The Power of Category and Networking

Human is the highest creature in the world. We can state it, because human has brains that have a function to think things. Other creatures also have brains, but that creatures not use that brain to think. Brains of human will to translate all things that human sees, human hears, human feels and human tastes. According to Emanuel Kant (1771) in the human mind, there are four works to translate things.
1. Qualitative
2. Quantitative
3. Category
4. Relationship

That works also used in mathematical thinking. Mathematicians also need other process to processing data in their minds. Mathematicians done abstraction and idealization in mathematical thinking, only take some characters or conditions. For example, “Five”, we as mathematicians only study the value of five and not with the color or form of five. After we do abstraction and idealization, the data will enter to EPOCHE. Abstraction and idealization are limited by space and time dimension. It creates awareness and intention. Awareness and intention included mathematics education phenomena. Mathematics education phenomena are very large. There is a science of teaching and learning phenomena of mathematics. Science of teaching-learning mathematics must be processed to create a work. Before we practice to create a work, we must look for some sources. We must read theory that getting reference from a book, journal, or research. We get a source it means that we have orientation to arrange a work. After we have orientation, we can do activity extensively, or intensively.

For example, we want to arrange a thesis. As a mathematics education we must attention some things. Prof. Katagiri said that we apply Mathematical thinking to our thesis. We must know about attitude of subject, method that will be used, and content of our thesis. It used in frame work and to get the nature of mathematics. The another, we also look other reference such as “The Nature of School Mathematics ( Ebutt & Scelen) “. In there explain that the nature of school math consist of three part. There are: pattern, problem solving, investigation, and communication. Mathematical thinking determines the nature of school math. From that relationship we get syntactic. Next we analyze the syntactic to get evidence. Addition we need instrument to do observation and question. We can get instrument for networking and category. The result of observation will be arrange and processing to be a conclusion. After we conclude our thesis, it means we have finished our thesis.