My Reflection in Learning Mathematics

Last Thursday, on March 12^th 2009, there is a surprise from Mr. Marsigit. What is it? Guess it! However, on Thursday morning we had a suddenly examination from Mr. Marsigit. Exactly, it was the first English examination in 2^nd semester in my class. But I think it’s no problem and it’s not a terrible thing, right?

The examination questions were about Mathematics in English, surely. Mr. Marsigit commanded us to take a piece of paper and write down what Mr. Marsigit’s Indonesian speaking into English. On the other hands, that morning we learned to be a translator. For example, when Mr. Marsigit said, “garis lurus”, we had to write it down on our paper but in English of course. So, we had to write “straight line” on our answer sheet. Mr. Marsigit gave us fifty questions in limited times. So, we had to work quickly.

Frankly, the questions are easy, but I don’t know why it tasted more difficult for me – my friends too-. The materials had been given by Mrs. Iin before (in 1^st semester) and honestly, we had to be able to answer its. But, in fact, we couldn’t do that exam (maybe it happen because we forgot about that materials). So, don’t be shock if my mark is ‘not good’ (I got ‘48’ for my first English test). For your information, the highest score in my class is ‘60’. It’s very amazing and also it’s a surprise mark for us.

After the test finished, like usual, Mr. Marsigit commands us to make a semicircle with our chair close to him. That day Mr. Marsigit began to talk about reflection. He said that self introspection is difficult. He also said a proverb (maybe), “It’s better to break the mirror than repair our face”. Actually, I don’t know what does is means. But, may be it means that we must not to break the mirror because the mirror is not wrong. We are wrong. So, we must repair our ‘face’, our attitude, etc.

He also said that the exam just a little part, it’s just about 0.1 %. The others is depends on ourselves. So, we must study and work harder. We must up grade our knowledge and improve our competences, for example, we can make use references, using internet, exercise TOEFL, and make research. We must explore our competences in Mathematics and English (how to communicate, understand, write, etc)

What is the really meaning of math? Whatever, Mathematics thinking always starts with our assumption:

1. Steps
2. Concept of math (def of numbers, etc)
3. Establish axioms

Mr. Marsigit said that mathematics without experiments is called applied mathematics, while mathematics with analyzing is called pure mathematics. Schematically, we can write:

The thinking methods of Mathematics are:

Inductive --> assumption --> axioms --> definition --> theorem --> solve the problem (deductive)

Mathematics truth is based on logic (its consistence and has no contradiction). The one of important things is we must have sincere intention to study Mathematics, because doing something with compulsion give negative effects and bad results. We also should learn many things about Mathematics. It’s not enough to study Mathematics just in University, we must learn it by ourselves. It means that we can learn Mathematics from our environment, our friends, our family, etc. So, Mathematics is universal, isn’t it?

The Story of Mathematics...

Mathematics. What do you think of Mathematics? Is it a fun lesson? Or maybe is it a boring lesson for us?
Last Thursday, March 5th 2009, Mr. Marsigit -my English lecturer- command us (me and my friends) to express our speaking. OK, let’s talk about Mathematics. There are some definitions about Mathematics according some Mathematicians.
Prof. Shigeo Katagiri from University of Tsukuba, Japan said that Mathematics is Mathematical thinking itself and he concludes that there are three types of Mathematical Thinking:
I. Mathematical Attitudes
It’s mean that we must have a good attitude in learning Mathematics, during thinking mathematically. Mr. Marsigit gave examples with a student who always have and ask a question when he / she didn’t understand what the teacher said, be a critical student and always consistence.
II. Mathematical Thinking Related to Mathematical Methods
This second thing is a formal object in Mathematics and we can use logical methods (for example is inference method to get a conclusion).
III. Mathematical Thinking Related to Mathematical Contents
When we learning Mathematics, we must know what we’re talking about, what we’re thinking about, what contents we’re discussing about. But if just a content, it’s not enough, is it? We have to think larger, from general to particular (deductive thinking) or from particular to general (inductive thinking). It seems like a syllogism, for example:
~ If Tommy always study, he is smart
~ If Tommy is smart, he succeed
~ If Tommy always study, he succeed
The objects of Mathematics are very abstract because the objects also abstract and the idea is in our mind, not concrete, we can’t hold it. The types of Mathematics are also different between in Senior High School and in University, because in University we get pure mathematics and also applied mathematics.
There are two ways to learning Mathematics:
1. Use our abstraction
‘Abstraction’ is not the same with ‘abstract’. ‘Abstraction’ is finding the similarity in Mathematics to get the simple shape/form or the simple characteristic that become Mathematical Thinking object.
2. Use our idealization. We must thinking ideal, assume that something is perfect, decide the goal or dreams compose logically to mathematics characteristic and also we must consistence.
While, according to Mrs. Arini (a Mathematics Teacher), Mathematics is come from Latin word, manthanein or mathema having mean ‘study’ or ‘something that we learn’. Mathematics come from Dutch language ‘wikunde’ (exact knowledge), related to logical. The most important of the characteristic of Mathematics is deductive logical. It’s mean that a truth of a concept / statement got from logical effect of a truth before, so there are consistence relationships inter concept. But in understanding the concept, we can start inductively.
In the other hands, Prof. Kaye Stacey, from Melbourne University divide Mathematics into 2 aspects:
a. Conjecturing (thinking predict)
b. Convincing (how we can communicate the result that we get to people. For example are: we can make some questions, make paper, article, book, etc)
Nowadays, there is a trend in Mathematics Learning; Realistic Mathematics Learning (Pembelajaran Matematika Realistik). For your information, it’s come from Dutch and now it’s “booming” in Indonesia. Realistic Mathematics Learning divides into 2 parts:
~ Vertical mathematics (pure mathematics in University).
~ Horizontal mathematics (daily mathematics, the objects are concrete).

In the last his speaking, Mr. Marsigit said that the power of Mathematics is critical thinking.

Generally, in fact, Mathematics has many definitions. But for me, Mathematics and English are fun, make me want to 'eat' again, again, and again...

English

Bismillahirrahmanirrahim....
Assalamualaikum...
This is my first posting in my blog. Today is Tuesday night. I’m sleepy but I supported my self not to give up and try to write this writing.

Some days ago, on Thursday morning, February 26^th 2009 was the first day of the B. Inggris II lesson in 2^nd semester of Mathematic Education class. Frankly, it was the second meeting of B. Inggris II lesson. But on the first meeting, Mr. Marsigit couldn’t accompany us (me and my friends) to study about English because he was in Bandung.

Let me introduce Mr. Marsigit. Who is he? Mr. Marsigit is an English lecturer of Yogyakarta State University. He is 51 years old. He lives near my house, in Plosokuning 2 Minomartani. He has a wife and two sons.

Last Thursday, he told little things about his dreams, about his life. He commanded us to make a half circle with our chairs in the class – it remind me to telenovela “Amigos” and ask three students (Aziz, Riyan, and me) to sit beside him on the small stage under the green board. He told us that go abroad is one of his dreams. And now, he had made his dreams come true. In 1995, he got a change to continue his study in London University. He had gone to Thailand twice in 2000. He also went to Japan and now he almost go to Japan every year. Last year, he went to Australia.

If we look Mr. Marsigit’s blog, we can see that there are many articles about Mathematics in English. Yesterday, I saw his blog and I read an article with title elegy. Mr Marsigit said that elegy expresses his sympathy to the condition of the environment (about teacher, lecturer, student, and natural environment). “Elegy” also explains about unfinished problems that happen in nowadays.

Mr. Marsigit commanded us to make a formal blog to for Bahasa Inggris II lesson. For the information, Mr. Marsigit has many blogs and he said that he learn about blog from his son. He also made a Bilingual Mathematics Book for Junior High School and published by Yudhistira.

Everyone has many different kind of the meaning of Mathematics. In my opinion, Mathematics is fun and useful for us. How about English lesson? Well, I think English is fun too and can help us to refresh our mind. There are some preconditions to work in Bahasa Inggris II and we can sum up it to “SCUEMA”. What is “SCUEMA”? OK, let me tell you about it –it’s Mr. Marsigit says-.

1. S is for Skill. Skill is our ability to face up our problem with our creativity. We must use our mind and our competence.

2. C is for Communication. It is one of the most important things., because without communication, we can’t learn English well. We can’t get the taste and the knowledge. Active communication between the lecturer and the student can help us to improve our English.

3. U is for Understanding. We must understand that knowledge is very important for our life. We must understand what we learn.

4. E is for Experience. Experience is the best teacher. We can learn anything from our experiences in our life.

5. M is for motivation. Motivation is high spirit to learn, to do something for make our dreams come true. Motivation to learn English is important for us.

6. A is for Attitude. Our behavior. Because knowledge without good attitude is nothing.

I think it’s enough. I’m sorry if I can’t write English well, because I still learn, learn and learn…

Thank you for reading…

Wassalamu’alaikum…