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...
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...
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