THE POWER OF CATEGORY AND NETWORKING

In the 1771, Immanuel Kant was explain four category of thinking.
1.Category
2.Quality
3.Quantity
4.Relation

In Kant's philosophy, a category is a pure concept of the understanding. A Kantian category is a characteristic of the appearance of any object in general, before it has been experienced. A category is an attribute, property, quality, or characteristic that can be predicated of a thing.
“The Categories do not provide knowledge of individual, particular objects. Any object, however, must have Categories as its characteristics if it is to be an object of experience. It is presupposed or assumed that anything that is a specific object must possess Categories as its properties because Categories are predicates of an object in general. An object in general does not have all of the Categories as predicates at one time. For example, a general object cannot have the qualitative Categories of reality and negation at the same time. Similarly, an object in general cannot have both unity and plurality as quantitative predicates at once. The Categories of Modality exclude each other. Therefore, a general object cannot simultaneously have the Categories of possibility/impossibility and existence/non–existence as qualities.”
(http://en.wikipedia.org/w/index.php?title=Category_%28Kant%29&action=edit)
A quality is an attribute or a property. Attributes are ascribable, by a subject, whereas properties are possessible. Some philosophers assert that a quality cannot be defined. In contemporary philosophy, the idea of qualities and especially how to distinguish certain kinds of qualities from one another remains controversial. (http://en.wikipedia.org/w/index.php?title=Quality_%28philosophy%29&action=edit)
In the wikipedia, we can find that,
“Quantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. Quantity was first introduced as quantum, an entity having quantity. Being a fundamental term, quantity is used to refer to any type of quantitative properties or attributes of things. Some quantities are such by their inner nature (as number), while others are functioning as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little. One form of much, muchly is used to say that something is likely to happen. A small quantity is sometimes referred to as a quantulum.”
(http://en.wikipedia.org/w/index.php?title=Quantity&action=edit)
Another information is said that,
“A Relation of Ideas, in the Human sense, is the type of knowledge that can be characterized as arising out of pure conceptual thought and logical operations (in contrast to a Matter of Fact). In a Kantian philosophy, it is equivalent to the analytic a priori. It is also closely coincident with the so-called Truths of Reason of Leibniz, which are defined as those statements whose denials are self-contradictory.”
(http://en.wikipedia.org/w/index.php?title=Relation_of_Ideas&action=edit)

Person’s attention always begin by awareness. Sourced by Wikipedia,
“Awareness is the state or ability to perceive, to feel, or to be conscious of events, objects or sensory patterns. In this level of consciousness, sense data can be confirmed by an observer without necessarily implying understanding. More broadly, it is the state or quality of being aware of something. In biological psychology, awareness is defined as a human's or an animal's perception and cognitive reaction to a condition or event.” (http://en.wikipedia.org/w/index.php?title=Awareness&action=edit)
When we notice at mathematics, we will find that there are two kind objects.
1. Abstraction
2. Idealisation
Abstraction is about shape and measurements, then idealisation is assuming that everything is perfect.
Covert awareness is the knowledge of something without knowing it. A philosopher, Edmund Husserl said that in the Hermeneutics Phenomenology, the truly knowledge is not mind invention, but an existence of awareness. From this argument, we can take abstraction and idealisation into a place, called as Epoche.
Awareness forms a basic concept of the theory and practice of Gestalt therapy. The theory of Gestalt is according to deduction method. So, its possible to grows bottom-up and top-down thinking.
Katagiri define three categories of mathematical thinking:
1. Mathematical Attitudes
2. Mathematical Thinking Related to Mathematical Methods
3. Mathematical Thinking Related to Mathematical Contents
Then, there are three categories of the nature of school mathematics:
1. Pattern
2. Problem Solving
3. Investigation
4. Communication
When we analyse student’s mathematical thinking in the framework of the nature of school mathematics, we can find that there are some agreements of them.
The nature of school mathematics
pattern Problem solving Investigation Communication
Attitudes    
Methods    
contents    

This activity show that there is a network between students mathematical thinking and the nature of school mathematics. This activity also proof the power of category and networking in the mathematics.

REFERENCES
http://en.wikipedia.org/w/index.php?title=Category_%28Kant%29&action=edit (Accessed 14th Dec ’09, 10:21)
http://en.wikipedia.org/w/index.php?title=Quality_%28philosophy%29&action=edit (Accessed 14th Dec ’09, 10:21)
http://en.wikipedia.org/w/index.php?title=Quantity&action=edit (Accessed 14th Dec ’09, 10:21)
http://en.wikipedia.org/w/index.php?title=Relation_of_Ideas&action=edit(Accessed 14th Dec ’09, 10:21)
http://en.wikipedia.org/w/index.php?title=Awareness&action=edit(Accessed 14th Dec ’09, 10:21)
http://pbmmatmarsigit.blogspot.com/ (Accessed: 10/27/09)
http://marsigitpsiko.blogspot.com/2008/12/psikologi-siswa-belajar- maematika.html Accessed: 10/12/09)