Ika Kusumawati
(09301241020)
Mathematics Education 2009
A. INTRODUCTION
Mathematics is a unique science because we can use many methods to solve mathematics problem. We also can use various methods to teach mathematics concept. Different country has different way in mathematics teaching learning process. From this different way, mathematics can more interesting because each country try to make an innovation to make mathematics easy and make students love and enjoy mathematics learning.
Several countries that incorporated in APEC were hold International Symposium 2011 in Ubon Ratchathani, Thailand. They discuss about mathematics teaching in their each country. From this symposium, we know the different of mathematics teaching learning process in several countries. There is no the best way to educate, so we have to explore the various way to get the better way to teach mathematics. But should be noted is whatever the way to teach mathematics, the based is students center.
The various ways have been done in many countries, here the context of mathematic teaching learning in several countries using students-center approach.
B. Indonesian Context
Students’ achievement in Indonesia, especially in mathematics is still low. Based on this problem, Indonesian develop problem solving approach in mathematics learning. The goal is to improve students’ achievement. In problem solving, students need to be creative and develop their idea to find alternatives answer. Problem solving is work in develop mathematical models, and estimate the solution. To encourage problem solving in teaching process, teachers also need various resources, various media and knowing technology. The important thing is change the paradigm, from teacher-centered to student-centered. To develop problem solving, teacher can use small group discussions. In small group discussion, students can share, discuss, and compare their idea with their groups. The activities in problem solving are understanding problem, make a plan, do the plan, and check the solution.
Developing problem solving in teaching process can begin from the source, for example in textbook. Teacher should use good textbook. Good textbook is easy to understand, meaningful, and contains of good examples. Most of teachers also say that good mathematical textbook should be comprehensive in term of mathematical content and students’ competencies (affective, psychomotor, and cognitive. Good textbook can use in individual or collaborate in students group, should make students feel confident and joyful, and has exercises. The important thing from textbook is capable of connecting mathematics with students’ daily activities.
The obstacles in developing good textbook are the lack of skill and knowledge of writing mathematical textbook, the lack of budget, difficult in collect of data, difficult in make good illustration, it is not easy to make interesting textbook, etc. Mathematical textbook usually consist of graph, table, graph, and theorem, so good textbook must be accommodate them in interesting form. With good and interesting textbook, we hope students can interest with mathematics, enjoy mathematics and the final goal is can improve students’ achievement.
C. Vietnamese Context
Vietnamese try to developing e-textbooks to improve their students’ ability. Students’ ability in there is the skill of make inference. So students can make good inference. Inference is the process of deriving logical conclusions from premises that is known. Inference can get from inductive, deductive, and abductive view. Deductive inference is find he conclusions from premises known, inductive inference is find general rules from right particular cases, then abductive inference is find the best explanation to previous conclusions.
The forms of abduction are selective, creative, non-sentential, and manipulative. Selective abduction is selecting existing reasons that caused the phenomenon. Creative abduction is create a new reason because these current exists do not fit the result. The non-sentential is using five senses to find clues that able to explain the result. And manipulative abduction is the logical thinking so we can get the result not just a perception.
One of e-textbooks that use in Vietnam is DGS (Dynamic Geometry Software). DGS can well support selective, creative, non-sentential and manipulative. In this model, students create selective abductions to choose the way parameters changing, non-sentential and manipulative abductions to observe and explain the behavior of graph when parameters changed. DGS can used to explore the influence of parameters. The example is given linear equation f(x) = ax + b. Then students can plot them in DGS, after plot it, students can change the value of a, b or both a and b then observe the change of the graph.
In developing DGS, teacher must prepare students’ worksheet and distribute it in student or students group. The worksheet should give opportunity for students to develop their knowledge and ideas so they have new experience. They can experiment with the textbook guide or worksheet.
D. Philippines Context
Philippine try to develop textbook with some application in daily life, so students can understand the concept easily. Philippine make textbook that consist of students’ work activity and the application of concept in daily life. The focus concept is about polynomial. Other textbook that was used do not has real-life applications for polynomial function. So with this textbook, students would be more interested to learn polynomial function if they saw its applications. The textbook provided a good example of the application of polynomial function in real life which related with students.
The example problem in this textbook is formulating polynomial function using an open box volume. Students can make an open box from paper that the length and the width have been given. If the height of the box is unknown, students can write it as a variable (suppose x). Student can estimate the effect of height change of volume. In other hand, students can find relation between height and volume. Because the height is x, then the volume of the box can be presented as a polynomial function in degree 3.
Based on the textbook activity, teacher must develop problem that need more students thinking ability, in this case especially in polynomial function. The problem should require the students to think and devise their own method to solve the problem. Teacher can make question using problem solving approach. The question should make students more creative. Teacher can use open-ended question, so there are many students’ answers.
The example activity is how to make as much as possible open boxes if the length and the width of the box have known. The steps to do that work activity are teacher divides whole class into small group. Each small group has grid paper and the tools that needed. Then teacher give chance for students to make an open box use that material. Students must make boxes as much as possible. Then students present their work in front of class and explain how to get it. After students have the box, then each group tabulated data on the height, length, width, and volume of their boxes as well as the perimeter and area of the different faces of these boxes.
E. Japanese Context
We know that teachers have to develop their skill and knowledge, so they van make a new innovation in mathematics learning process. Professional teacher can accommodate professional students, so teacher must be professional to change and improve their students’ ability. One of way that can used to develop professionalism of teacher is Lesson Study. Lesson study is a supporting structure that enables teachers to make fundamental changes in their practice, by developing their skills to design, observe and reflect on lessons through collaboration. Teacher need some ways to enable them to participate in lessons study while developing their skills for observing lessons, collecting data, and reflecting the data.
Japanese try to develop a tablet computer in Lesson study. It provides the teacher’s necessary and help teacher collect useful data and use it in discussion. The benefits of tablet are first, it should help teachers focus on the most important data; second, it should emphasize collection of factual information through time stamps, audio recording, and photographs; third, it make flexibility about the data to be collected; fourth, it should enable users to organize their data and report it in different ways; finally, it should allow the exchange of data with other users who observe the same lesson.
Teacher can improve their Lesson Study quality by improving the quality of data collecting during the lesson. Teacher can make the change of the view by dragged the item that he/she want. With tablet, teacher also can make the notes in their data using magnified writing area or write directly into the note area, teacher also can create photographs of student work to provide factual documentation. The tablet users agree that it provides significant benefits for most data collection and analysis. Tablet has advantages, but tablet also has a weakness, such as in analyzed over time, important observations may not be aired, organizing data is not easily captured, the timeline view needs to enable zooming out to provide a good view.
F. Brunei Context
Brunei people make an innovation in problem solving approach. In problem solving approach, teacher is supposed to emphasize the process and skills of communication, connection, visualization and reasoning when teaching the topic. Brunei teacher use game to teach fraction concept to students. They use comparison fraction in grade 4 to develop problem solving approach. In this case, the goals of this lesson are students can compare two given fractions, determine which of the two given fraction is greater/ smaller, arrange a set of given fraction in ascending or descending order two fraction.
Teacher hopes that students can compare two given fractions that have same numerator, same denominator, and different numerators and denominators. Teacher can use things that common in daily life, for example is chocolate because it easy for the pupils to visualize and transfer their idea to manipulate it in the class. The game was made attractive as possible, so students were active, participative and looked interested in the lesson.
The game is dividing a whole class into small group. Then teacher play musical game to represent what is “compare” and what is “size”. Teacher ask students to guess who is the winner in this game?, the big students or a small student. Then teacher distribute worksheet to students group and give a chance for students to discuss and solve it together. The worksheet is consist of comparing two given fraction with have same numerator, same denominator, and different numerators and denominators. Then teacher give some question or quiz for student, and give the mark for the students who have right answer. The last is students make conclusion about the comparison fraction. The result of this game is children were active, participative and looked interested in the lesson, however they still need to improve their communication, reasoning or mathematical thinking skill.
G. Thailand Context
One of the goals of mathematics learning is teacher can make students understand mathematics concept and use it in real-world or make real-world situation in mathematical model. Teacher can use real example and mathematical model to develop students’ understanding about mathematics concept. Mathematical model can help students to translate encountered problems into mathematical forms and solve it to get the solution. Then the solution is adjusted with the problem.
Thailand people try to develop hands-on and e-learning activity to make students understand the concept of mathematics. The first step is makes a mathematical model. The processes of making mathematical model are observing a problem, identify information in problem to interpreting mathematical model, applying appropriate mathematical analysis to the model, and obtaining results and reinterpreting it to solve the problem. Teacher should to give exercise that related with daily activities and make in the best and interesting form. Teacher also makes exercise attractive as possible.
In other side, Thailand people develop e-activities. E-activities can be accessed every where and every time, so students can learn mathematics easy and practice. Computer and internet are used in daily activities. Almost people in the world can use them to complete their work. So e-activities can used to make students and teacher easy to access all about mathematical model.
H. CONCLUSION
From the explanation above, we know that several country have different way to teach mathematics. Whatever the way, the goal is to make mathematics easier and fun. For example in Indonesia, teachers in Indonesia developing mathematics textbook, teachers in Vietnam use dynamic mathematics e-textbook, teachers in Philippine developing textbook with work activity, teachers in Japan using tablet computer in Lesson Study, teachers in Brunei developing comparison fraction concept using game, and teachers in Thailand developing hands-on and e-activities for learning mathematical model.
All of the way that use in many countries are good. Different country has different way, because the way is adjusted with their culture. After knowing the different way to develop mathematics learning process in several countries, we hope teachers and other related parties can improve students’ achievement with making mathematics learning as a fun, meaningful and easy learning. The important thing is use students center learning, because with students-center, students can explore their knowledge, idea, and skill to understanding mathematics concept.
