " attending lessons ", or either, the biggest difficulty
is to make with that the pupils leave simply of being " receiving "of knowing
and starts to be " constructors" of knowing.
Benesses of the mathematical modeling for the pupils is diverse, therefore
they live deeply the process all and develop an understanding accomplish
of the learning being able to connect school and reality.
According you the NCTM (1989), "cultural Students ' background should be
integrated into the learning experience". The pupils live deeply the transformation
of problems of a social context for a mathematical context through the quantitative
and qualitative analysis of the phenomena and leave to only use algorithms
and formulas in an isolated and descontextualizada way. The permanent contact
of the pupil with its reality is a decisive factor that collaborates to awake
the interest in the learning of the contents to be worked. The pupils obtain
to also perceive the application of the mathematical concepts in the professional
field, facilitating to its insertion and performance in the work market.
Through the direct contact with the interdisciplinaridade, the pupils possess
a vision global, integrated and interacted of the mathematics with other
areas of knowing, what he facilitates the development of the mathematical
modeling for the elaboration of the models, to raise hypotheses, to develop
research habits, to select given and the posterior adequacy of these data
to its necessities.
The work in group will make with that the pupils share the tasks, learn to
hear critical and opinions, respects the decision of the group, coexists
the problems and learns to solve them, facilitating its interaction with
the society. The pupils if become versatile and creative and can acquire
abilities that will be essential for the convivência in community.
One of the aspects most important in the pedagogical work through the Mathematical
Modeling is the requirement of a dialógica attitude enters the elements
of the group, and between the groups, that permeia all the process, since
the choice of the subject, as well as in the survey and election of the questions
that must be worked, of the elaborated models and the decisions that will
be taken.
Of this form, the mathematical modeling can be considered as a methodology
capable to interrelate experimental and theoretical factors not to lose of
sight the essence of the mathematical attitude, taking in consideration the
specific realities of each region, the interests of the students and the
community, with the objective to develop the motivation for the participation
accomplishes in society.
It is certain that the practical pertaining to school contain, explicit or
implicitly, its estimated theoreticians and metodológicos. The way
as the teachers selects and works the contents or chooses education techniques
and on evaluation they depend very on as they see the practical professor.
Of this form, the Ethnomathematics Program also has its estimated theoreticians
and metodológicos that give to support á practical professor.
Thus, through the analysis of the pedagogical trends in the practical pertaining
to school used currently, we intend to effect a correlation between " liberating
" the progressive trend, more known as of Pablo Freire and the progressive
trend " of the contents pedagogy" defended by Demerval Saviani, that accents
the priority of the contents and its confrontation with the social realities;
therefore, we consider that the estimated ones of these practical pedagogical
are similar to the estimated ones of the Ethnomathematics Program idealized
for Ubiratan D'Ambrosio.
"the progressive" term was loaned of Snyders (1974) and here is used to assign
trends that, leaving of a critical analysis of the social realities support
the purposes social political of the education.
We can affirm that practical the pedagogical pertaining to school can influence
decisively in the pedagogicalwork of the professionals in education. In this
way, the great majority them teachers base pedagogical practical its in traditional
education, or then they look examples for application of practical its with
its teachers and older colleagues or still support themselves in exceeded
didactic books and without connection with the reality.
However, it has a great number of teachers whom they desire to carry through
a more effective work, but do not know which procedures must adopt. The courses
of formation of teachers teach the pedagogical conceptions, but generally
the contents are education or learning theories that never have correspondence
with the situations lived deeply in classroom or with the reality.
1) " Liberating Progressive Pedagogy
This pedagogy has as inspired, mentor and developed by Pablo Freire,
who has applied its ideas personally in diverse countries, in the whole world.
The Pedagogy" Libertadoria " had its origins in the movements of popular
education that had occurred in Brazil in the end of the 50 and beginning
of years 60, when had been interrupted by the Military Blow of 1964, having
retaken its development in the end of 70 years and beginning of years 80,
influenced for the opening process politics. Pablo Freire emphasizes the
character essentially politician of its pedagogy, hindering that it is placed
in practical in official institutions before the social transformation occurs
of fact in the society. In Brazil, this pedagogy exerts a expressiva influence
in the popular movements and unions and, are practically confused with the
great majority of the experiences that we call of " popular education " or
" non-.formal education ".
Although the formularizations techniques of Pablo Freire are restricted to
the education of adults and the popular education, innumerable teachers and
educators come adopting the estimated ones of this pedagogical trend and
trying to place it in practical in all the education levels.
Thus, in this pedagogy, the teachers and pupils are mediatizados by the reality
whom they live deeply and of which they remove the content of the learning,
reaching in this way, a level of conscience of this reality, to act in the
one in the direction of social transformation. The professor is a coordinator
of activities that he jointly organizes and he acts with the pupils. This
type of education is critical therefore is always in search of the transformation,
questioning the relations of the human being with the nature and of the human
being with other human beings.
Most important it is not the transmission of specific contents, therefore
with the use of the generating subjects that are extracted of the "problematização
" on the experience of life of the educandos, it is intended to search the
wakening for a new form of lived deeply relation with the practical one.
Of this form, the pertaining to school activity is based upon in the quarrel
of social subjects and politicians and in actions on the social reality,
analyzing problems and organizing an performance form so that this social
reality and politics can be transformed.
The relationship between teachers and pupils is of authentic dialogue and
the adjusted form of work more is the group of quarrel of where it has broken
the self management of the learning and where is defined the content and
the dynamics of the activities to be elaborated. The professor must behave
itself as an entertainer, who must go down to the level of the pupils, adaptando
itself it its characteristics, to the development of each group, having therefore,
walk together and only intervine when necessary, to more supply some systemize
information.
The steps of the learning happen through the codification, decoding and problematização
of a situation caused through the exchanges of experiences around practical
the social one what it allows the educandos an understanding of that had
lived deeply until the elaboration of a more critical knowledge of its reality.
A lived deeply evaluation of the practical one between professor is admitted
and pupil in the group and to the times the auto-evaluation is made in terms
of the commitments with practical the social one. Relation of authority between
professor and pupil for not making impracticable the awareness work does
not exist. One is therefore about a non-directive position where the professor
is present and remains vigilant to assure to the group a human space so that
they can will express themselves without will be neutralized.
The assignment "problematizadora education" in discloses the force to them
of the learning motivadora where the motivation occurs from the codification
of a situation-problem, to analyze it criticamente. Thus, to learn is an
act of the knowledge of the concrete reality, of the real situation lived
by educating and that only it has meaning it will have as resulted the critical
approach of this reality. The learning is not memorized tax or, therefore
it is a process through which if it arrives at the knowledge through the
understanding, of the reflection and the critical one, or either, what it
moves is the knowledge that was incorporated in reply to the oppression situations.
This pedagogy values the life experience as base of the educative relation,
emphasizing the process of group learning (groups of quarrels, assemblies
and votings) and as practical educative only makes sensible in one practical
social together one the people.
The pedagogy of Pablo Freire values the autonomy of the practical cultures
and its, therefore it has an emphasis in the valuation and the incorporation
of the cultural aspects of the life of the educandos in the pedagogical process,
the dialogue occupying a central place in this process that it searchs to
establish a bridge between knowing more distant places to them and, particular
and the generalities.
2) Progressive Pedagogy of the Contents
This pedagogy considers the school as integrant part of the society and all
the actions that happen in are directed for the social transformation. Thus,
the function of this pedagogy is to contribute for the transforming paper
of the school. In this way, the condition to reach the popular interests
is to guarantee to all the pupils an education of good quality, from the
appropriation of the knowledge of the basic contents so that they can have
meanings.
Understood in this direction, the education must be a mediating activity
where the pupil through its proper active participation in the process and
for the intervention of the professor, passes more of an experience initially
confused and broken up (sincrética) for an organized and unified vision
(Saviani, 1985).
In this context, the school starts to act in the preparation of the pupil
for the adult world and all its contradictions, supplying to it the necessary
instruments so that through the contents and of its socialization they can
have a more active and organized participation in the democratization of
the society.
The school must be valued as instrument of appropriation of knowing
therefore contributes to eliminate the social selectivity, playing a basic
role in the diffusion of the contents that must be livings creature, concrete
and indissociáveis of the social realities.
Of this form, in this pedagogy, the function of the school is social and
politics by means of the work with systemize knowledge, with the objective
to place the popular classrooms in conditions of an effective participation
in the social fights. One understands that it is not enough to have as contents
the social matters, but that it is necessary that if has domain of knowledge,
ampler abilities and capacities so that the pupils can interpret its experiences
of life and defend its interests of classroom.
Currently, accepted that the contents are exterior realities to the pupils
and that they must widely be assimilated. However, it is not enough that
the contents well are taught therefore are necessary that they are tied with
the significação social human being and. This conception of
resume does not establish an opposition between erudite culture and popular
culture but, establishes a relationship of " continuidade"(o access of the
pupil to the contents is related with the concrete experience of it) where
the pupil passes gradually of the immediate and disorganized experience for
the systemize knowledge.
Currently, accepted that the contents ploughs exterior realities you the
pupils and that they must widely be assimilated. However, it is not enough
that the contents well ploughs taught therefore ploughs necessary that they
ploughs tied with the social significação human being and.
This conception of summarizes donates not establish an opposition between
popular erudite culture and culture but, establishes relationship of "continuidade"(o
access of the pupil you the contents is related with the concrete experience
of it) where the pupil passes gradually of the immediate and disorganized
experience will be the systemize knowledge.
The work of orientation of the professor is directive because it has more
experiences on the social realities, possesss an adjusted formation to teach
and possesss the knowledge necessary to lead the analysis of the confrontation
of the contents with these realities. The necessary pertaining to school
work to be evaluated more to prove for the pupil its progress in direction
to the systemize slight knowledge, or either, to verify when it had the overcoming
of the partial and confused vision of the reality for a clearer and unifying
vision. Thus, to learn in this pedagogical vision is to develop the capacity
to process information, to work with stimulatons of the environment, to consider
models of education directed to the interaction social conteúdo/realidades,
to guarantee the democratization of education to the popular layers and the
structural transformation of the society.
From ch 1
---------
Conclusion
An ethnomathematics program presents ample possibilities for research and
exploration – what we refer to as “pedagogical action”. Pedagogical action
is an essential step in becoming a free, empowered, contributing human being
in a democratic society. The traditional or “Euro-centric” standard has taught
us to look for, to understand, to explore. Yet it coldly ignores unique “non-western”
context of many an individual. Its processes of thought – chiefly the scientific
paradigm - the tool for seeking new forms of information, explaining, and
understanding represent the prime example of this reality and demonstrate
its powerfulness (D'Ambrosio, 1993). Yet the unintended consequences of this
act are that thousands of languages, cultures, and ways of doing mathematics
and solving problems are being lost at an alarming rate on this planet.
Learning to understand and respect the unique cultural and social reality
of others, as we learn mathematics is one of the basic aspects of this learning
paradigm. The teacher must guide participation, so that concepts can be constructed
and tasks carried through in the construction of knowledge.
In this program, the teacher is the person who orients and guides the process
of the learning. While working in partnership with the child; the teacher
instigates ideas; guides the direction, in the work of the child – developing
a mentor / coaching relationship with the student. Thus, the teacher considers
how to develop the subject with their pupils, so that together they can build
a starting point, or they might rank sub-problems or tasks in importance
and need. So that as a part of their daily activities, they initiate a “clash
of ideas” central to the subject in question or debate. The teacher does
this by considering the mathematical objectives they need to reach with the
activity.
The goal for the teacher then becomes to find ways to fully understand a
situation that the pupil chooses to reflect upon, by:
1. Assisting the student in developing a strong or reasonable
hypotheses;
2. Getting the student to search for ways to solve
problems;
3. Helping the student to look for new applications of
concepts;
4. To get the student to deepen their understanding
of the same concepts;
5. To get the student to exercise their own creativity;
6. To get the student to generalize mathematical properties
and ideas;
7. To get the student to discover other solutions
and possible connections to other disciplines; and
8. To get the student to discuss with the group /
or class the validation of their discoveries and ideas.
At this point, one integrates the child’s basic need to communicate with
others, by encouraging verbalization and encouraging the development of logical
reasoning. The teacher also encourages them to defend their opinions before
the group, and to critically evaluate their own point of view by presenting
it to a colleague. This work is developed through trial and error, testing,
and resolving numerous complications that arise when learners begin their
own research.
Children gain added experience, as young mathematicians, in the process of
coming to agreement. They do this by testing the “rightness” and “wrongness”
of their ideas and solutions; by confronting and justifying their ideas;
and by listening to the arguments and comments of others. This process allows
the student to reformulate their ideas. This process of logical reasoning,
including the process of resolution of a considered problem, is a powerful
tool that the ethnomathematics program presents here. Verification of the
existence, or not, of other solutions, also becomes vital to the success
of their work.
Through integration of these experiences, children learn about existing problems
with more than one or multiple solutions. They come to see, as they do in
sports and computer games, that problems exist whereby more than one solution
is useful, indeed possible. The contrast and study of various solutions to
problems, forces children to reflect on the given data and on the conditions
necessary for choosing procedures to solve them. It also encourages an understanding
and development of the language that enables them to express their ideas
and thoughts to others. The job of the teacher becomes that of a facilitating
dialogue between the teacher / student and student / student.
The constriction of an ethnomathematical learning environment develops familiarization
and connections between formal mathematical concepts and daily or real-life
applications and problems. Through the development of representations through
mathematical modeling, students learn to demonstrate the necessity for using
language to successfully communicate their ideas, thoughts, and theories
to others. The resolution processes they practice, the development of the
results that they have found, lead to reflections that are true actions with
their own reality and culture.
Access to knowledge essentially connects a growing global reality to one
of our own. Allowing us to arrive at representations by which we elaborate
truly active strategies. Mathematical models function to mediate the important
process of communication between pupils, and serves to develop abilities
that elaborate powerful mathematical ideas. How to actually do this will
be fully elaborated in subsequent chapters. The process of connecting the
mathematics of the global (formalized mathematics) to the local (individual)
one, from many forms and representations is called modeling (D'Ambrosio,
1993).
An ethnomathematical program gives mathematics a concrete connection to the
real or outside life of the learner. It gives both teachers and students
the opportunity to explore the mathematics found in the day to day experience
of their own community or cultural context and learns to use mathematics
as a tool. It can also allow learners to see more clearly why they learn
the math they are doing in the classroom, by allowing them to give it purpose
and meaning.
The ideas as outlined here have the objective of being active ones. They
strive to give learners the tools to develop a sense of conscience and meaning
to their studies. They represent a qualitatively different approach to learning
mathematics, from moving total control of the learning from the teacher,
to a form of shared democratic experience for the whole class or group. This
enables learners to practice learning mathematics in a context appropriate
for their participation in the society of the next millennium.
The application of an ethnomathematics program in the classroom brings students
a way to learn diverse and alternative forms of mathematics. This seems to
be in accordance to the fact that the important thing for life in a complex
society is that diverse ethnomathematics is necessary for the resolving diverse
types of problems (Borba, 1993).
Numerous alternative proposals for an action-based pedagogy, while recognizing
the intimate relation, indeed the mix, between socio-political-cultural aspects
of mathematics with that of the auxiliary objectives of schools and curriculum
is vital. This can lead us to the basic understanding that as children come
to dominate the necessary mathematical content for their growth and development
they thereby become active citizens who plainly understand what it is to
be conscious participants in their own and that greater world society.
|