Minggu, 12 Oktober 2014

The Nature of Mathematical Thinking

What Do You Know About Mathematics?

In many perception mathematics is difficult, complicated and boring. But, if you know in there are many wonderful thing which can't be founded in other aspect in our life.
Mathematics in an old, broad and deep discipline (field of study). People working to improve mathematics education need to understand “What is Mathematics?”
Mathematics is the science that deals with the logic of shape, quantity and arrangement. Math is all around us, in everything we do.

Who Are Mathematicians?

Mathematicians are people of all ages and from all over the world who enjoy the challenge of a problem, who see the beauty in a pattern, a shape, a proof, a concept. Some of the best young mathematicians compete in mathematics olympiads, state and national science fairs, or the fun who wants to be a mathematician game. To be a mathematicians we must to abstracted (to think only selected characteristics of object) and idealized (assuming to be perfect characteristic).

Mathematical objects are what we talk and write about when we do math.

Numbers, functions, triangles, matrices, and more complicated things such as vector spaces and infinite series are all examples of mathematical objects. This chapter discusses how we think about math objects in general.

Mathematics objects are not physical objects, but we think about them and talk about them as if they 
were. That is one of the more important aspects of thinking about mathematics objects. (Another one is how to prove statements about mathematics objects.)

Mathematics is not just a study of numbers, nor is it simply about calculations.
It is not about applying formulas, either. It can perhaps be better described as “a field of creation through accurate and logical thinking." Mathematics has a long, rich history and continues to grow rapidly.

Mathematical thinking is not the same as doing mathematics, at least not as mathematics is typically presented in our school system. School mathematics typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school mathematics is to learn to think inside the box. In contrast, a key feature of mathematical thinking is thinking outside the box, a valuable ability in today’s world. This course helps to develop that crucial way of thinking.

VOLCANO OF MATHEMATICS


Mathematics in University

Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its intrinsic interest. For some people, and not only professional mathematicians, the essence of mathematics lies in its beauty and its intellectual challenge. For others, including many scientists and engineers, the chief value of mathematics is how it applies to their own work. Because mathematics plays such a central role in modern culture, some basic understanding of the nature of mathematics is requisite for scientific literacy. To achieve this, students need to perceive mathematics as part of the scientific endeavor, comprehend the nature of mathematical thinking, and become familiar with key mathematical ideas and skills.


Any high mathematics you are, do not exceed your spiritual! (by: Prof.Dr. Marsigit, MA)