Kamis, 26 Mei 2011

The Nature of Mathematics, School Mathematics, and Student Learn Mathematics

Now, let’s talk about the definition of “Mathematics”. Mathematics come from the Greek. Mathematics is the study of quantity, structure, space, and change. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". David Hilbert defined mathematics as follows: We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein  stated that "as far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality." Mathematics continued to develop, for example in China in 300 BC, in India in AD 100, and in the Muslim World  in AD 800, until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day. Mathematics was built systematically as the system. It will be develop became formal system, where the built was what will we learn. As you know that the basic of Mathematics were definition, axiom, and theorem.
Our main problem as the teacher is the development to communicate the Mathematics with younger students like Kindergarten, Junior High School, and Senior High School. We were need confidence of Mathematics, we must adapted with the younger students’s psychology and it is as the aware of teacher to face the students. So, the answer key is Mathematics must adapted the students, because in real school must be the students’s world. How can we adapt?  The answer was appreciation. If we can’t do it , we will psychologically thrown.
For make students become like mathematics according to (Ebbut and Straker, 1995) teachers should not use axiomatic mathematical definition, but defines mathematics as school mathematics. Here is the essence of school mathematics according to their :  
1.   Mathematics is the search activity patterns and relationships    
Give students the opportunity to conduct discovery and investigation to determine patterns of relationships. Provide an opportunity for students to perform experiments premises in various ways. Encourage students to discover the sequence, difference, comparison, grouping, and so on. Encourage students to draw general conclusions, and help students understand and find a relationship between understanding one another.
2.       Mathematics is the creativity that requires imagination, intuition and invention
Encourage the initiative and provide an opportunity to think differently.
Encourage curiosity, the desire to ask, the ability to refute and ability estimates.
Appreciate the unexpected discovery as beneficial rather than take it as a mistake. Encourage students to discover the structure and design of mathematics. Encourage students to appreciate the discovery of other students. Encourage students to think reflexive. Does not recommend the use of a particular method.
3.      Mathematics is problem solving activities
Provide an environment that stimulates learning math mathematical problem. Help students memecahhkan mathematical problem using his own way. Help students find the information needed to solve mathematical problems. Encourage students to think logically, consistently, systematically and develop a system of documentation / records. Develop the ability and skills to solve problems. Helps students learn how and when to use various visual aids / media math education such as: term, calculator, etc.   
4.      Mathematics is a means of communicating
Encourage students to recognize the nature matemaika. Encourage students to make examples of the nature of mathematics.  Encourage students to explain the nature of mathematics. Encourage students to justify the need for math activities. Encourage students to discuss math problems. Encourage students to read and write mathematics. Respect the students' mother tongue in talking about mathematics.

To define the nature of Mathematics as follows : Mathematics is a search for pattern and relationship, Mathematics is problem solving activity, Mathematics is investigation activity, and Mathematics is a main of communication. Based on that, we need the nature of student learn mathematics : the students learn mathematics effectively if they have good motivation and apperseption, the student will learn mathematics individually, the student can learn mathematics in collaboration with others, and the student learn mathematics contextually.

The teachers need to change the paradigm of teaching. The old paradigm called traditional paradigm was the teacher supposed that the students as empty vessel and be passive students, the teacher transfer of knowledge, give and direct. Let’s change with new paradigm : suppose that each of students as a seed,who if we give it opportunity, it will grow and develop and on uncertain time will product the fruits. The teacher as the facilator and the task of teacher is make the active students. In new paradigm, there are a lot of ways for students to improve their skills and to be active students. Students must interest in finding solutions of problems. .
 You must know that the problem of teaching are always different. The innovative teaching or progressive are consist of system, curriculum, syllaby, lesson plan and student worksheet. Principles of teaching mathematics are effective mathematics teaching requires understanding and knowledge students need to learn to attract and sustain them for a good learning, effective learning requires knowledge and understanding of mathematics, students as learners, and education strategies, effective learning requires a class challenging and supportive learning environment, effective learning requires a continuous search for improvement.
The otology of student of Mathematics is try to publish the student’s English. It will subjective based on yours and it must be justify by the lecturer. So, the students will get new knowledge of Mathematics which objective ( although it still in a group and not pure ). Remember, don’t be afraid if you can not solve the problems. In Mathematics, there are a lot of ways to solve the problem. If you still can not solve the problem, you can ask to your teacher to help you. The nature of learning Mathematics is interaction among the students and the teachers. translations and translating each other.

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