Freudenthal (1991) states that there are four approaches in
mathematics i.e mechanistic, emperistic, structuralist and realistic and going to describe follow as:
1. Mechanistic,
or ‘traditional approach’, is based on drill-practice and patterns, which treat
the person like a computer or a machine(mechanic). It means the activities of
students in this approach are based on memorizing a pattern or an algorithm.
The errors will be occurred if the students are faced with other problems that
are different from the one they have memorized. In this approach, both
horizontal and vertical mathematization are not used.