By
Name: Lina Dwi AS
Prodi: Mathematics Education
A. Introduction
Mathematics is universal knowledge that basic of development of modern technology, moreover Mathematics be an important in a variety of branch of science and in forward capability of human thinking. The lesson of Mathematics need to be given for all students from primary school in order to the students have a capability in logical thinking, analysis, systematic, critical, and creative, and be able to work together in group. The capability has any for each student so that the student can have a capability of obtaining, processing, and employing the information to survive and to competition with other people. Various multicultural in the world affected teaching learning activity process of mathematics in each country are very different. Because each country has students with different skills, teachers with different competences in teaching learning of mathematics for students and curriculums are used in each countries are very different. The curriculums are used each countries has special characteristic. Therefore the teaching learning activity of mathematics carried out in each country adaptable with the context of situation in its country. This paper try to explain the context of teaching learning of mathematics is used in Thailand, Japan, Brunei Darussalam, and Indonesia in develop mathematics teaching across multicultural.
B. Mathematics Teaching Across Multiculture
In effort to increase the capability of mathematical thinking for the students, some countries as Thailand, Japan, Brunei Darussalam, and Indonesia has special context and characteristic of mathematics teaching. The following explain about mathematics teaching across multicultural in context of Thailand, Japan, Brunei Darussalam, and Indonesia.
1. Thailand context
The context mathematics teaching in Thailand is a learning mathematics with approach of mathematical models. Using the approach mathematical models so that the teacher can train his or her students to survive and get confidence to competition with their friends or other people in the real world. The mathematical models is the real form of shape of the problems there are in the real world, in where the solution of the problems can be finished with use the technique and formula of mathematics. The mathematical modeling is defined as translating that is faced in the daily life in to form of mathematics with make mathematics as a tool to solve the problem.
Learning mathematics with use approach of mathematical modeling to solve the problem that related with daily life, help the students to develop their skill mathematics to find the solution of the problem, and can help the student to develop their creativity to search the solution that easy to understand. Moreover, that is can to develop their understanding about the application of mathematics applicable to solve the problems there are in the real world. Almost of all problems in the world can be model by mathematics. Through mathematical model we can choose a way to solve the problem. The process of mathematical model consists of four stages according to context of Thailand (in Frank Swetz & J.S. Hartzler. (1991)), that is:
1. Observing a phenomenon, delineating the problem situation inherent in the phenomenon, and discerning the important factors (variables/parameters) that affect the problem.
2. Conjecturing the relationships among factors and interpreting them mathematically to obtain a model for the phenomenon.
3. Applying appropriate mathematical analysis to the model.
4. Obtaining results and reinterpreting them in the context of the phenomenon under study and drawing conclusions.
The activities of mathematical model amendable in form E-Activities. Implementation tutorial activities of mathematical model can be accessed in everywhere and every time through E-Activities. Teaching learning mathematics use the approach mathematics implementable use of teaching aid adaptable with the materials is presented. Moreover we can use the ICT as a computer with complete of special software to mathematical model to make easier the student in understanding of the new concept mathematics. The mathematical model can be use in arithmetic, linear programming and etc.
2. Japan Context
The context of mathematics teaching in Japan is learning using approach structure problem solving. Small group discussions were used in this context. In the group, the student can share their idea to other student to find the solution of the problem use their understanding and their knowledge are obtained previously. Through identification process the student can discuss the problems with their friends to formulate the strategy to solve the problems. Identification activity can develop mathematics thinking skill to apply their knowledge to choose the good method to solve the problems. The mathematics textbooks are used in Japan contain of instructions and steps to finish the problems.
The teachers’ Japan often underline that in structure problem solving, in truth the teaching learning mathematics get started after the student succeeded finishing the problems. The student build their comprehension to understand the new concept is not they found previously, after that the student explain the result of discussion in front of all students, and then the teacher review his or her student’s result. And the teacher guiding the students to make conclusion based on material are learned in the time.
At the same as they build understanding of the new mathematical concept, they also develop mathematical practices and dispositions, such as sense-making, perseverance, constructing and critiquing arguments, modeling with mathematics, organizing data, and so forth. In this way, lessons do double-duty, building both a specific mathematical concept and broader mathematical habits of mind, skills, and dispositions. There are some phases of a structured problem solving lesson according to context of Japan that are:
1. Phases one is posing and understanding the task (brief).
The purpose of these phases is teacher poses the task, student understand and become interested in the problem to be solved.
2. Independent Problem-Solving (10-20min).
Students bring their own prior knowledge to bear, and try to develop ways to solve the problem. There may be input from classmates after students work for a few minutes on their own, but students are individually exerting effort to come up with a solution approach. Students are not simply following the teacher’s solution example.
3. Presentation of Students’ Solutions and Class Discussion (orchestrated by teacher’s enrage “kneading” or “polishing”) (15-30min).
The purpose of phases three is the teachers select several students to present their work on the blackboard and explain it. Teachers carefully choose and sequence the student work that is presented, in order to support development of the important mathematical understanding. Class members actively study the solutions, supported by teacher question such as ‘’How many solved it this way? Students contrast solutions, supported by teacher questions such as ‘’what is the same and different about Kyoko’s and Mariko’s solution?’’ ‘’What are the good points and difficulties of each of solution method?’’ discussion focuses on the thinking and reasoning used to solve the problem and on the central mathematical ideas.
4. Summary/ Consolidation of knowledge (brief).
The purpose of phases four is the teacher and students make summarize what has been learned. Blackboard writing, class discussion, and math journals support students to revisit their thinking and consolidate their knowledge. Class often ends with a journal writing prompt like ‘’what I learned today’’.
To build the structure problem solving instruction need four support according to context of Japan, that is:
1. Mathematical task suited to structure problem solving.
2. Knowledge of student thinking.
3. Teaching strategies.
4. Motivation gained from personal experience of problem solving.
3. Brunei Darussalam Context
Usually the context of mathematics teaching in Brunei Darussalam is learning using a mathematics textbooks and E-textbooks as a primary source in process of learning mathematics. Mathematics textbooks are used by the Brunei Darussalam’s teachers is provided by the ministry of education Brunei Darussalam. In implement activity of learning the teacher must obey all of rule under mentioned the curriculum development department is all this time is guidelines in execute learning activity in all of institute of education in Brunei Darussalam. This case purpose so that the student can get new idea so that learning activity can take place effectively agree with the material will be teach.
In the curriculum development department Brunei Darussalam, the student expected can communicate well in study to expression their understanding, connecting the mathematics ideas with the other concepts agree with daily life, experience, and it other knowledge, the student can indicate the gift of the gab with mathematics mental and mathematics estimation, develop and apply the knowledge as a tool to study and solve the problem, develop visualization skill to help the student in process information, make connection and solve the problem, and develop positive attitude to mathematics value. In addition using the mathematics textbook in the teaching learning process, the teachers’ Brunei Darussalam are demanded to can communication well when the teachers extend the material to the student. In addition good performance in the class, the teachers’ Brunei Darussalam are demanded to use the teaching aid and ICT in learning activity. This case has purpose so that learning activity held can take place effectively and can develop student’s skill in understanding the new concept of mathematics well.
4. Indonesia Context
The context of mathematics teaching in Indonesia there are two types that is Indonesia use contextual and realistic approaches in teaching learning of mathematics in primary school and use problem solving approach in teaching learning of mathematics in vocational senior high school. With use contextual and realistic approaches in teaching learning of mathematics in primary school, there is a hope that students can master mathematics enthusiastically with step by step. To make the teaching learning of mathematics in primary school are done by the teacher’s Indonesia more effective, the department of education in Indonesia give suggest to the teacher’s Indonesia that the teacher’s Indonesia need to develop resources such as information technology, teaching aids and other media in teaching learning of mathematics.
Using approaches problem solving in teaching learning of mathematics in Vocation Senior High School so that the student engages in learning process directly. Small group discussions were useful to share ideas on problem solving activities. To promote problem solving activities the teachers need to develop teaching methods, develop various strategic of teaching, develop various teaching materials, and develop teaching evaluation. There are steps of problem solving according to context of Indonesian as follow understand problem, devising plan, carrying out the plan, and looking back. So that using approaches teaching learning of mathematics in Indonesia can implement smoothly, the teaching learning process needed support by mathematics textbook. The teacher’s Indonesia is exercising to make good mathematics textbooks. In order to motivate the students, the teachers perceived that mathematics textbooks should have a good lay out, supporting references, clear cognitive scheme, clear applications of mathematics, examples of daily life, and history of mathematics. According to Polya and Pasmep in context of Indonesia developed the strategies to problem solving activities as follows trial and error, making diagram, trying the simple problem, making table, finding the pattern, breaking down the goal, considering the possibilities, thinking logically, reversing the order, and identifying the impossibility.
C. Conclusion
There is from discussion above can make a conclusion that to develop student’s mathematics thinking skill, each of countries such as Thailand, Japan, Brunei Darussalam, and Indonesia has different ways in carry out teaching learning activity of mathematics. From the discussion we can look for that Thailand use approaches mathematical modeling in mathematics teaching, Japan use approaches structure problem solving in mathematics teaching, Brunei Darussalam use Mathematics textbooks and E-textbooks as a primary source in mathematics teaching, and the last country is Indonesia, Indonesia use two types of approaches in mathematics. That is contextual and realistic approaches in mathematics teaching in primary school and use problem solving approach in mathematics teaching in vocational senior high school. The each context of mathematics teaching has characteristic, aims, excess, and lack. Across the multicultural mathematics teaching, we can study how to develop the method and approaches mathematics teaching is used by other country. And we can apply the method and approaches the mathematics learning in our country with beforehand us adaptable the method and approaches with our country’s context. Thereby we can improve our mathematics teaching quality to develop student’s skill to understanding of new mathematics concept.
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