THE ROLE OF ETHNOMATHEMATICS TO ENCULTURE MATHEMATICS

A.    How did Ethnographic Research Develop

Denzim in Evaluating Qualitative and Quantitative Research by Cresswell (2005:437) said that Ethnographies need to include perspective drawn from feminist thought, racial views, sexual perspectives, and critical theory, and they need to be sensitive to race, class, and gender. Ethnographies today are now “messy,” and find presentation in many forms, such as a performance, poem, play, novel, or a personal narrative.

B.     The Characteristics of An Ethnographic Design

The following characteristics typically mark an ethnographics study are:

1.      Cultural themes

Ethnographers typically study cultural themes drawn from cultural anthropology. Ethnographe do not venture into the field looking haphazardly for anything they might see. Instead they interested in adding to knowledge about culture and studying specific cultural themes.

2.      A culture sharing group

Cresswell (2005:443) said that ethnographers learn from studying a culture-sharing group at a single site. A cultural-sharing group in ethnography is two or more individuals who have shared behaviors, beliefs, and language.  Table of the study of a culture-sharing group in a third grade elementary classroom:

Table 1
The Study Of A Culture-Sharing Group In A Third Grade Elementary Classroom
Characteristics of a culture-sharing group	An example
1.      The group consists of two or more individuals, and it may be small or large 2.      The group interacts on a regular basis 3.      The group has interacted for some time 4.      The group is representative of some larger  group 5.      The group has adopted some shared patterns of behaving, thinking, or talking	A small group- two readers in classroom A larger group-six to ten readers in classroom For a period three times a week, the groups meet to discuss a reading Since the beginning of september, the reading group has meet three times a week for three periods The small reading group is representative of third-grade readers The group has certain rituals they perform as the begin to read, such as sitting on the floor, opening their book to assigned page, and waiting to speak until the teacher calls on them to answer a questions

3.      Shared patterns of behavior, belief, and language

It is a common social interaction that stabilizes as tacit rules and expectations of the group.

4.      Fieldwork

5.      Description, themes, and interpretation

6.      Context or setting

7.      Researcher reflexitivy

C.    The Nature of School Mathematics

Ebutt and Straker in Marsigit (2003) define the nature of school mathematics like below:

1.      Mathematics as a searching pattern and relationship, some aspects that include in here are given a chance for students to do a discovery activities and find the patterns to determine the relations; give a chance for students to try by their own way; support them to fins the arrange, difference, comparison, group, etc; support them to make a general conclusion; help them to understand and find the relationship between the meaning one others.

2.      Mathematics as a creativity that need imagination, intuition, and discovery. Some aspects that include here are support students creativity and give a chance to different thinking, support their feel to like to know, support their estimate and their discovery,etc

3.      Mathematics is problem solving, some aspect that include here are give a space to learn mathematics to guide a mathematics problems, help students solve mathematics problems by their own way, help students to get some informations that needed to solve mathematical problems, etc

4.      Mathematics as a communication tool, some aspects that include here are support students to know about mathematics, support students to make an example about mathematical properties, support students to give a reason why we need mathematics, etc.

D.    Mathematics Teaching Learning Design based On Ethnomathematics

From ethnograph explanation above, we will know that it reflect to ethnomathematics and hermeneuthic. Then from those we will get many values that influenced by the nature of school mathematics and the nature of students learn mathematics in many times start from archaic, tribal, traditional, feodal, modern, until post modern. These also affected by anthropology that focused on subculture, such as career and life histories or role analyses of individuals; microethnographies of small work and leisure groups within classrooms or schools; studies of single classrooms abstracted as small societies; studies of school facilities or school district that approach these units as discrete communities. Cresswell (2005:437). And also affected by society psichology based on logic and experiences of educational components by ice berk process (concrete mathematics, concrete model, formal model, until formal mathematics ) by using mathematical value to gel teaching and learning process then we get how to enculture mathematics, like the scheme below:

A.    What Kind of Mathematics Teaching and Learning that can Enculture Mathematics

There are some models that effective to enculture mathematics like constructivism models.  Richard and Helen (2008:61)  said that there are many ways to evaluate students ability to understand the material, like below

...So, there are two possible evaluation methods that these studenys use as certaining the fit of an activity to their personal dispositional profile, and to some extent, socially identifying with their teachers and other students. These task evaluations can then be consolidated into a task-specifics self concept, the degree to which the parameters for involvement in a task fit the personal beliefs a students has about their abilities, desires, and aspiration.

Constructivist teaching is associated with learning that is made up from some or all of the following; critical thinking, motivation, learner independence, feedback, dialogue, language, explanation, questioning, learning through teaching, contextualisation, experiments and/ or real-world problem solving.

To enculture mathematics, students must compare their own knowledge with other, and one of model that suit with it is collaborative learning. Interpersonal collaboration is a style for direct interaction between at least two co-equal parties voluntarily engaged in shared decision making as they  work toward a common goal. (Marilyn dan Lynne, 2007: 7).

Beside those, teacher also must using manipulatives teaching aids. The use of manipulatives in mathematics instruction-especially in primary schools- is wide spread. In particular, there seems to be a very extensive and at times uncritical, in any case these working materials are strongly recommended as essential learning aids by publishing companies abd in (mathematical-didactical) textbooks

Concrete materials and representations need different forms of practice in relation to their physical nature. The use of manipulative seems to be more like the use of a tool.

Fischbein 1977 p 163f said that material objects have to elicit mathematical thinking, they must do it by their inner, specific properties[...] Concrete models are not necessarilly initialiting techniques in the teaching of mathematics. Their efficient use depends on their nature and on their relationships with the corresponding mathematical concepts.

For mathematics instruction in preschool in primary school as well as in secondary school I (grades 1 to 10, ages 5/6 to 16) manipulatives are in many regards an indispensable means to learn and to understand the abstract and symbolic mathematical knowledge

In the centre of our theoritical analysis of the role of mathematics teacher education is the relation between manipullatives and mathematical knowledge. The relation between these two elements is always produced by a person (a students, the practicing teacher or a researcher). Shcemes like below:

 

Figure 3. Manipulatives as an epistemological learning medium for students and prospective teachers.

 

Figure 4. Manipulatives as an epistimological learning medium for prospective and practicing teachers.

B.     References

Manipulatives As Tools In Mathematics Teacher Education Volume 2. 2008. Netherlands: Sense Publishers.

Cresswell, W. John. 2005. Educational  Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research. Netherlands: Pearson Education.

    http://www.tammypayton.net/courses/collab/what.shtml access on Monday, 26^th March 2012