MATHEMATICS TEACHING ACROSS MULTICULTURE CONTEXT

A.           Introduction

Ubon Ratchathani International Symposium 2011 APEC held on 2 to 5 November 2011 in Thailand discuss about the Innovation Based on Problem Solving Mathematics Textbooks and e-textbooks. In accordance with the themes, delegacy from each country present their paper about innovation based on mathematics problem solving. The contents of this paper is derived from the research results in their countries. In these meetings, there were representatives of 11 countries that participate in the delivery of their research findings related to the theme.

B.        Mathematics Teaching Across Multiculture Context

Each country has a distinctive culture which identifies the country. With the existence of these cultures and different human resources, the education of each country was different, especially in the learning process.

1.      Thailand context: the works of Supot Seebut et.al

Supot Seebut argue that one form of relationship between the real problem and Mathematics is mathematical modeling. Mathematical modeling can be defined as a translation problem into mathematical form by seeing mathematics as a tool to solve the problem. Mathematical modeling process consists of four main stages, namely to observe the phenomenon, described the situation of the problems inherent in the phenomenon, and determine the important factors (variables/parameters) that affect the issue; estimate the relationship between factors and interpret them mathematically to obtain a model of the phenomenon; approach mathematical analysis corresponding to the model; and reinterpreting them in the context of the phenomenon of study and drawing conclusions. Sometimes, it need to repeat this process until the obtained mathematical model appropriate to the problem. One of the activities that can motivate students in solving problem using a mathematical models is activities that involve students directly (hands-on activities). This gives students direct experience in these activities so that students will better understand the material through the activities they perform.

For example, Mr. Adam want to know the number of fish in the pool by taking a sample form part of the pool. This information will be used to determine the possibility stock fish in the pond and the possibility of many fish. How would you approximate the size of the pond's fish population?

Mathematical modeling for this type is using ratio and proportion. We suppose that the fish population is n, the number of tagged fish is p, the number of fish sample is q, and the number of tagged fish in fish samples is x, then We get mathematical models:

 

In addition, the activity can improve directly into electronic activities (E-activities) to support word wide learning about mathematical models. The advantages of e-activities are accessible anywhere and anytime. E-learning would help more teachers and students to perform mathematical modeling.

2.      Vietnam context: the work of Hoang Hai Nam

According to Hoang Hai Nam, the ability to read and understand information is necessary in an era full of statistical information. Creating students' ability of reading and understanding of statistical information is a task that every mathematics educators need to develop to help them become educated citizens, applying what they learn at school to adapt and wisely solve the practical problems in their life. Reading and understanding of statistical information is defined as the ability to identify, explain and make-his judgments and conclusions of the articles relating to statistical information.

As an ability, reading and understanding information of each student differ between students with each other. The ability of reading and understanding statistical information is presented in different forms based on three criteria

¾      Being aware of and understanding of statistical information;

¾      Explaining and reasoning from the statistical information including trends, causal relations;

¾      Applying and participating in the fields of socio-economic activities.

If there is a problem that is presented with a table or chart, students who read the information without  ability of reading and understanding  information can only separate the information, and they cann’t analyze and conclude information provided.

To train the ability to read and analyze the information, students are given information presented in the form of tables, charts or tables and charts. Then teacher gives question relating to that information. Matters raised can be conclusion, calculation, or comparison value.

3.      Russian context: the works of Ivan Vysotskiy

In 2003 Russian Science and Education Ministry had accepted the decision to include the probability theory and statistics into the regular school course. According to Ivan, to prepare for junior high school students get the material on statistics and opportunities, we need to introduce the concept of the theory of statistics without opportunities. So, the only thing can be discussed at grade 7 is - how to represent the data after collecting them into convenient forms, with tables method (when we want to set the data in exact way) and charts method (when we want more visibility then exact values). Important data is a representation deal for intuitive understanding statistics. For sixth and eighth graders, the main descriptive parameters (means, median, amplitude, deviance, and variance) are understandable. In discussing the real statistical data, we can well illustrate the random changeability in the world. Thus we prepare the visual and conceptual foundation for new important conceptst: random experiments, and probability of the elementary outcomes. Then students can see the data formalization and description on lifelike statistics material. Having set the statistics on the first stage, We are made to talk about parameters without random numerical values ​​and distributions. So we use the numeric characteristic sets of numbers but no samples and no rows.

To expalain about random experience, We must take to use the concept of elementary outcomes set without any features of a space. The attempts to make-school teaching "strict", "exact" and "modern" are doomed. So we need to make-our students to understand the underground of the random experiment in every formalization specify the concept without problems.

Random events can be explained by combining elementary events, we can obtain new events. And event consist of the elementary outcomes of elementary outcomes That favour to an event. To claim the set, we can use the substantial educational element, ie teach students to transform an abstract description into verbal (synthetic) form and back. Next very important concepts (in point-to-practice) are rare (practically impossible) and sure (practically sure) events. The practical importance of these ideas is to form the right and sure thinking about rare events in the single experiment.

Like a number, the incidence can also be operated. Basic operation of the event is an operation pad set, namely union, intersection and transition to the complementary event. For eighth grade, the basic method to teach students to operate with events is the Euler-Venn diagrams. We count in this stage as necessary ideas of independent events and antithetical events (in living thinking often both the concepts are confused).

The main task of the Combinatorial Analysis is to provide students of understanding that many kinds of changeability may by counted in lifelike situations. Such combinatory rules come from problems in the natural way. To explain CA, graphs are of great importance in primary learning. Making trees multiplying illustrates not only the rule but gives a natural algorithm for enumeration.

4. Indonesian context: the work of Marsigit

According Evidences of Marsigit's research, Improving the quality of teaching learning mathematics in the senior high school was take time for teachers to shift from teacher-centered to student-centered. To encourage students to be active and engage in problem solving activities, teachers can use more hands-on activities, and small group discussion will help them share ideas in solving problems. Promotes problem solving activities to the teachers need to en-culture their efforts in the which innovating teaching learning processes to meet students academic needs, encouraging students to be active learners, developing strategic various of teaching, developing various teaching materials, and developing teaching evaluation.

By developing learning materials, teachers could encourage the students to do problem solving more efficiently. So, the students enjoyed problem solving because they were involved in observing and doing things. Therefore, one thing should be done when pembbelajaran problem solving is to create a comfortable atmosphere and provide students with opportunities to develop their initiative.

Providing a book or textbook is one thing that is important weeks to support the improvement of education. The books containing the problem solving approach should not come from a single issuer or a company. But can be tailored to the needs of each school. In addition, teachers can also use the books of his own works. Unfortunately, there are still many teachers who have not been able to produce their own books. One reason is the lack of skills to write and produce good quality textbooks, ie books that contain problem solving approach. However, the most fundamental problem is the understanding of problem solving itself.

To overcome this problem, teachers need to be given counseling and simulations to make books and textbook-based problem solving. In this simulation, the books that have been circulating reviewed and teachers are allowed to comment the book. After that, teachers completed a questionnaire regarding criteria for a good book and the textbook approach to problem solving. In addition, teachers are also divided into several groups and each group make a textbook that fit the criteriaapproach to problem solving. Then each group presented the results of their group discussions. The results are discussed to get your own discussion group conclusion orsummary. Then, the teachers reflected their results of the review and wrote Them Followingthe criteria of the strategies of problem solving outlined by Polya.

A book or textbook should provide various airways to solve the problems. It was suggested that it provides such a space is to get students feedback in order to communicate their ideas with their teacher. Therefore, though the teachers how to develop communicative textbook. The writer of textbooks should consider how the students are able to understand the procedures. Short and long sentences can not be employed. The combination of good developed teaching content, curriculum based cognitive schema and the clear of the guidance make the students have their ability to develop their cognitive schema in learning mathematics. In addition, the book also should be based on student activities, so that textbook should employ realistic approach in which the students learn mathematics from the concrete daily life to get direct experiences and useful schema to prepare their activities in developing various model and mathematical procedures. For problem-solving activities, problems should be based on Trial and Error, Making the 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

            Proses of education in each country are different. In learning mathematics, it is recommended to use problem solving approach. however, due to different educational process, then learning to use problem solving is also different. In thailand, problem solving of mathematics emphasis on mathematical modeling so that the issue was brought into the form of mathematics, and mathematics are used as tools  to solve them. In Vietnam, to train the ability to read and analyze the information, students are given information presented in the form of tables, charts or tables and charts. Then teacher gives that question relating to information. Matters can be raised conclusion, calculation, or comparison value. In Russia, to explain about statistica seventh graduate, we must take to use the concept of elementary outcomes set without any features of a space. In Indonesia, to improve of education, we can provide books or text books in accordance with the approach to problem solving. In order to use the book in accordance with the material covered, the teacher can use the book the work itself.