We have get knowledge since we were child and we had already learned it indirectly. We began to study it formally started from kindergarten then elementary school, junior high school, senior high school, high school, graduate and maybe until post graduate. Mathematics education has some problems such as how to empower and developed student, and how to change traditional teaching into a progressive teaching. There are few levels on teaching and learning, which are:
1. Material, in this level there are factors which support this level that are class, teaching, book, building and student.
2. Formal, in this level there are factors which support this level that are curriculum, syllabi, and book.
3. Normative, in this level there are factors which support this level that are law, educational system, paradigm of education, and theories of education.
4. Spiritual, in this level there are factors which support this level that are spiritual, teacher vision, good or bad, and ways of life.
Traditional teaching and progressive teaching have big different. In traditional teaching, teaching has a different mean with teaching in progressive teaching. In traditional teaching, teaching means to give, transfer of knowledge directly. Student controlled by teacher and teacher is teaching. It makes student passive and between teacher and students have a passive interaction. In progressive teaching, teaching means develop, construct their own knowledge. Students don’t depend on teacher and teacher is facilitated. It makes students be an active learner and between teacher and students have an active interaction.
In view of traditional teaching, it have different student, but the traditional teaching give same time, same mathematics, same facilities, same objects, and same result. It makes student can construct and develop their own knowledge. But in view of progressive teaching, it has different student, different time, different mathematics, different facilities, different objects, and different result. It makes student can construct, build, and develop their own knowledge.
Traditional teaching has single method that is explain, give example, give rules and give task. The students just do what the teacher said and follow the instruction. So the students are controlled by teacher. But progressive teaching have no method because there is no the best way to educate. Students have variant method that they can create depend on their ability and their knowledge.
Students as younger learner don’t match with pure mathematics but match with school mathematics. Curriculum in traditional teaching is context and purpose but in progressive teaching is student’s competence. Traditional teaching make study as obligate or invest for the students, but progressive teaching make study as need for student. To make student as active learner we must motivate students. Motivation each student, collaboration between students and teacher make it fun to learn together and build every character that they have because every individual is unique and contextual which can learn everywhere as a group or individually.
Source : Lecture from Dr. Marsigit, M.A