How is the realistic approach related to the constructivist approach?

Due to many similarities with RME, the theory of constructivism in mathematics is included in this review. Some differences will be discussed as well. In general, constructivism means that programs start from the philosophy that give learners the freedom of their own construction or reconstruction. Three types of constructivism that are used in mathematics education are known as:

1.Radical constructivism: knowledge can not simply be transferred ready-made from parent to child or from teacher to student but has to be actively built by each learner in his or her own mind (Glasersfeld, 1992). Here, students usually do deal with meanings, and when instructional program fail to develop appropriate meanings, students create their own meanings. But Ernest (1991) argued this type of constructivism is lack of a social dimension in which the students learn dependently;

social-constructivism: Ernest (1991) comes up with a new type of constructivism that is called

social-constructivism which views mathematics as a social construction which means that

students can better construct their knowledge when it is embedded in a social process

(Ernest, 1991); and

2.Socio-constructivist: this type of social constructivism is developed only in mathematics education. The characteristics of this type are almost similar to the characteristics of RME such as mathematics should be taught through problem solving, students should interact with teachers and other students as well, and students are stimulated solve problems based on their own strategies (Cobb, Yackel & Wood , 1992).

The fact that socio-constructivist is closely related to RME was stated by Gravenmeijer (1994) as well as de Lange (1996). There are two main similarities between RME and socio-constructivist mathematics education (de Lange, 1996). First, both the socio-contsructivist and realistic mathematics education are developed independently of constructivism. Second, in both approaches students are offered opportunities to share their experiences with others. In addition, de Lange (1996) stated that the compatibilities of socio-constructivist and RME are based on a large part or similar characterizations of mathemathics and mathematics learning. Those are: 

(1) both struggle with the idea that mathematics is a creative human activity; 

(2) that mathematical learning occurs as students develop effective ways to solve problems (Streefland, 1991; Treffers, 1987); and 

(3) both aim at mathematical actions that are transformed into mathematical objects (Freudenthal, 1991).

The main difference between RME and constructivism is that RME is only applied to mathematics education while constructivism is used in many subjects (de Lange, 1996). Moreover, Gravenmeijer (1994, p.81) pointed out that "the difference between socio-constructivist approach and realistic approach is that the former does not offer heuristics for developing instructional activities for students". In other words, in socio-constructivist approach, the teacher does not use heuristics, a method of solving problems by learning from past experience and investigating practical ways of finding a solution. In RME, it is known as guided reinvention.