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1.13.2012

MATHAMATICS TEACHING ACROSS MULTICULTURAL CONTEXTS

By : Nurmanita Prima R.
NIM : 09301241014 (PmatSub’09)

I. INTRODUCTION
Based multicultural education is important applied in an educational system. The meaning of the word itself is multicultural diversity. Thus, based multicultural education is education for or about the diversity of cultures in response to changing demographic and cultural environment of certain communities or even the world as a whole. Through-based multicultural education, attitudes and thinking more open students are expected to understand and appreciate the diversity that can change the thinking of learners to truly sincere respect for differences of ethnicity, religion, race, and Intergroup.
Multicultural education would succeed only if teachers understand the insights of multiculturalism. Meanwhile, major constraints faced by the strengthening of multicultural awareness is access to information that is difficult to achieve teacher. Consequently, teachers do not understand the meaning of multiculturalism that is insensitive to the problems of difference. The solution, of course by enabling teachers to get information from print and electronic media. For example, by providing reference books and newspapers in the school library. For teachers that are easier to get information, be more active to implement multiculturalism in the classroom. If possible, helped spread the multiculturalism diligently shared, for example by writing on blogs, newspapers, and magazines.
In fact, speaking at local forums, national, and international levels. That way, peers will be motivated to try to implement a way of learning a matching multiculturalism. After learning the importance of the implementation of multiculturalism education in Indonesia, the only thing to do is start. It is not easy, especially for teachers who are spearheading this update. It is impossible simply to rearrange the views and attitudes that brought the child from the family and social environment. Things you can do is to tell the teacher to students, that there are other social views in addition to the social view that is embedded through family education. Expand the horizons of students so that teachers can compare the social outlook of the social views of others. It also can compare mathematics learning systems between a country with another country.
II. CONTENT
Mathematics learning system in a state is not same as the system of learning mathematics in another state. Likewise with math learning system in Indonesia is not same as other countries such as Japan, Vietnam, Korea, America, etc.. Each has a different character in accordance with the policy of the education system in each country. The following will discuss the differences between the education system, particularly in mathematics learning among Indonesia, Japan, Vietnam, and South Africa.
A. MATHEMATIC’S LEARNING IN INDONESIA
How to learn an active and constructive will be able to improve the quality of human resources significantly. Therefore, if we want the learning of mathematics in our schools can truly improve the quality of Indonesian human resources, presumably a way of learning an active and constructive mathematics also need to be used by our students. As has been described by Schifter and Fosnot, the process of using this way does require a strong will, given the students and teachers in Indonesia, as it also occurs in many other places in the world, have been accustomed to the old paradigm (the teacher explains - students listen and follow the instructions of teachers), coupled with the presence of socio-cultural factors that differ from those existing in other states. However, if we really really want to overcome the weaknesses that exist in mathematics education in our country, the changes we have to do.
Purpose of Mathematic’s Learning in Indonesia :
1. Characteristically purpose FORMAL
School mathematics learning has a purpose that is formal. In this case the learning school mathematics provided to students is intended to organize and form a logical learner personality.
Objectives contained in this formal aspect of the values associated with the daily life of students present and future. In terms of these values, the learning of mathematics in the past more emphasis placed on achievement, the more likely are not designed, but by itself. Currently learning the values contained in many mathematical subjects studied through lesson plans that are deliberately structured towards the formation of these values on students.


2. Objectives that are MATERIALS
Learning math has a purpose that is material. In this case the learning school mathematics provided to students is so that learners can solve math problems and can apply mathematics. Objectives that are material that has been the only goal for almost everyone.
In addition, it is mentioned also that the purpose of teaching mathematics at each educational unit are as follows:
a. In the Elementary School (SD):
 Growing and developing numeracy skills (using numbers) as a tool in everyday life.
 Develop student's ability to dialihgunakan through mathematical activities.
 Develop a basic knowledge of mathematics as a further study in junior high.
 Establish a logical manner, critical, careful and disciplined.
b. In Junior High School:
 Students have the ability to move through mathematical activities.
 Students have knowledge of mathematics as a preparation to proceed to secondary education.
 Students have the math skills as an enhancement and expansion of elementary school mathematics to be used in everyday life.
 Students have a fairly broad view and an attitude of logical, critical, careful and disciplined as well as appreciate the usefulness of mathematics.
Based on these symptoms, can be presumed that the learning of mathematics in Indonesia today has not been able to actualize the potential possessed by the mathematics on students.
Discussed above have the goal of learning mathematics, namely the formation of the students' reasoning ability that is reflected through the critical thinking skills, logical, systematic, and have an objective nature, honest, disciplined, in solving a problem both in the field of mathematics and other areas of daily life .
However, the actual situation is not as expected. Applied learning that nearly all school text book oriented and tend to be less related to students' daily lives. Which tend to be abstract mathematical learning, while most teachers in teaching is still less attention to students' thinking ability, or in other words a creative learning. As the methods used are less variable, do not perform meaningful teaching, and as a result the students' motivation to be difficult to be grown and patterns tend to memorize and mechanistic study.
In addition, if we look at the learning of mathematics in schools in Indonesia today, there are several symptoms that stood out, among others:
• Learning materials are very dense compared to the time available.
• Learning strategies are more dominated by efforts to complete the learning material in the time available, and the lack of prosed in the student to digest material actively and constructively.
• Orientation of learning that focused on general tests.
• Lack of linkages between the materials and processes to real world.

B. MATHEMATIC’S LEARNING IN JAPAN
The purpose of education in Japan is different with the aim of education in Indonesia. In the Imperial Rescript on Education stated that the purpose of education in Japan is to increase the loyalty and obedience to the emperor in order to obtain unity of the people under the same father, the emperor. The purpose of education according to the Fundamental Law of Education is to enhance the development of personality as a whole, respecting individual values, and instilling a free spirit.
Developing student’s mathematical thinking in Japan:
1. Putting student’s activities in the center of classroom and these activities to be creative or inventive for students.
A lesson (classroom) develops mathematical thinking by students’ problem solving. Teachers guide and support their activities.
2. Creative activities (problem solving) should be meaningful both for students and teachers.
We try to analyze the elements and structures of mathematical thinking and to help students acquire them.
What is Beginning to Be Expected of Mathematics Teaching in Japan
a. Teaching the Basics
Efforts toward helping children acquire the basics of mathematics should be integrated with the aim of getting them to think on their own and express their own character and individuality. Furthermore, it is considered that acquiring the basics does not mean notonly knowledge and skills but also includes abilities and attitude in learning content, the core of which requires thinking mathematically and problem solving. It is necessary, in order to carry out instruction based primarily on guidance for learning the basics, for the teacher to get as clear a grasp as possible of the content.
(1) The Content Aspect
One aspect of and the basics basics is the content. It includes the contents in the textbooks, which are generally consid ered the knowledge and skills that are divided into the instructional content for each grade. Another part of the content aspect is thinking mathematically as the basis for producing knowledge and skills. It is the core of the content of learning the basics. It is necessary to foster an ability to understand content, appreciate its usefulness and learn to apply it to other things on the basis of the child's development up to the present grade in school through the content of the instruction in the different areas of mathematics. The following are examples of thinking mathematically :
 Expressing numbers in terms of place value, and thinking in terms of units, rate, ratios.
 Thinking logically—drawing analogies, reasoning inductively and reasoning deductively 108.
 Thinking in terms of functions and paying attention to constituent elements in figures.
(2) The Method Aspect
The method aspect of the basics consist of problem solving and learning abilitites. Although not all of the method aspect can be distinguished from the content aspect, it is a good idea to distinguish the following kinds of abilities and attitudes in instructional practice:
 Proceeding with classroom instruction on the basis of the children's own questions concerning what is being sought and how to find it.
 Letting the children themselves form a general idea on how to solve the problem themselves, plan how to go about it, and then find the answer on their own.
 Encouraging the children to utilize already acquired content and experience and develop it further.
 Having the children take notes on the classroom proceedings to be used in group exchanges and self-evaluation.
 Encouraging them to actively communicate with one another so as to learn from one another as a group.

b. Emphasis on Children's Own Initiative
There should be more emphasis placed on children's own initiative in classroom learning of mathematics. It is important that children discover the meaning of quantities and figures and come to have an awareness of mathematics and increase their depth of knowledge through experiences such as observation and experimentation and moving their bodies inside and outside the classroom.
The different ways individual children think should be given importance in instruction of mathematics. Furthermore, by sharing their ways of thinking, children are able to acquire more versatile viewpoints. In classroom instruction, deductive, inductive and analogical reasoning are frequently required of children. Also, in many cases they can solve new problems using knowledge and reasoning that they have already learned. What is being asserted here can be expected to contribute significantly to nurturing the basis for their
creativity.
c. Emphasis on Enjoying Mathematics
Mathematics should be taught in such a way that children enjoy it and obtain satisfaction from it. The basis for making mathematics fun for children is to help them feel that they understand it, which will lead to the feeling that "thinking mathematically is fun." That being the case, the teacher has to show ingenuity in mathematics class from the viewpoint of showing how much fun and how interesting and worthwhile it is to learn mathematics and how wondrous it can be. If the children use the mathematics that they have learned to solve problems in various situations around them, they will learn to appreciate how much fun and how useful it is learning it.
Examples of application of methods of learning in Japan:
Learning mathematics, especially in elementary and secondary schools in Japan is very interesting, the teachers are always prepared to learn a very simple materials such as paper, scissors, tongs clothing, or other materials that are easy to find.
For instance, an elementary school teacher at Tsukuba University affiliation to teach children about numbers 5 th grade material lined with paper and scissors. With the fold and cut the principle of `` the children lined up in a fun learning numbers.
The way is by cutting A4 paper folded twice lengthwise, then cut to follow the pleats so that the paper lengthwise into 4 pieces. Furthermore, the paper extends the first foldable 1 time and then cut. Thus, by folding the first time and cut out 1 time, will produce two new pieces of paper. What if folded 2 times, then cut in the folds of the latter? How many pieces of new paper that will be generated? the result is three new pieces of paper. So already established series of numbers 0, 2, 3. Furthermore, if folded three times and then cut out, how many pieces of paper that will be generated? Before practice, the teacher asked the students beforehand. Most of the students answered 5, others answering 6. Why answer 5, why answer 6, everyone was asked to explain why. Blackboard was filled with graffiti and illustration of children.
Interestingly teacher was not patronizing to tell you the answer directly, but as if he did not know, and ask students to explain. Through this way, it is known that Japanese children are very rich in ideas or creativity. There are three principles of teaching and teachers in Japan, namely:
1. Anoshii jugyou (class should be fun)
2. Wakaru ko (child must understand)
3. Dekiru ko (child must be able to)
Through such learning models, we can see how the kids in Japan are taught to analyze a problem, or find a solution, no formula was bombarded with this formula. They had taught the formula after they understand the origins of a theory, and can use it in everyday life. They are also not taught many things, few are important to understand. Therefore teachers in elementary school was shocked to discover children grade 1 in Indonesia has been studying numbers to 100.
C. MATHEMATICS’S LEARNING IN VIETNAM
In Vietnam, the classroom mathematics teachers have learnt more on the innovative teaching strategies to implement more effective lessons focusing on mathematical thinking. A case study will be analysed using the observed students' activities in a videotaped lesson.
In Vietnam, teachers encourage their students to invent their own procedures for solving problems. The teachers use the teaching strategies that aim to:
 Promote active, initiative and self-conscious learning of the learners.
 Form and develop the ability of self-study.
 Cultivate the characteristics of flexible, independent, and creative thinking.
 Develop and practice the logical thinking.
 Apply problem solving approaches.
 Apply mathematics to real life situations.
Activities by teachers in the process of learning mathematics in Vietnam:
1. Teacher manages students to work and achieve the following aims:
 Examine the students previous knowledge;
 Consolidate the previous knowledge involved with new lesson;
 Introduction to the new lesson.
2. Teacher facilitates students explore mathematical knowledge and construct new knowledge by themselves.
3. Students practice the new knowledge by solving exercises and problems in the textbook.
4. Teacher concludes what students have learnt from new lesson and assigns the homework.
Engaging to the lesson, the pupils will have opportunities to show their mathematical thinking through:
 The ability of observing, predicting, rational reasoning and logical reasoning;
 Knowing how to express procedures, properties by language at specific levels of generalization (by words, word formulas);
 Knowing how to investigate facts, situations, relationships in the process of learning and practicing mathematics;
 Developing ability on analyzing, synthesis, generalization, specifying;
 Starting to think critically and creatively.
The key windows for considering mathematical thinking are as follows:
 Students learn mathematical concepts with meaningful understanding;
 Students construct individual algorithm and techniques themselves with understanding to solve some specific problems;
 Students use learnt mathematics to solve mathematical problems effectively;
 Students show mathematical thinking by communicating (talking, writing, arguing, discussing, and representing);
 Students reflect critically their mathematical thinking in order to improve their learning;
 Mathematical thinking is social and relative to each individual student;
 Students apply logical and systematic thinking in mathematical and other contexts;
 Students use thinking operations in solving problems: comparison, analogy, generalization, and specialization;

D. PEMBELAJARAN MATEMATIKA DI SOUTH AFRICA
Like other countries, South Africa also has its own learning system, which is different from the learning system that is in another country. In South Africa, this short presentation reports on an in-service training programme of Primary School teachers in a mining town in Mpumalanga, one of the nine provinces in South Africa. At this particular session, teachers were placed in a simulated classroom situation where they were exposed to the van Hiele levels of Geometrical thought. This session mainly concentrated on van Hiele level zero (visualisation). Various two dimensional shapes were provided to teachers in groups. The following procedures were followed:
• One teacher would choose a shape, and the rest of the group would then describe the shape.
• The groups were asked to classify the shapes according to given properties
The videotape which will be shown, reveals most interesting thinking processes of teachers, which can be used fruitfully in any teaching environment. In another video clip, an example of intervention that was not conducive for mathematical thinking will be shown, which can be used as a sample for discussion.

III. CONCLUSIONS
Learning mathematics is essential to apply. It can be used as a reference system of mathematical learning that exist in Indonesia, learning mathematics is applied in foreign countries such as Japan and Vietnam have proved successful. It can be seen from the intelligence level of students in the country compared to Indonesia and the country's level of progress which marks the creativity of its citizens. Therefore, it is time for Indonesia to start using the system multicultural learning mathematics, not to stay glued to the existing system now.

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