Kant(1771) said that our mind consists of intense, idealism, abstraction, and epoche. The source of intense is awareness. There isn’t something perfect in the world, so we only assume that something is perfect. Assume something perfect is called idealism. When we learn about something we must not learn all characteristics of this object,we only learn some characteristics of this object. When we learn about a cube, we must not learn about the color, the material and the age, but we only learn about the shape and the size. Learning about important characteristic is called abstraction. Epoche consists of characteristic which is not important.
When we think about something, we must categorize the characteristic of the object. What is characteristic concluded abstraction? And, what is characteristic concluded aphoce? By category we can easier learn about the object.
There are phenomena and neumena . phenomena is something which realistic. something which unrealistic is called neumena.
There are two strategy to learn mathematics bottom up and top down. Study form bottom is called bottom up. Study from top to bottom or study from theories by read references from journal ,book or essay is called top down.
There are three learn system routine, intensive and extensive. Routine is learn by schedule. Learning from general object to special object is called intensive. Extensive is opposite intensive, so extensive is learn from special object to general object.
The nature of school mathematics is pattern, problem solving, investigation and communication. The instrument is observation, question, analysis than conclusion.
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