The Power of Category and Networking

Human mind consists of many aspects, such as quality, quantity, category, relation. Those aspects are used to value about an object from many points of view. We can value the quality of an object, categorize it in a certain group, and make a relationship between this object and the other object that we’ve ever known. Immanuel Kant (1771) stated that our mind has abstraction, idealization, intension and epoche. Abstraction means learn something which is important to learned. Idealization means assume that something is perfect. Intension comes from our awareness. And epoche is a place to save unimportant things or a place to hide something that we don’t want to think on a certain time.
In mathematics education phenomena, we should use categorization to divide what characteristics which is in abstraction or epoche. Categorization means put an object in a group which is suitable for it. With categorization, we can learn mathematics easier because we’re helped to choose what we should learn. For example, when we learn about cube, we don’t need to know what its material, what its form, what its price. We just learn its size, its length, its width.
This world consists of Noumena and Phenomena. A phenomenon is something that is real. To make the phenomena become knowledge. We need a good thinking from bottom and from upside. Learning can be done by two methods. First, bottom up method. We learn from a real thing then we get a new concept from it. Second is top down method. We learn from some references like books, journals, research reports to get some theories then we practice them in our real life. Both of them are very useful for us.
Besides learning methods, we also have learning system. There are routine, intensive and extensive. We learn routinely when we learn based on the given schedule. We learn intensively when we learn from the general to specific. And extensive learning happens when we learn from the specific to find the general form.
Students who learn mathematics have mathematical thinking. It consists of mathematical attitude, mathematical method and mathematical content (Katagiri,2004). Those aspects have a relationship with the nature of school mathematics. Making a pattern, solving a problem, investigating and communicating need attitude, method and content. That’s why categorization and networking are very important for us. Categorization helps us learn easier and make networking will help us to combine and relate the knowledge that we’ve ever got. From that, we can make a theory then try to prove it. we can find the evidences using analysis.