The Power of Category and Networking

If was was asked about what is category? So, what is our answer? Many people can give several definitions about category. But hold by Kant, 1771 that in our mind there is a something and we can called are category and relation. In category, we must can to chose to do and we must enter so save in epoche’s house and which still phenomena form. 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. Such a category is not a classificatory division, as the word is commonly used. It is, instead, the condition of the possibility of objects in general, that is, objects as such, any and all objects, not specific objects in particular. Meaning of category that the word comes from the katēgoria, meaning that which can be said, predicated, or publicly declared (describe) and asserted (explain), about something. A category is an attribute (characteristic), property, quality, or characteristic that can be predicated of a thing. Kant said, "I remark concerning the categories that their logical employment consists in their use as predicates of objects." So Kant called it ontological predicates.
For example, we will discus about mathematics from definition of mathematics, characteristic of mathematics, and type of mathematics. There are difference between school mathematics and university mathematics. In university mathematics, study pure mathematics and applied mathematics. But in school mathematics, study general mathematics. The object of mathematics is abstract while abstract is our mine. There are two steps to get mathematics concept are abstraction and idealization. Abstraction is search similarity to get simple form and simple characteristic so it will to can be object of mathematical thinking. When we will discuss about teaching and learning of mathematics in front of class so our students will take notice our. Let, we will describe a cube so they will think about shape and size. When we think about cube, in our memory or our brain, there are many points which mixed in our mind such think our family in home or our lovely. Consequently, we must make a grouping everything which enters in our mind because it is very important to ours. When we can not grouping points it so our mind will was boxes. Everyone has to priority or accentuate several points on their mind. Brain always was used human to think, work, and study so was trained to grouping everything. If our brain over long time to rest, it means vacuum to think so it will cause we lazy to grouping everything.
”What is mathematical thinking?” Prof. Katagiri from Japan when his presentation in Sapporo-Tokyo in said that mathematics is mathematical thinking consist three aspects, and I conclude that:
1. Mathematical attitude.
It is very important in determining student’s behavior in mathematical thinking. A good attitude is always asks to be perfection. Mathematical attitude is very important affective factor in determining student’s behavior in mathematical thinking depend on how interested, they are in problem solving on the lesson. Student’s expectation that mathematic will be useful and their personal attitude such as confidence, persistence, and organization are mentioned by Stacey (2006) as some of the skill and abilities required from problem solving.
2. Mathematical method.
Why we prove that? We can study from the specifics to general is called inductive thinking, from general to specifics is called deductive thinking, logical mathematics, or syllogism is one choice to it. We also use preposition. What is preposition? Preposition is sentence which consists true or false. We use conjunction, disjunction, implication (if then), or if then if. Beside that, we use direct or indirect prove.
3. Mathematical content.
Mathematical contents include ideas of set or unit operation, algorithm, or approximation. These can be compared to mathematical skill (as well as estimation mental computation) or deep mathematical knowledge as stated in Stacey’s requirement from problem solving.
In Ebbut and Straker, 1995 the nature of school mathematics has four aspects are pattern or relation, problem solving, investigation, and communication. From Katagiri’s idea and Ebbut’s idea so we can write it in a table in this bellow:
pattern problem solving investigation communication
atitude √ √ √ √
method √ √ √ √
content √ √ √ √
If the people think from top to down so we use reference such book, journal, or research report. We have a reference to grouping everything in our memory. So, for example when we will write essay with title “Student’s Mathematical Thinking in the Framework of The Nature of School Mathematics of Geometry” we has reference so we can grouping everything. We must to think extensive, intensive, and routine as a spiral dynamic. The people must group everything in our mind so they are habitual to it.