Mathematics is a study on the changes, space, structure and quantity. Mathematics arises because human thoughts and ideas related to reasoning. Mathematics is divided into 2 types. These are pure mathematics and mathematics school. Pure Mathematics is the mathematics which underlies all applications. Pure Mathematics is just for Student in university. And, Mathematics school is Mathematics which taught in Elementary School, Junior High School, and Senior High School. Mathematics School, Containing concret and factual problem. Ebutt and Straker (1995) defined Matemathics School as follow:
* · Mathematics is a search for pattern and relationship, enlarge the student to search pattern and relationship.
* · Mathematics is problem solving activity.
* · Mathematics is investigation activity.
* · Mathematics is a mean of communication.
The teacher needs teaching paradigm of teaching mathematics. Actually, There are two types of paradigm of teaching mathematics. The first one is old paradigm. In the old paradigm of teaching, the teacher’s knowledge is transferred to passive learners. So, there just one way communication, that is from teacher to student. So the student can’t improve their talent optimally. In a research, most teacher spend 75% their math time (closer to 90 persen for many) on paper-and-pencil drill, with students practising arithmathic skill in isolation from problem-solving situation. The absolute, necessary, and sufficient requirement for teachers in this context is complete mastery of the content. The classic classroom is the teacher lecturing and students listening. The students are silent, passive, and in competition with each other. It can cause Impersonal relationships among students and between faculty and students. If a teacher is still using the old paradigm, then students will not progress. The potential of student will lethal.
And the second one is new paradigm. The new paradigm of teaching is progressive teaching. In progressive teaching, the paradigm of education is to construct the student’s knowledge, by themselves. So, there is a reform from traditional teaching to progressive teaching with the new paradigm. In this teaching method, the student is similar with a seed that grow and blossom out. The teacher just facilitate the student as like a farmer. The final goal of progressive teaching is classroom based assessment which is much different from national examination . In new paradigm, there are a lot of ways for students to improve their skills. Students must interest in finding solutions of problems. Notice that don’t be afraid if you can not solve the problems. In mathematics, there are a lot of ways to solve a problem. If you still can not solve the problem, you can ask to your teacher. The teacher discuss the problem with the students until the student understand how to solve the problem.
The problem is if we deliver mathematics for younger student. We need appropriate methods for child and is equivalent to children’s physicology . As an educator, we must be able to customize the content of mathematics with children's ability not to adjust children with mathematics. Mathematic for younger student also must appropriate with world of children. So, we must know about the aspects of world of children. If our mathematics is not matching with world of children, we can be underestimated. The implication is the teacher need to change the paradigm of teaching. we need to break the old paradigm about teach mathematics. As a teacher our paradigm must be changed from old paradigm become new paradigm. Because with new paradigm, student must be active in learning process to construct on build mathematics. Because constructing mathematics not only an adult (teacher) obligation but also everyone or by the other students.
