Mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research. In my opinion, we should happy about math education because it’s not many only view of young people consist in mathematics education. Therefore, we have to know how to teach math as possible so students interested studying mathematics. In math teaching, there are four level of teaching. That is spiritual level, normative level, formal level and material level. In every level have purpose itself. In spiritual level explain about spiritual, future, vision, goal and ways of life. In normative level explain about law, education system, decree, paradigm of education, theory of education. In formal level explain about book, curriculum and syllabus. In material level explain about condition of class, teach content, the student, the physical of building.
There are two opinion about teaching, traditional teaching and progressive teaching. Although, both of traditional and progressive have similarity that is make people educated but they have several different.
a. Paradigm/ Theory of education
In traditional teaching, teacher as to teach and teach is to give and transfer of knowledge. Student as empty vase which only receive knowledge of teacher and be passive. But it reform to be progressive teaching. Here student as seed which let grow in their way, developing to be active learner and to construct their own knowledge. Teacher just as facilitator/ dynamist in their grow.
b. Curriculum
Traditional teaching use curriculum 1975 and 1980. While progressive teaching use KTSP where we translate by self.
c. Condition class
In traditional teaching usually use one method that is expository math, explain, give example and give task.
d. Book
Traditional teaching just text book oriented, but in progressive teaching it develop by teacher with appropriate the competence of student.
e. System/ Paradigm Learn
The last result fixed by UNAS (traditional teaching). In progressive teaching, class room base assessment and base of the process.