Maria Cecilia de Castello Branco Fantinato

Monique Ribeiro Garcia

mcfantinato@gmail.com

Universidade Federal Fluminense (UFF) Brazil

!! 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

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.

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.

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.

Some studies have already approached teachers’

education potentials under ethnomathematical

perspective (Domite, 2009; Monteiro, Orey & Domite,

2004).

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).

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.

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.

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).

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.

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.

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.

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.

!!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.

!!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.

!!The analyses 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.

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.

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.

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)

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)

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).

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.

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)

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.

(..) 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)

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.

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)

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).

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)

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.

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.

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)

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.

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)

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.

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:

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)

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)

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)

(..) 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)

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)

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)

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” .

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.

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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