A. INTRODUCTION
Multicultural education implies that education process is implemented on learning activities in the education unit element always put the difference as a matter of course, as the implications of multicultural education to bring learners to get used to and did not make any difference in principle to mingle and make friends with anyone regardless of background cultures, ethnicities, religions, races, and customs that exist. Multicultural education to prepare all students to work actively toward structural equality in organizations and school institutions.Multicultural education arose as a wing of a difference in the elements of culture, ethnicity, race, religion, and the like. A nation with all its plurality should not make a difference is the reason for the practice of dis-integration of the nation. A lot of things behind the importance of studying and implementing multicultural education in the learning process in the educational unit in Indonesia.
The learning process can be implemented based multicultural and implemented on the life and atmosphere of learning, then the horizontal divisions can certainly be minimized by understanding the true nature of the differences as a gift and wealth rather than a difference as a matter of a separation. Learners can certainly understand this, if the life she lived is not out of context and nature-based multicultural education.
Implications for the development of Multicultural Education is the inclusion of teaching materials containing ideas of various cultural groups. Education does teach its own cultural values, but in addition it also perpekstif and culture of other people in the region other people around the world. This can make students cultural literacy that is able to see a variety of cultural perspectives that have ever lived in various parts of the world.
Learning by reflecting on different materials. In particular, teachers incorporate the content of learning materials into the curriculum with some diverse perspectives. One common approach is to acknowledge his contribution, namely the teachers to work into their curriculum by limiting facts about the spirit of heroism from various groups. In addition, the design of learning and learning units are not changed. With some approaches, the teacher adds a few units or topics specifically related to multicultural material.
Each state's education system is different with the emphasis on a particular variable in education. In the variable contained goals to be achieved both long and short term. So that will provide direction for the country to create human beings and they want a State based on their human resources plan based on the educational system. With different educational systems to teach mathematics then the system is also different between Indonesia by Country - Other countries, such as Indonesia with Japan, Malaysia and America. Each - each State has the characteristics of the teaching of mathematics. The following will discuss the differences between systems of learning mathematics in Indonesia with the learning system in Japan.
B. CONTENT
1. Learning Mathematics in Indonesia
The development of mathematical learning in Indonesia is very alarming, because of the low mastery of technology and human resource capacity of Indonesia to global competence. Indonesia is a country with abundant natural resources. But Indonesia is still low ability children in mathematics, they assume that learning math is hard, and insufficient numbers of teachers who follow the development of mathematics. Creativity is the learning of mathematics in Indonesia should be developed, because it must be taught mathematics in an interesting and connected with the real world so that students are happy. Methods and learning strategies that have been implemented in Indonesia are so many, but not optimal in its implementation. So that teachers are still confused to implement good learning method for the participant students.
The goal is the creation of learning mathematics reasoning abilities in students, as reflected by the ability of critical thinking, logical, systematic, and have an objective nature, honest, disciplined, in solving a problem both in the field of mathematics and other areas of everyday 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.
The new paradigm of education is now more emphasis on the learner as a human being yan has the potential to learn and grow. Various approaches for learning mathematics is too influenced by the view that the mathematical tools that are ready to use. This view tends to encourage teachers to be informed concepts / theorems and how to use it. Teachers tend to transfer knowledge to the minds of students and the students accept it passively and uncritically. Sometimes students answer the questions with really but they can not reveal the reasons for their answers. Students can use the formula but do not know where it came from and why the formula is the formula that is used.
Such circumstances may occur because in the process of learning the students are given less opportunity in expressing their ideas and reasons for their answers. Change of mind to consider early on is that student learning outcomes is the responsibility of students themselves. This means that the results of student learning is directly influenced by the characteristics of the students themselves and their learning experience. The learning experience will be formed when students get involved in learning as seen from the learning activities.
In fact, many teachers stating the cause of low yields in Indonesia are learning mathematics is that students are less able to understand abstract material, students are less able to link the knowledge they already have, that this results in students less eager to follow the math. These conditions indicate the need for change and improvement in an effort to improve student learning outcomes is to improve the quality of theaching to improve mathematics learning outcomes.
If we look at the learning of mathematics in schools in Indonesia today, there are few obvious symptoms, among others:
a. Learning material is very dense compared to the time available.
b. Learning strategy that is more dominated by efforts to complete the learning material in the time available, and the lack of process in the student to digest material actively and constructively.
c. Learning orientation is fixed on the general test.
d. Less link between the material and the learning process with the real world.
School mathematics learning objectives that each time need to be adjusted and specified in accordance with relevant education.
· Characteristically the purpose of 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. (If it is understood and agreed, it is clear that ketercapaiannya is not only seen from the pass / not pass the exam).
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 emphasized the attainment of which is "by chance", which is less likely to be designed but by itself. Currently learning the values contained in many mathematical subjects studied through Lesson Plan that is deliberately intended toward the establishment of these values on students. This is commonly called "by design". (See appendix, a paper which the authors convey in an international congress recently in Japan, with the title: Designing Instruction of Values in School Mathematics).
· 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 sole purpose for almost everyone. If not as if "graduation" is the ultimate goal of learning school mathematics. The emergence of "courses" before certain tests confirm this opinion.
With the growing breadth of mathematical reality today, which is definitely not possible all the "stuff" should be taught to students, mathematics educators began to seriously pay attention to students, mathematics educators began to seriously pay attention to the formal aspects of the lesson mathematics it self, especially with relation to the requirement set which parts of mathematics that includes mathematics for all.
Gave a general purpose math in elementary and secondary education are:
a. Preparing students to be able to face the changing circumstances in life and in the world that is always evolving, through the practice of acting on the basis of thinking in a logical, rational, critical, careful, honest, efficient and effective.
b. Preparing students to use mathematics and mathematical thinking in everyday life and in studying various science.
Each of the learning process must show active learners. In the most important mathematical learning is the process of thinking done. Students are trained to develop ability logical thinking, analytical, systematic and consistent. To assist in the process of thinking and or animated images can be used so that students will more easily and overcome difficulties in the natural. Thus, learning in Indonesia that are still monotonically with various methods and strategies should be developed for the purpose of learning to run properly. Learning mathematics is indeed difficult, but the difficulties it can be easy when students are already interested in the methods applied by teachers can be fun, attract attention and motivate them to learn mathematics.
2. Learning mathematics in Japan
A particularly noticeable accomplishment in the past 20 years of lesson study in Japan has been the transformation from teacher-directed instruction to student-centered instruction in mathematics and science. The success of lesson study can be found in two primary aspects: improvements in teacher practice and the promotion of collaboration among teachers.
Classroom instruction based on problem solving makes the most of activities by children based on their own initiative and judgment and emphasizes having children themselves finding solutions to problems.
Ø 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.
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.
There ought to be a lot of situations in mathematics class where children can encounter discovery, emotion and satisfaction of attainment. What it takes to make mathematics seem interesting and fun is to have them experience those feelings as often as possible. The more children come to like and enjoy mathematics through experiencing how interesting and even how much fun it can be, the better. We must not give up on children who have not been very good at mathematics so far. They, too, can learn to think "That mathematics class was interesting." We must not continue with teaching methods that produce feelings in children like "I don't want to do mathematics anymore!" and "Thank goodness there isn't mathematics anymore!" What we have to aim for is the kind of classroom instruction that can turn the consciousness of children concerning mathematics in the direction of "mathematics is really interesting!".
Ø Concretization of Instruction by Problem Solving Methods
In order to build instruction based on problem solving, it is necessary to consider what makes instruction characterized by emphasis on acquisition of the basics. In that connection it is important to consider the following points:
a) Awareness of the overall curriculum plans for mathematics
b) Formulation of concrete instruction plans for the different units of instruction
c) Definition of how the class hour of instruction is to proceed and how the situation regarding acquisition of and the basics is to be determined
The following points are also important in the case of instruction based on problem solving:
a) Achieving the result of initiative on the part of the children themselves in instruction based on problem solving.
b) Preparation of materials for the instruction that are suitable for the content to be taught and in tune with the needs and lives of the children.
c) Setting of instructional goals in tune with the actual conditions of the children and the educational tasks of the school and relating the difficulties of acquisition of the basics with the methods of evaluation of such instruction.
d) Supporting activities that stimulate the enthusiasm and problem awareness of the individual children and that encourage them to think and pursue solutions on their own.
e) For group discussion activity that can lead to better problem solving, changing from the kind tailored to the teacher to the kind based on the viewpoint of the children the mselves that can serve as a forum for discussion and communication in which they themselves share their values.
In general, instruction processes such as those indicated below come to mind regarding classroom instruction based on problem solving, the aim in each process (step) being acquisition of ability and the necessary attitude concerning problem solving.
a) Formulating the problem.
b) Understanding the problem
c) Planning solution of the problem
d) Carrying out the solution
e) Consideration of the solution
3. Learning mathematics in Vietnam
In Vietnam, teachers encourage their students to invent their own procedures or algorithms 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.
In the teachers’ guidebook for primary mathematics teachers at each grade there are four main activities in a lesson that teachers should follow to develop mathematical thinking:
a) 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.
b) Teacher facilitates students explore mathematical knowledge and construct new knowledge by themselves.
c) Students practice the new knowledge by solving exercises and problems in the textbook.
d) Teacher concludes what students have learnt from new lesson and assigns the homework.
Key windows for considering mathematical thinking are as follows:
a) Students learn mathematical concepts with meaningful understanding;
b) Students construct individual algorithm and techniques themselves with understanding to solve some specific problems;
c) Students use learnt mathematics to solve mathematical problems effectively;
d) Students show mathematical thinking by communicating (talking, writing, arguing, discussing, and representing); Students reflect critically their mathematical thinking in order to improve their learning;
e) Mathematical thinking is social and relative to each individual student;
f) Students apply logical and systematic thinking in mathematical and other contexts; Students use thinking operations in solving problems: comparison, analogy, generalization, and specialization;
Teaching primary school mathematics aims to equip young pupils with basic mathematics skills and develop their mathematical thinking to solve problems. Some senior classroom teachers have experienced to foster and develop students’ mathematical thinking without theoretical background. Most of teachers in Vietnam really need a practical framework to develop pupils’ mathematical thinking in their actual classrooms.
4. Learning mathematics in Malaysia
Malaysian practicing mathematics teachers agreed that a good lesson plan or good teaching practice should encompass the following characteristics:
a) Student centered activities that encourage conceptual understanding
b) Related to students’ daily life experiences
c) That the students understand what is being taught and can apply what they have learned to solve problems
d) Good planning of student activities
e) Active participation of students in fun and meaningful activities
f) Use of teaching aids that enhance students’ conceptual understanding
Ø Challenges to Good Teaching Practices
a) Examination oriented culture
The Examination oriented culture is still very much prevalent in the Malaysian society. Examination results play an important role as a yard stick of accountability to the school performance. Hence, students’ performance in examinations is used by school principals as a yard stick to evaluate teachers’ teaching competency. Consequently, most teachers set their teaching priority on finishing the syllabus so as to ensure their students achieve excellent performance in these examinations. Very often, teachers need to spend a considerable amount of time conducting additional classes to prepare the ir students for these public examinations. This leaves teachers with very little time for professional development and innovative teaching.
b) Time constraint
Good practice of mathematics teaching requires student centered activities that promote conceptual understanding and active student s participation. However, these activities are usually time-consuming. Due to the examination oriented culture as discussed above, teachers need to cover a fixed amount of syllabus within a limited teaching time. Hence, many teachers tend to adopt the traditional teacher centered approach that requires lesser preparation time.
c) Teacher’s beliefs
Although most Malaysian teachers support the characteristics of good practice in mathematics teaching as mentioned above, many of them also believe that by giving clear explanation with suitable examples (teacher-centered approach) is more practical and good enough to achieve most of the teaching objectives. They feel that it is too much a hassle to allow students to construct their knowledge through student-based activities. They are not confident if their students could have acquired enough knowledge and skills by exploring the lesson themselves. Hence, the teachers tend to use the teacher centered approach where they can control the teaching and learning pace of their students. In other words, the teaching culture and school context failed to promote teachers to adopt innovative and good teaching strategies. Under such circumstances, it is a real challenge for many teachers to incorporate good teaching practice.
C. CONCLUTION
Teaching learning process of mathematics in Indonesia today, there are few obvious symptoms, among others:
a) Learning material is very dense compared to the time available.
b) Learning strategy that is more dominated by efforts to complete the learning material in the time available, and the lack of process in the student to digest material actively and constructively.
c) Learning orientation is fixed on the general test.
d) Less link between the material and the learning process with the real world.
Teaching primary school mathematics aims to equip young pupils with basic mathematics skills and develop their mathematical thinking to solve problems. Some senior classroom teachers have experienced to foster and develop students’ mathematical thinking without theoretical background. Most of teachers in Vietnam really need a practical framework to develop pupils’ mathematical thinking in their actual classrooms.
In Japan, instruction processes such as those indicated below come to mind regarding classroom instruction based on problem solving, the aim in each process (step) being acquisition of ability and the necessary attitude concerning problem solving.
a) Formulating the problem.
b) Understanding the problem
c) Planning solution of the problem
d) Carrying out the solution
e) Consideration of the solution
Malaysian practicing mathematics teachers agreed that a good lesson plan or good teaching practice should encompass the following characteristics:
a) Student centered activities that encourage conceptual understanding
b) Related to students’ daily life experiences
c) That the students understand what is being taught and can apply what they have learned to solve problems
d) Good planning of student activities
e) Active participation of students in fun and meaningful activities
f) Use of teaching aids that enhance students’ conceptual understanding
