Nurul Husnah Mustika Sari (http://nurul-husnah.blogspot.com/)
Nim: 09301241027
A. Introduction
Mathematics is important. Almost all of the knowledge especially science need mathematics. That is one of the some point that made mathematics learnt from young age. To develop good ability in mathematics thinking we must consider mathematics teaching because from mathematics teaching, students can understand and develop their mathematical thinking.
Every county has paradigm that may be different with another. Paradigm of mathematics affected on how mathematics teaching will they do. Different paradigm happen because every country has different need. Each of them have different problem. Through share about idea of mathematics teaching with others, we will have more knowledge about how they conducting teaching learning process. It also can give us enlighting so if their teaching method appropriate with us, it can be applied in Indonesia.
B. Mathematics across multicultural
1. Vietnam context: works of Tran Vui
Communication is an important part of formative assessment. Sometimes students can solve problem but can not explain it clearly. The aims of mathematics education are to help students achieve knowledges, skills, thinking, and attitudes. To reach that aims, teacher need to think about teaching mathematics with visual representation, using realistic approach, and open ended tasks.
Students expect to construct their own mathematics concepts based on real life problem. And also, to improve students creativity, teacher need to use open ended problems. With open ended problems, teacher help students to have deep understanding, not surface understanding.
Visual representations in mathematics give some positive effects in learning mathematics. Visual representatios can be used to achieve more than just a basic, procedural, and mechanical understanding of mathematical concepts. Students also have something to share to the others about their ideas.
The main point of Tran Vui idea is about using open ended with virtual representation in formative assessment. Formative assessment is said to be good if they can assess what they will assess or we often esay it is reliable and valid. When we use open ended with virtual representation, we have many form because open ended problem may students to explore the problems. They may share their ideas. It is no problem that their ideas are different. Open ended problem also may have many answer. With virtual representation, teacher will know how students can communicate their ideas to the others. Teacher may know how thery responds comment from their friends and how deep their understanding from their explanation.
2. Japanese context : works of Takahashi
Japan have changed their paradigm from teacher centered learning to the student centered learning. Now, japan is developing mathematics lesson trough structured problem solving. It is different with American context, problem solving stategies. In America, they consent to process and the result. But in japan, not only process and result but also consent to develop students skill.
There are two main goals of structured problem solving that develop by japanese goverment. They are students interest in learning mathematics and students creativity. There are three mayor of teaching mathematics with structured problem solving :
a. Carefully selected word problems and activities, and their cohesivenes
Teacher carefully selects a problem an activity for one meeting. Usually, a lesson include only one problem solvig activities although teacher might give students extended problem.
b. Extensive discussion (Neriage)
The role of teacher in teaching and learning process is to be facilitator. Teacher give problems to the students and then helps students to achieve the goal of the lesson. In the end, teacher also explain all different method that students use and explain the weakness or limitation of method that used by students so that students may choose most efficient method.
c. Emphasis on blackboard practice (Bansho)
Japanese classrooms are equipped with large balckboard at the front. The reason why japanese teacher use balckboard are:
- To keep a record of the lesson
- To keep a record of the lesson
- To help students remember what they need to do and to think about
- To help students see the connection between different parts of the lesson and the progression of the lesson
- To compare, contrast, and discuss ideas that students present
- To help to organize student thinking and discovery of new ideas
- To foster organized student note-taking skills by modelling good organization
3. Hongkong context : works of Litwin
Litwin State that fractions learning should also include the investigation of fraction so that students could do investigation. And also, while it is better to use example in real life to attract the attention of students in learning fractions. There are two types of question about fraction: first, investigation on fraction addition with positive integral value and the sums add to 1. Second, solving problem based on equivalence fractions or using algebraic equation. The second one also included finding fractions that has positive integral value and certain relation of the numerator and denominator. A good question for investigation is question that could allow students to explore and could provide different question. It similar with open ended approach, students could solve problems in many ways and there are many answer.
Investigation method motivate students to learning mathematics. Students have confident that they can solve the problem. It is also make students construct their own knowledge so that they could have new skill. Trough investigation they can learn new ideas based on their own knowledge.
4. Brunei Darussalam : works of Madihah
Curriculum of Brunei provide teacher to emphasize the process and skills of communication, connection, visualization, and reasoning when teaching a topic. The aims of the education in Brunei are expect students to communicate in order to learn and express their understanding, connect mathematics with daily life, demonstrate fluency with mental mathematics and estimation, develop mathematical raesoning, and develop positif attitude towards mathematics.
In teaching mathematics with the material about fraction, teacher bring concrete thing like chocolate bars to be divided. Students expect to know the meaning of compare and size. Students expect to understand why a fraction is bigger or smaller than the one it was compared.
In the lesson that conduct by them, the study begin with teacher plays the musical chair game with students to introduce the definition of word “compare” and size, and then teacher clarify that in comparing fractions, the size of the fraction is important. Teacher also asked why they need to compare fraction in real life.
Through this lesson, it can be seen that students were active, participative, and looked interested in the lesson. However, they still need to improve in the terms of communication because there is constraint n this lesson. It is about language.
C. Discussion
In vietnam, Tran vui prefer to use open ended with visual representations in the formative assesssment. Mathematics teaching with open ended approach is good because it could encourage students creativiy and motivate students to learn mathematics. The visual representation is used to provide students ability in communication because sometimes, students could solve problem but they can’t explain it clearly. They can’t communicate why they use tis idea and how their idea being used. Formative assessment trough open ended problems with virtual representation provide teacher to made many of form. From students side, it is very useful because students could use their own concepts to solve the problem independently. But from teacher side, it is quite hard for teacher to make many form of assessment. It is happen because open ended problems might have many different ways to solve or many answer. Trough open ended with virtual representative, students should learn how to communicate their own ideas to the others. It can improve students ability in communication especially in presentation.
In Japan, Takahashi with structured problem solving let students to improve their skill and interesr in mathematics learning. He used textbook that contain basic consepts and the way usually students did to solve problems. In this mathematics teaching, students could solve the problem with their own understanding. They can explore the problems in different way from others. Then, while they discuss with their group, teacher help them to guide students so that they can achieve the objective of the lesson. It is good because there is communication between students to the others and between students and teacher. Then students could share their own ideas to the others in front of the class. It very useful for students because they could see other students perspective. It can improve their knowledge and let them choose the most effevtive method. With these presentation, students as presenter also can improve their ability to communicate with others. They should know the way to communicate their own ideas so that the others could understand. In the end, teacher reviewed the method that students used. This section is very useful because trough this section, students will know the effectiveness and the weaknis or limitation of method they used.
In Hongkong, Litwin conducting mathematics teaching with investigation. In this section, Litwin use fraction as a material. The lesson let students to investigate the problems and let them improve their creativity because their answer might be different with others. There are more than one answer for one problem. Students could einvestigate the number that can satisfied with the problem. They could use their own ideas to solve the problems. It can improve studnts confident. But in my opinion, it is hard to implement in same level in Indonesia. In formal mathematics, some of the problems need high concepts like algebra to be conducted. They need to understand first about how to make algebraic form from the problems.
In Brunei Darussalam, the lesson about fraction that conducted by Madihah is interesting. Madihah make students to be happy and ready first then slowly explain with games about the material. To explain about comparation, madihah used students definition about smaller bigger, taller, etc. Madihah also used concrete thing like chocolate bar to helps them understand about size and comparation. Then students divide in to group.they can communicate with other students in this group. Student ask about the comparison, what fraction that bigger or smaller with another one. The problems are simple and let them to make the denominator same. The result state that students are interested with the lesson but the constraint is the language they used because they used english as second language of the students.
D. Conclution
From another mathematics teaching method, we can improve our knowledge how they teach mathematics. Sometimes that method can be applied in our school but simetimes it can’t because the objective of learning mathematics in different country may be different. The context of teaching also affected. Their context of daily life may be can not used in Indonesia.
E. References
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