2. MOTIVATION
A murderer is sentenced into
death. He has to choose
between three rooms. The first
room is full of furious flame. The
second is full of murderers with
loaded guns. And there are lions
in the third room who had not
been fed for years. Which room
is the safest? Answer:
The room of the lions because they’re
dead if they haven’t been fed for years.
3. WHAT IS
PHILOSOPHY?
Alternative definitions:
From Wikipedia
the discipline concerned with questions
of how one should live (ethics); what
sorts of things exist and what are their
essential natures (metaphysics); what
counts as genuine knowledge
(epistemology); and what are the
correct principles of reasoning (logic)
From the American Heritage Dictionary
investigation of the nature, causes, or
principles of reality, knowledge, or
values, based on logical reasoning
rather than empirical methods
4. ALTERNATIVE
DEFINITIONS:
From Penguin English Dictionary
the study of the ultimate nature of existence, reality, knowledge and
goodness, as discoverable by human reasoning
From Kernerman English Multilingual Dictionary
the search for knowledge and truth, especially about the nature of man
and his behavior and beliefs
From Oxford Dictionary of Philosophy
the study of the most general and abstract features of the world and
categories with which we think: mind, matter, reason, proof, truth, etc
5. OTHER DEFINITIONS OF
PHILOSOPHY
• The Historical Approach
• Philosophy as Criticism
• Philosophy as The Analysis Of Language
• Philosophy as a Program Of Change
• Philosophy as a Set Of Questions And Answers
• Philosophy as a Word-view
6. AS USED ORIGINALLY BY
THE ANCIENT GREEKS, THE
TERM "PHILOSOPHY"
MEANT THE PURSUIT OF
KNOWLEDGE FOR ITS
OWN SAKE, AND
COMPRISED ALL AREAS OF
SPECULATIVE THOUGHT,
INCLUDING THE ARTS,
SCIENCES AND RELIGION
7. PHILOSOPHY IN THE ANCIENT WORLD WAS THE PARENT OF
MOST SCIENTIFIC DISCIPLINE THAT SOUGHT THE KNOWLEDGE
OF ALL THINGS ON EARTH AND IN HEAVEN.
• Knowledge of natural things and their causes lead to the
creation of physics and metaphysics.
• Knowledge of human affairs and their constitutive
relations lead to the creation of ethics, politics, and the
philosophy of history.
• Knowledge of heavenly things leads to cosmology and
speculative theology.
8. IN ORDER TO UNDERSTAND PHILOSOPHY,
YOU MUST NOT ONLY GRASP THE SUBJECT
MATTER, SUCH AS METAPHYSICS AND ETHICS,
BUT ALSO ITS METHOD.
In Western Philosophy – the method to obtain
knowledge is rooted in the Philosopher’s
ability to form and evaluate arguments
In Asia – the philosophy there has greater
emphasis on knowledge of the Way (Dao) to
live a life harmonizing the individual with her
natural and social world.
In all cultures – philosophy requires that we
think critically: to be clear, precise, well-
organized, truthful, complete, and be able to
handle objections
9. DIVISIONS OF PHILOSOPHY
Epistemology - a Greek word translated as the
theory of knowledge.
It is a foundational area for other areas of
philosophy
It involves three main areas:
(1) the source or ways to knowledge.
(2) The nature of knowledge.
(3) The validity of knowledge
10. METAPHYSICS
Metaphysics is another Greek word
which refers to the attempt to describe
the nature of reality.
it involves many questions such as the
nature and makeup of the universe,
whether the world is purposive or not,
whether man is free, whether the world
is eternal or created, and many other
issues.
11. LOGIC - A TERM USED TO DESCRIBE THE VARIOUS TYPES OF
REASONING STRUCTURES, THE RELATIONSHIP OF IDEAS,
DEDUCTION AND INFERENCE, AND IN MODERN TIMES.
SYMBOLIC LOGIC WHICH BECOMES QUITE MATHEMATICAL.
Axiology - Axios, the Greek word of worth, is related to two different areas
of worth. There is, first, moral worth, or ethics.
Ethics is a discipline concerning human moral behavior and raises the
questions of right or wrong. It has generally been the science or
discipline of what human behavior ought to be in contrast to a discipline
like sociology which is the study of what human behavior is.
Aesthetics - the philosophical study of beauty and taste. It is closely
related to the philosophy of art, which is concerned with the nature of
art and the concepts in terms of which individual works of art are
interpreted and evaluated
12. "PHILOSOPHIES OF"
Another category of philosophy is called
"philosophies of" because of the term being
related to various other subjects or disciplines.
For example:
philosophy of art
philosophy of biology
philosophy of history
philosophy of law
philosophy of philosophy
philosophy of physics
philosophy of the natural sciences
philosophy of religion
philosophy of sociology
philosophy of science
The "philosophy of" is basically the
application of metaphysical and
epistemological questions to a certain
subject area. It is concerned with the basic
structures of the discipline and the
presuppositions needed for the study
13. WHY DO WE STUDY
PHILOSOPHY?
The study of philosophy enhances one’s ability to:
think, speak, and write clearly and critically
form original, creative solutions to problems
develop reasoned arguments for one’s views
appreciate views different from one’s own
analyze complex material, and
investigate difficult questions in systematic
fashion
16. A CONVERSATION WITH PAULO
FREIRE
• The conversation was between the
philosopher and educator Paulo
Freire and two Mathematics
educators from the University of
São, Ubiratan D’Ambrosio and
Maria Do Carmo Mendoça
17. SUMMA
RY
The conversation started by Maria
and Ubiratan by recognizing Paulo
Freire as the great philosopher
who has been the inspiration for a
number of new measures and
proposal in education
Ubiratan asked a question: “Do
you see an equivalent to literacy,
a form of 'mathemacy'? Is there a
mathematical equivalent to
'alphabetization' in your work?”
18. • Paulo answered with honesty and say:
“'Ha! Even back then, forty years ago, I was
concerned with this ' No, indeed I did not think
about this before. But today I understand this. I
have no doubt about the importance of every
effort, which should not be exclusive to
mathematicians, to the professor of mathematics,
but that in my understanding of every man and
woman, mathematician, physicist or carpenter,
that is exactly the effort to recognize ourselves as
conscious bodies mathematised.”
• as a transition of the support from the world, culture was
installed, as well as the invention of language, and a way
of thinking that attends not only to the object that is
being thought, but which enriches itself with the
possibility of communicating and communicating itself. I
believe that in this moment we also became
mathematicians
19. PAULO FREIRE:
Life, which became existence, was
mathematised.
to propose to youth, students, pupils,
farmers, at the same time as they
discover that four· times four is
sixteen, they also discover that there
is a mathematical way of being in the
world.
20. “I believe at this congress
one of the things I would do
is to make, not really an
appeal, more a suggestion
to mathematics teachers
that, at the same time as
they teach that four times
four is sixteen or square
roots, or this and that, they
try to awaken their students
to seeing themselves as
mathematicians.”
21. Ubiratan: We recognize the
political importance you give to
the acquisition of language. You
say that in order to be free,
human beings have to be capable
of expressing themselves, must
be able to read, must be able to
discourse. Do you see something
equivalent in mathematics?
Paulo: I believe that, unquestionably, this possible mathematical
'alphabetization', this 'math-alphabetization' [mate-alfabetizaçao] or
math-literacy, would help the very creation of citizenship.
22. PAULO:
I believe that at the moment in which you translate the naturalness of
mathematics into a condition for being in the world, you are working against a
certain elitism that the studies of mathematics have, even contrary to the desire of
some mathematicians
“it became accepted that understanding mathematics is something profoundly
refined, when indeed it is not, and should not be.”
“to the extent to which you do not do it simplistically, but you render the
understanding of the mathematical existence of human existence simpler, then
without any doubt you help in the recognition of the importance of mathematical
understanding, which is as important as language”
23. Maria: This is natural mathematics, the mathematics that says
something about natural quantification.
example how a boy understands multiplication, and the
teacher does not see this other vision of mathematics as valid
Paulo:
This does not happen only with mathematics; this has to do with
the presence of men and women in the world.
This has much to do with an elitist posture prevailing in schools,
which downplays every contribution that the student can give to
the school
this involves an over-valuation of knowledge called academic
and the devaluation of common-sense knowledge.
This is the epistemological position according to which there is
a definitive rupture between one form of knowledge and the
other.
24. PAULO:
I feel that the beginning of an educational
practice must be the understanding of the
world that the learner has or has had, and not
the world-view and the knowledge system of
the educator
We start from what the learner knows in order
that he or she can know better, know more and
know what he or she does not know yet.
I believe that what we do, to start from the
world-view of the teacher, shows disrespect,
which is an elitist disrespect The strengthening
of a democratic posture resides in overcoming
this disrespect
25. Ubiratan: I know that one of your current
projects is to write a book about the
preparation of teachers. Is it possible for you
to say something about this project, in a way
more directly related to our concerns, as
mathematics educators? How do you think
the preparation of teachers can be
revitalized?
Paulo: The provisional title of the book will
mention teacher preparation and
fundamental knowledge which is necessary
for a critical teaching practice. My concern in
writing this book is to show that, sometimes
even more than knowledge, some
awareness's are absolutely necessary for a
teacher and should be present in the
education of an educator.
26. PAULO: (AWARENESS)
• Education is founded on these two feet, one the
inconclusiveness, the other the conscious awareness
of this inconclusiveness Human educability has no
explanation other than the assumption of aware
inconclusiveness
example: the Jaboticabeira (a common Brazilian fruit tree) which I
have in the garden of my house is also inconclusive, since the
phenomenon of inconclusiveness is a vital phenomenon, it is not
exclusive to human beings.
27. PAULO: (AWARENESS)
• to realize that change is very difficult, but it is possible.
I move as a teacher because even knowing that it is so difficult to
change, I know it is possible to change. It may even be possible that
the agent of a radical change does not belong to my generation, yet
without my generation the other generation will not be able to
change
28. PAULO: (AWARENESS)
• to teach is not to transfer knowledge, to transfer contents.
To teach is to struggle, together with the students; it is to create
conditions for the construction of knowledge, for the reconstruction of
knowledge
It is necessary for the teacher to have a historical perception that men
and women learned first, then they taught. Learning has always
preceded teaching.
29. BUT WHAT IS HAPPENING
IN SCHOOLS? (PAULO)
Paulo said:
Teaching became more important, and learning was
bureaucratized with the bureaucratization of teaching
the teacher must know that both learning and teaching, are in a
contradictory dialectical process, in which the better one learns,
the better one can teach, and the more one teaches, the more it
is possible to learn
30. UBIRATAN TO PAULO:
Ubiratan: “Schools must provide an environment, must
indeed be an environment, for sharing the process of
search and must not be the place where knowledge is
transferred”
Paulo: Unquestionably, the role of the teacher, the role of
the one who teaches, is a major role. The teacher has a
great responsibility. And the teacher who does not teach
does not justify him- or herself.
32. • The conversation ends with the words of gratitude
from Maria.
• Paulo Freire also said to Ubiratan that “you go beyond
the adjective 'mathematics' and can say 'in
education' too. Indeed, I see D'Ambrosio as more
than an educator, he is a philosopher of education”
• Thereafter, he (Paulo Freire) excused himself and
rush to his doctor.