The aims of the education system include : a) enhancing full devotion to God Almighty, b) developing the intelligence and skills of individuals, c) fostering positive attitudes of self reliance and development, d) ensuring that all children are literate. Since 1968/1969, a more systematic approach to develop education in Indonesia has begun to be evident. Since that time up to the late of 1990, the approach to develop education has designed under the assumption that curricular objectives could be logically derived from national and system-wide goals and then broken down into a precise hierarchy of instructional objectives, and that learning could be made individualized and ‘teacher-proof’ so that students could learn what they needed to learn with minimal assistance from teachers (Shaeffer, 1990, pp.22). However, in 1984, evidences indicated that the approach was perceived not to able to mobilize resources and to embark the model to the nationwide application. The challenge for educators in the next decade is to improve students' learning of higher order skills in mathematics; teachers should organize instruction to involve children so that they actively construct their own knowledge with understanding (Peterson in Grouws, et al., 1988). To face the challenge for educators in the next decade, we must understand the psychological aspects of mathematics learning. There we will know about how and methods to be good teacher of Mathematics.
DISCUSSION
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.
The nature of Mathematics Education ( Mathematics Educationists )
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.
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 main 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.
The nature of Mathematics ( Phylosophere Mathematician )
1. Mathematics is a search for pattern and relationship
2. Mathematics is problem solving activity
3. Mathematics is investigation activity
4. Mathematics is a main of communication
Learning
Learning is acquiring new or modifying existing knowledge, behaviors, skills, values, or preferences and may involve synthesizing different types of information. Active learning occurs when a person takes control of their learning experience. Since understanding information is the key aspect of learning, it is important for learners to recognize what they understand and what they do not. By doing so, they can monitor their own mastery of subjects. Active learning encourages learners to have an internal dialogue in which they are verbalizing their understandings. This and other meta- cognitive strategies can be taught to a child over time. Studies within metacognition have proven the value in active learning, claiming that the learning is usually at a stronger level as a result.
The nature of students learn Mathematics
1. The student learn Mathematics effectively if they have good motivation and perception
2. The student will learn mathematics individually
3. The student can learn Mathematics in collaboration with others
4. The student learn Mathematics contextually
Paradigm of teaching
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 ( hermenitika ).
Learning Methods in Schools
There are many variety in learning methods in schools. There are two methods of learning they are the traditional methods and progressive methods.
The traditional method is very focused on the activity of teachers rather than students, although the structures have a plus side. Students generally follow the teacher with a monotone way. Monotonic which means that only teachers who provide ideas to learning that will be promoted in the classroom. The role and activeness of students in learning is necessary for the continuity of learning. In contrast to the method of progressive student-centered activity. So that teachers act as managers and school as a laboratory development of students. In this method, students are given extensive opportunities to solve problems with multi-disciplinary science. But the weakness of this method is less structured learning structure.
The traditional method is very focused on the activity of teachers rather than students, although the structures have a plus side. Students generally follow the teacher with a monotone way. Monotonic which means that only teachers who provide ideas to learning that will be promoted in the classroom. The role and activeness of students in learning is necessary for the continuity of learning. In contrast to the method of progressive student-centered activity. So that teachers act as managers and school as a laboratory development of students. In this method, students are given extensive opportunities to solve problems with multi-disciplinary science. But the weakness of this method is less structured learning structure.
Each method has both positive and negative. Expected to collaborate both methods. Because basically there are students who are active and activeness that makes him wonder at a certain material. And if only one method that focuses on learning in the classroom will lead to homogeneity in the class.
Given the teachers in organizing learning most often use the textbook as a reference, then so too can be an obstacle for its innovation efforts (Schifter, 1993); further he stated that even if the teacher had intended to make innovations, such things may not be realized when policymakers do not provide opportunities for it.
Based on some views show how disagreement over the concept of plural potential starting point (starting point) for the start of teacher innovation. So that teachers can bring innovation to stimulate student learning, there are some concepts that need to be understood about the nature of science includes understanding each field, the nature of the subject students, and changes in attitude and implementation associated with the change of paradigm.
Based on the research, the majority of Mathematics teachers still use traditional methods of teaching mathematics, which is expository with cycles: explaining, giving examples, ask questions and give the task in the classical style. With these methods, teachers of mathematics have difficulty in: 1) serve various needs / demands of the students in learning mathematics, 2) encouraging low achievers to improve student academic achievement, 3) encourage students to learn actively, 4) use and develop teaching aids of mathematics and , 5) encourage students to learn through collaboration. The method of course give bad impact to students. Because they will become a passive student, individually, and be afraid with their teacher. To change it all, Mathematics teachers should be able to realize the selection of one or several methods of dynamically and flexibly: (1) Method Exposition, (2) Method of Discussion, (3) Method of Exercise and the provision of Duty, (4) Method of discovery, (5) Method of Problem Solving, (6) Usage Viewer Tool . Such methods will certainly provide benefits for students such as encouraging students to learn actively, encourage cooperation, students will brave, students can receive the lessons with pleasure, and no stress.
CLOSING
Conclusion
The teachers need to change the paradigm of teaching from traditional paradigm to new paradigm. 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 the students’ skills and to be active students. The nature of learning Mathematics is interaction among the students and the teachers. Development of mathematical learning have a good impact for students, but in the implementation of teachers found several problems. It was a task for the teacher to solve the problem of learning mathematics through improving the competence of teachers, resulting in students who are really smart and high quality.
Suggestion
For teachers, in order to streamline active student learning and support student achievement.
Sources :
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