Minggu, 27 Desember 2009

The Power of Category and Networking

According Kant’s theory, in our mind there are some category. With the categories which are in our mind, we can get some knowledge. In Immanuel Kant’s theory, category involves four things. They are Quantity, Quality, Relation, and Modality.
Every category consists of three aspects:
1. Quantity
• Universal
 Universal is only one
 It can load all of everything
• Particular
 Form a parts or groups
 Easy to be in groups
• Singular
 Form a parts or groups
 Be autonomous
2. Quality
• Affirmative
 All of things which has positive character
 Explanation of some statements
• Negative
 All of things which has negative or abjuration character
 Explanation of some statements
• Infinite
 All of things which has infinite character
 Restrictive
3. Relation
• Category
 Has function to difference thing with another
• Hypothetic
 Explanation about cause and effect relation
• Community
 Interaction between active and passive
4. Modalities
• Probabilities
 Has problematic character
 In between possible and impossible
• Asetorik
 In between exist and not exist
• Apodictic
 Work based on consistency
With those categories, we can build knowledge that we get it before. With use those category, contains of experiences are managed and then will be product.
We study to understand about category, it means we study to aware that there are things that should be in phenomena, there are things that should be in mind, and there are things that should be in “epoke”.
We study about category, will make us easy to face some knowledge. And we can get knowledge from school or from daily life. The example of category is mathematics education phenomena.
In the teaching and learning of Mathematics, there are idealization and abstraction. What are they?
1. Idealization
Idealization is only in our mind. We assume that the characteristic of Mathematics is absolutely true. So we consider that something is perfect. It is just to consider because there is no anything in this world can be perfect.
2. Abstraction
Abstraction is not same with abstract. Abstraction is only to learn some characteristics from object, not at all. There are differences between abstract and abstraction. We know that abstract is not concrete. We can’t see, touch, and observe, but we can imagine about it. On the other side abstraction is the value which is contained in mathematics.
Mathematics consists of three aspect:
1. Math-attitude
As mathematicians which have good attitude, we must always positive thinking, consistent, diligent, and always have questions about problem.
2. Math-method
How to learn mathematics? We can use one of some methods of mathematics. They are deductive, inductive, syllogism.
o Deductive is based of each lesson about formal logic
o Inductive
o Syllogism can be used to make new conclusion from some premise
3. Content
Mathematics consists of two kinds:
o Horizontal mathematics
Example: daily mathematics. The object of this mathematics is real object.
o Vertical mathematics
It is pure mathematics, which is developing in college.

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