ETHNOMATHEMATICS AND ADULT STUDENTS: CHALLENGES TO TEACHERS´CONTINUING EDUCATION by Maria Cecilia de Castello Branco Fantinato Monique Ribeiro Garcia

2. Maria Cecilia de Castello Branco Fantinato
Monique Ribeiro Garcia
mcfantinato@gmail.com
Universidade Federal Fluminense (UFF)
Brazil

3. !! Paper´s aim
!! Ethnomathematics, Young and Adult
Education and its relations
!! Contextualizing the research
!! Analyses of the interviews
"! ethnomathematical concepts
"! teachers’ practice characteristics
"! identification with YAE students
"! teachers’ work dilemmas under
ethnomathematical perspective
!! Final considerations
!! Bibliographic References

4. To contribute to the debate related to the
challenges of working in teachers’ education
according to ethnomathematics principles.
To bring some results of an investigation that
has analyzed the role of ethnomathematics
in adult mathematics teachers’ continuing
education and possible effects in classroom
practice.

5. The increasing preoccupation of what D
´Ambrosio (2001) has named it the
ethnomathematics educational dimension
appeared on the majority of works sent to
the 3rd Brazilian Congress of
Ethnomathematics - CBEm3.

6. Young and adult education has been under
growing interest to ethnomathematics
researches due to the fruitfulness of both
fields.
Three related topics where this production
has been growing from: teachers´ education,
pedagogical and didactic proposals and
numeracy /literacy practices among
youngsters and adults.

7. Some studies have already approached teachers’
education potentials under ethnomathematical
perspective (Domite, 2009; Monteiro, Orey & Domite,
2004).

8. It motivates teachers to throw themselves into
students´ ways of reasoning, into legitimating these
knowledges built in different contexts and into the
construction of pedagogical strategies which deal
with learning processes that happen both inside and
outside school walls. (Domite, 2004).
In YAE, due to its huge cultural diversity and students’
exclusion condition, the ethnomathematics approach
can legitimate both students´ and teachers’
knowledges as this relationship configures a dual
carriageway validation. (Fantinato & Santos, 2007).

9. Studies which relate ethnomathematics and
YAE also point to didactic and pedagogical
proposals centered in students’ daily life
knowledges, specific to young and adult
students.

10. The papers grounded on this topic suggest that in
YAE, the didactic and pedagogical proposals and
selection/usage of didactic material, such as
games, books, audio visuals resources, etc,
should be chosen according to an
ethnomathematics perspective, stimulating
teachers to broaden their action into favoring
attitudes of immersion in their students’ way of
thinking, legitimating knowledges, supporting
every day life and respect to cultural diversity.

11. The third related topic which emerged from
literature review was on numeracy /literacy
practices among adults who had low levels of
education.
Under an ethnomathematics perspective,
“mathematical knowledges productions can take
place in many diverse social contexts, and it
happens differently from the school practices,
with objectives, values, conceptions, roles and
legitimizing processes that are very specific from
the contexts where these practices are present
(Mendes, 2007, p.26).

12. It is a qualitative research, grounded on a socio-
anthropological view which has up fronted interviews with
a few math teachers from the municipal schools in Rio de
Janeiro who have been working with a Young and Adult
Educational Program called PEJA, with groups in PEJA II (in
these groups students range from the 6th to the 9th year)
and who had already taken part in continuous teacher
training programs under an ethnomathematical approach.

13. The Young and Adult Program, in Rio de Janeiro,
sees a meaningful number of students (30.265
enrolled students in 2009). The main
characteristics of the population supported by
PEJA is the heterogeneity - with differences in
gender, race, origin, age, religion, family
constitutions, parents’ schooling level and their
different insertion and non insertions in the
market.

14. One of the educational activities implemented by PEJA was
the development of a theoretical and methodological
reference for math teachers who deal with this schooling
mode, which lead into a document to be attached to
Elementary core Curriculum Multieducação, proposed by
Rio de Janeiro’s Municipal Education Bureau.
The document was collectively elaborated from the years
2004 and 2005 by 12 math teachers, coordinated by two
outside consultants who shared ethnomathematics as a
research area.
All these teachers, except one of them, took part in the
writing of the document mentioned above.

15. There were five interviews with seven teachers,
where two of the interviews were made
simultaneously with two people.
The interviews took place in 2008 either in the
Math Education Laboratory at Education Faculty
in Universidade Federal Fluminense (UFF) or in
the interviewee’s working places.

16. !! The subjects followed this profile:
"! they were mostly graduated in Mathematic expect one
who was in Physics.
"! All of them were born in Rio de Janeiro.
"! They ranged from 41 to 49 years old.
"! had nearly twenty year experience in teaching and had six
years or more of experience working with young and adult
students.
"! They were three female and four male teachers.
"! In 2009 three of these teachers were in post graduation
courses, taking Master in Education, two of them tutored
by the author of this article.

17. !! The questions on the semi-structured interview
script rested on:
"! the reasons a professional would choose to be a math
teacher in YAE;
"! his/her participation in continuing education activities
developed by PEJA –SME through out the previous years;
"! the contacts with an ethomathematical approach and a
critical analysis of its contributions to teachers practice
in young and adult education.

18. !! Theanalyses of the interviews carried out with
the seven teachers produced four categories:
"! ethnomathematical concepts;
"! teachers’ practice characteristics;
"! identification with YAE students;
"! teachers’ work dilemmas under ethnomathematical
perspective.

19. The understanding of the meaning of
ethnomathematics, exposed in the speeches,
revealed diverse among the teachers.
This diversity can be explained, among other
reasons, to their longer or shorter time in the
continuous education programs and/or
participation in research groups which deal with
this subject.

20. Several teachers claim they applied an
ethnomathematics approach in their classes
even before they got to know what it meant.
However, to face this theoretical approach
meant ways to provide foundations and
legitimize this dialogical teaching practice.

21. I used ethnomathematics, but I didn’t know (...)
I guess it is indeed intuition, you know? We
acquire experience; feel it while working, we
change a little here, a little there, till we get
the gist of it and feel it is good. .. We feel the
need to adapt and change, we look into their
eyes, we can see…what the student can’t
understand… what is going on. We start thinking
about it… We search for other ways (…) the
theory came along with the continuing courses
we had.. It legitimized what I did. It named it:
ethnomathematics. (Teacher Osmar)

22. It became more thoughtful (..) before, I was more
intuitive, tried things out, well.. I keep trying
them out, but then it was more under intuition
and I didn’t have the theoretical grounds I have
today (…) Now, I know why I can do it. I know
every step I take will lead into other steps and
the relationship with students tends to improve.
We start giving importance to what they know and
by assuring them of what they already know; we
grant the learning of new topics. It gave us great
support. (Teacher Coraci)

23. These teachers faced, however, under an
ethnomathematics perspective, a theoretical
support to a certain teachers´ practice which
acknowledges students knowledges
permanently. We named it the process of
knowledge legitimacy as a dual carriageway.
(Fantinato & Santos, 2007).

24. To work under the ethnomathematics
perspective, for these teachers, also mean to
develop dialogical spaces in the classroom so as
to allow different reasoning ways to blossom.

25. Ethnomathematics goes way beyond
legitimizing, respecting students knowledge. It
means trying to see, respect the meanings, the
representations that specific knowledge implies,
what it means to the group, not something
merely constructed at school. It is a lot more
than take the students´ view on it; it is to listen
to him/her. (Teacher Núbia)

26. An ethnomathematical attitude supposes a
disposition to dialogue, an attitude of
respect to differences. This disposition to
dialogue is related to teachers´ availability,
working under an ethnomathematics
perspective, to dialogue with students´
different knowledges, not only legitimizing
them but also learning from them.

27. (..) it can´t be an imposed class because the
young student has already showed he/she is has
dropped out from regular daily school for many
reasons (…) the teacher can’t be rude, can’t
impose (..) So, basically, an YAE teacher, can’t
inflict, he/she has to be able of having
dialogues. (Teacher Sandra)

28. YAE´s teachers practice under an
ethnomathematics perspective seems to
develop the capacity to establish relations
among the most varied topics, a central
concern with contextualization, in bringing life
into mathematical concepts which become
clearer in their relations with every day life.

29. Many of my students are homebuilders; one of them is building
my house. Now he’s thinking about taking up engineering. When
he started attending classes he was awfully desmotivated. Then
in a certain class, we were discussing area and I called him,
“Gésse”, this homebuilder. (…) How many bags of cement will I
need? And he answered me. And I asked him: “Will you teach me
how to make these calculations” He was ashamed.. but he
talked, and took part in the class. (...) After that he became a
very interactive student in class. The day I was talking about
sine and cosine. I drew a triangle on the board and he said:
“Teacher, I think I can use it when I am building a stair” He
managed to have this kind of relation and shared it with the
group. His knowledge interacted with knowledge itself there, in
the classroom. (Teacher Osmar)

30. Therefore, an ethnomathematics attitude
implies “a multicultural and holistic conception
of education” (D´Ambrosio, 2001, p. 44).
“Ethnomathematical education emphasizes the
connection between mathematics and other
areas” (Katsap & Silverman, 2008, p. 92).

31. The third characteristics, experience of autonomy, teachers make
known that in PEJA, they can work with autonomy:
As for decimal numbers matters, I would never test them
on that, basic arithmetic and that is all. An YAE student will
hardly ever apply a decimal division, as much as roman
numerals, but we have to teach in the regular classes (...) In
PEJA, I teach them the symbols and tell them which ones they
will likely use. What they are really going to need. I don’t ask
them, for example: “write a thousand in roman numerals”. I
know they aren’t going to use it, but for you to have the chance
to select what to teach or not, for you to have this autonomy to
select what to teach, you need to do some reasoning, an
autonomy which supports you and provides you with this
insurance. (Teacher Núbia)

32. When teaching math in YAE, it is necessary to
have an autonomous and reflexive teacher
who is capable of selecting syllabuses and
evaluation procedures which are more
adequate to reach students diverse reality.
Ethnomathematics is a theoretical approach
that can provide the teacher with the
necessary support in this sense.

33. Identification with YAE students rises as a
connecting aspect between teachers and students,
favored by the reciprocal listening atmosphere,
encouraged by the teacher’s ethnomathematical
posture.
According to one of the interviewee, she identifies
with YAE´s kind of work because throughout the
development of the work with the adults she can
establish a greater transparency, a dialogue, a
different conversation from the one she can
develop with a child.

34. When you are working with an YAE group, it
seems you are a lot more transparent. You’ re
talking about real life. In regular groups, you
aren’t. You go there, fulfill a task; it doesn’t
seem transparent. It’s as if nothing had
happened, you talk about nothing, as if life was
as it should be. Perfect. At night, it isn’t like
that. You let of steam, you speak your heart.
(Teacher Núbia)

35. Teacher Núbia feels close enough to her young
and adult students to, not only be able to listen
to them, but also make them listeners of her
own outflows. This closeness might happen
because both students and teacher are in the
same age range and also for the reason that
many of these teachers didn’t have such a
different family background from the students
they have today.

36. My parents have studied only till the 4th year, but
they have always invested in education. They came
from the northeastern city of Aracajú, and my
elderly sister was already born. They came to Rio de
Janeiro and they kept this concept in mind. They
have always been able to handle lots of problems
despite their low education. They have always been
aware of their rights. So, I can’t see school as the
place where one should supply it. (...) they invested
in education. Their children are all graduated. We
are eight and all of us went to university because
they thought it was the best way. They believed it.
(Teacher Luciana)

37. Teacher Luciana gives the education she got
from her parents, northeastern migrants, a
lot of importance. Not just because of the
motivation to formal school education but
also because she can also recognize aspects
of her own non formal education which
contributed to her education as an YAE
teacher, impelling her to ethnomathematics
principles.

38. Among the main dilemmas to embody a math teaching/
learning proposal under an ethnomathematical
approach, they name necessary time as an important
issue to develop this kind of work.
In teacher Luciana’s point of view, working in a PEJA
group, which has one third of its time reduced, one
needs to make options in terms of syllabus to be taught;
one has to choose what syllabuses are a priority and
which are not. According to her, these places where
they are given the chance to have continuing education
are the sources to provide them the proper conditions
to make this selection:

39. For me, it’s a contradiction. You have to
contextualize, redeem and there is also the syllabus
issue. I have always stood for syllabuses above all
and in ethnomathematics, syllabuses are not above
all. So, it’s an internal crisis. What is priority and
what is not one. If I think about ethnomathematics I
realize it doesn’t mean it is slower, but I do need
more time to deepen it, to talk about it. It’s
different from an ordinary class where I couldn’t
care less if they’re learning or not. So, when you
start working thought an ethnomathematics view,
time becomes a main concern, if YAE offered as much
time as regular classes we would be able to produce
a lot more. (Teacher Luciana)

40. For teacher Núbia, time restrains teachers’ from
getting closer to their students, in a movement which
demands very specific ways of reasoning:
If you keep to your mind that you have little time to
develop your work, you won’t get anywhere. You
will get anxious because there are very few classes,
even if you wanted; anxiety is so huge you just
ignore getting to know your student better. Sitting
with him/her, and let him explain how he/she
reached that result, which reasoning he/she applied.
You can’t usually do it, mainly with the shier ones,
who never get close to you. (Teacher Núbia)

41. Another interviewee also mentioned that the
required time for learning, added to the number of
students in class, stands for a dilemma for teachers
who work according to an ethnomathematics
approach:
(..) the number of students is surely
determinant. Under the premise that once one has
quantity we lose in quality, and I tend to agree with
it as you just can’t legitimize knowledge of 55
students as evenly as you would be able if you had 30
students. You can’t be dialogical with 55 the same
way you are with 30. (teacher André)

42. (..) an educational process under
ethnomathematics perspective claims for sorted
transformations within school organization, such
as in time/space relations, in spaces to include
diversity, to appreciate every day life knowledge.
So as to understand the curriculum as a system of
principles and identity, which stands for socially
valid knowledges and, furthermore, which allows
students and teachers to be actors of this process.
(Monteiro, 2004, p.445-446)

43. For example, the characteristics of their education at
graduation course at university were presented as a
drawback to the changes demanded by an
ethnomathematics posture:
So, I think these continuing education classes help you to
feel secure enough to choose what to exclude and what to
keep. Our previous mathematics education wasn’t
grounded on dialogue. It was on imposed knowledge, with
models to follow. In YAE groups, it doesn’t happen like
that. Students reasoning ways are way different and they
want the so called formal knowledge all the time. They
demand it from us. (..) as if there was a school way, they
copy everything we do. If I go to the board to develop a
problem, they make a point in copying my solutions, even
if they have done it correctly. (Teacher Luciana)

44. Teacher Luciana’s speech also signs to the importance of
continuing education significance to the constructions of
the teacher’s professional autonomy, pointing out to
straight relation towards his/her student’s intellectual
autonomy stimulus:
I rarely go to board these days. I know that I’ll become
their role model. I always ask a student or another to go.
So they can show how they got to the answer and also
show that it was valid reasoning. And I learned it way
later after I graduated. When I was 19 I didn’t do it that
way. Now at the age of 30 I can accept it as right. It took
me a long time, a lot of continuing education to take it.
At university, we had to follow a routine. There was a
model to follow. Despite the right answer I was given
plenty zeros. (Teacher Luciana)

45. The teachers´ ethnomathematics concepts,
though diverse, have reached some common
grounds: working under this perspective mean
voicing students, creating dialogical spaces in
the classroom, legitimizing their mathematical
knowledges built in different social contexts.
The main motivation to the dialogicity in YAE
is the inclusion of these students in the school
context. The idea is to stop them to quit
school five times “due to power” .

46. The interviewed teachers are committed with
their adult students even identifying themselves
with these students. The narrow relation
between teachers and students supported by a
teachers´ work under an ethnomathematics
perspective is present in the legitimization
process in a dual carriage way. When opening to
learning with their students and the ways they
create to mathematize, when bearing their
knowledges and their experiences, the teachers
legitimize their own teachers’ knowledge and
strengthen their professional autonomy.

47. We know we can not associate all the results on
YAE teachers practice to the influence of this
approach. The interviewees have had different
experiences in the proposed continuing education
processes.
Ethnomathematics can’t be seeing as a new
panacea to the math teaching/learning problems,
whether in young and adult education, whether in
regular education. It means a tendency in math
education which YAE teachers, whom have been
open to students’ cultural diversity, will identify
themselves with.

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