Mathematics education has some problems in improving the quality of learners. To overcome these problems we can change traditional teaching into progressive teaching. There are few levels on teaching and learning, which are: 
- Spiritual level, In this level there are factors which support this level that are : spiritual, future vision, know about good or bad, and way of life.
- Normatif level, In this level there are factors which support this level that are : low, decree, education system, and paradigm of education.
- Formal level, In this level there are factors which support this level that are : curriculum, syllabi.
- Material level, In this level there are factors which support this level that are : class, teacing content, student, book, building and student.
Traditional teaching and progressive teaching have large differences. In traditional teaching, teacher base on expository method with cycle : to explain, to give example, give problem, and give task classically.
In traditional teching Student controlled by teacher and teacher is teaching, It makes student passive and between teacher and students have a passive interaction.
In progressive teaching use variation method, can choose one or more method dynamically and flexible :  (1) Exposition Method, (2) Discussion Method, (3) Training Method and give task, (4) Invention Method, (5) Problem Solving Method, (6) Using props. 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.
According to Plowden Report (1976) in (Delamont, 1987, p. 48) from Dr. Marsigit, M.A, in “Pembelajaran Matematika Berdasarkan Kurikulum Berbasis Kompeensi di SMK” describe the characteristics of traditional teaching and  the caracteristics of progressive teaching as shown below:
| Characteritics of   Traditional Teaching | Characteristics   of Progressive Teaching | |
| 1. | Separated subject matter | Integrated subject matter | 
| 2. | Teacher as   distributor of knowledge | Teacher   as guide to educational experiences | 
| 3. | Passive pupil role | Active pupil role | 
| 4. | Pupils   have no say in curriculum planning | Pupils   participate in curriculum planning | 
| 5. | Accent on memory, practice and   rote | Learning   predominantly by discovery   techniques | 
| 6. | External   rewards used, for example, grades, i.e.   extrinsic motivation | External   rewards and punishments not necessary   i.e. intrinsic motivation | 
| 7. | Teachers   give highest priority to academic   attainment | Teachers   give high priority to social and emotional   development | 
| 8. | Regular   testing | Little   testing | 
| 9. | Accent   on competition | Accent   on cooperative group work | 
| 10. | Little   emphasis on creative expression | Accent   on creative expression | 
