The Third International Conference on

Ethnomathematics 

The Third International Conference on

Ethnomathematics 

February 2006 New ZealandFebruary 2006 New Zealand

 Maria do Carmo S. DomiteUniversidade de São Paulo

Brasil

 Maria do Carmo S. DomiteUniversidade de São Paulo

Brasil

  The primary reason of my research is:  The primary reason of my research is:

-understanding more and more the advantages of taking into account culture in the process of teaching and learning mathematics

- leading teachers to validate the students’ previous knowledge in their teaching. By doing so the students previous knowledge becomes a source of dignity and self-esteem for those students and an integrative force in the classroom situation.

- to understand the connections/principles between ethnomathematics and teacher education movements - to develop a closer connection between both movements - to understand what ethnomathematics educators would like to see in teacher education movements

  The other reasons are:   The other reasons are:

  What I have found out?   What I have found out? 

What I have found out, however, is the lack of reference to the student’s knowledge (to the students in general) in most research carried out by those involved in teacher education. 

 Looking at the history of teacher education, we see that :   Looking at the history of teacher education, we see that :  

…there is almost no concern for the student’s knowledge (or first knowledge) in most of the researches that are going on in teacher education.  

 Most of the models proposed regarding teacher education have dealt with the teacher as a social subject of his/her actions and are centered on the formative dynamics of the processes of transformation.

  When we take a deep look at the work of people like…  When we take a deep look at the work of people like…

SCHÖN, D.; ZEICHNER K.; NÓVOA, A.; PERRENOUD,P.; SHULMAN, L.S.; THOMPSON, A.; PONTE, J.P.; LLINARES, S.; COONEY, T.; KRAINER, K.; CARVALHO, A. M.; FIORENTINI, D.; POLETTINI, A.; PIMENTA, S.; FUZARI, J. among others  

  

a) learning by doingb) cooperative workc) relationship between theory and practiced) starting the lesson by using the student´s discourse e) letting problems be formulated by the student

…their works take into account very fruitful ideas, most of them inspired by Dewey´s ideas, such as:  …their works take into account very fruitful ideas, most of them inspired by Dewey´s ideas, such as:  

  

Surely, these educators consider that the students’ knowledge must be within these formative proposals – but sometimes it is not very clear how they explicit it!

As we have been involved with Ethnomathematics studies and they always focus on identifying quantitative and space relations in the knowledge of the student (the “other”) – on his/her own rationality and terms - our starting point is always the student.

Therefore we believe that the focus of teacher education must be on a curriculum of teacher preparation that problematizes the processes based on the student’s social reality – in which the student’s knowledge becomes the heart for instruction.

  It is therefore of paramount importance   It is therefore of paramount importance

- to work with the relationship of teachers with their culture conceptions, their models of knowledge, beliefs and teaching processes…

- to what extent teachers take into account cultural patterns of knowledge, beliefs and behavior,

 We also need to know We also need to know

In this respect FREIRE. and D’AMBROSIO are two of the few who consider the educational action centered on the student’s or on the students group’s culture

In this respect FREIRE. and D’AMBROSIO are two of the few who consider the educational action centered on the student’s or on the students group’s culture

Background

If we consider boundaries within mathematics education and culture and teacher education issues we can see that the distinction between mathematics education and teacher education by one hand and cultural matters on the other is not easy to draw. Most of our research on ethno mathematics and teacher education are generated on these special principles stressed by P. Freire and U. D’Ambrosio:

From Paulo Freire: From Paulo Freire:

- In a teaching and learning relationship, both sides learn. That is, to say, to teach something to students, the teacher learns something about them as well. Because for Freire in the relationship, as a whole, between the “educator” and the “educated” there is always something to be known.

- The learners already possess an understanding of reality… the teacher will just help the learners to make a re-understanding of their

own reality.

  

From D’Ambrosio: From D’Ambrosio:

Ethnomathematics is the art or technique (techné), of explaining and understanding reality (mathema) inside of a proper cultural context (ethno)

and, dealing with space, time, classification, comparison, which are proper to the human species, the codes and techniques to express and communicate the reflections on these behaviors is undeniably contextual.

- Ethnomathematics studies/reveals the cultural roots ofmathematical knowledge that is given by ethnic, social andprofessional groups   

“

 In order to gather systematic information and carry on analyses of the mentioned lack in teacher education I organized my research in two different parts:

 In order to gather systematic information and carry on analyses of the mentioned lack in teacher education I organized my research in two different parts:

Questions are being asked to 25 Brazilians and non-Brazilians in-service teachers, as below:   

1a. What have you heard about teacher education as an activity inside the school system? 

1b. What have you heard about teacher education as a line of research? 

2. What are some ideas, challenges or suggestions in teacher education you have seen or heard about? 

3. What are the most essential characteristics that we, as teachers, need to keep in mind when we decide to put our students’ feelings, attitudes, beliefs and previous cultural knowledge at the center of learning and teaching process? 

Tasks are being given to a group of Undergraduate and Graduate students and some in-service teachers, under the topic “ How we, as teachers, are prepared to teach the diversity of students we will face in our classes…”

  AND,    AND,  

 Place of work____________________________________

Time of service as a teacher (of mathematics): _________________________________

 

Dear teacher: If you were in a classroom situation how would you continue the

lesson, taking into account the reports of two teachers, Mário and Janaína (two actual cases). Suppose, in a first moment, that you are Mario and in a second moment, Janaína, both “special” teachers who propose to “start a lesson by taking into account the discourse of the students”....

  INTERVEW  INTERVEW

 1. Mário starts, in one of his fifth grades classes, to chat with his students on division calculation, by asking:   1. Mário starts, in one of his fifth grades classes, to chat with his students on division calculation, by asking:  

Mário (teacher) : “How do you divide 125 by 8?”

José, who sells chewing gums at a traffic light downtown, begins to speak: José: “There are about 10 guys of us, boys and girls, almost every day at our sales point. Then, we divide like this: a bigger amount for the girls as they are more responsible than the boys, and also a bigger amount to the older ones, following the same principle”.

Mário (teacher): “Give an example, José. For instance, how was the division yesterday or the day before yesterday?” 

José: “Ah! Like this... there were 4 girls, 1 is a very young one; 6 grown-up boys and 2 younger ones. Then there were 12 of us and there were 60 chewing gums units… the chewing gums were divided into two halves, but the girls received a few more units. The youngest girl got 3 and the other ones got 6 or 7, I don't remember well ...The boys...”

To be continued by the teacher… be as explicit as possible.

2. Teacher Janaina started out from a question related to percentage, in a 2nd grade evening class for Adult Education.2. Teacher Janaina started out from a question related to percentage, in a 2nd grade evening class for Adult Education.

Janaina (teacher): “What do you know about percentage? How do you calculate a given percentage? Let us think about...”

Luiz (student): “Earlier this morning I needed to make a calculation like this... 35% out of 195 and that is how I do it ...19 + 19 + 19. So, I add 10+10+10 and 9+9+9. It came up as 30 plus 27… and then I add 9,5… that is half of 19”

Janaina (teacher): “How did you come up with 19? Talk about the way you figured it out.”

Luiz: “Oh! I dunno why I do it...every time there’s a percentage I divide it by ten because someone thought me like this and I add the times, that it is… 30% I add three times ten, 40% I add 4 times.”

Janaina (teacher): “And how did you get to 9,5? Tell me how you thought.”

Luiz: “I know that when it is 25% or 35% or 45%, I have to divide by 2 but I dunno why I do it...” 

To be continued by teacher… be as explicit as possible.

 The questionnaire and the practical situations can shed some light on the kind of attitudes teachers need to have to become the ones who validate the (culture) knowledge of the students. - Educating the mathematics teachers towards the development of culture concerns is not incompatible with teaching them on how to teach mathematics to young people; on the contrary, it can be one of the aspects involved. - While national education developments can interpret/imagine the teachers´ actions they cannot make sense of the students and teachers social and cultural identities and therefore incorporate them to the national curricula.

Preliminary conclusionsPreliminary conclusions