Summary of Subchapter 2.2 (Understanding RME) of the following reference:

Zulkardi. (2002). *Developing a Learning Environment on Realistic Mathematics Education for Indonesian Student Teachers* (Doctoral dissertation). University of Twente, Enschede.

The concept of RME is based on Hans Freudenthal’s views of mathematics as a human activity which implies that the students should be encouraged to find and reinvent the mathematics themselves. In order to reach the target, the learning process should start from the real world problem, or things which is well known by the students. Such strategy is then called ‘didactical phenomenology’.

In addition to that, Van Hiele identified three levels of learning mathematics. It starts when students can play with the pattern which is familiar to them. The next phases are when they could recognize the relationships among the patterns, and elaborate its internal characteristics.

Following the ideas, RME is resulted with **five main characteristics (tenets)**, that is:

**1. The use of context**

This tenet best matches with ‘conceptual and applied mathematization’ proposed by de Lange (1987). The idea positions ‘real world’ as both the starting and final point of learning cycle. So, the students would find mathematics concept in reality, explore it, identify the related-mathematics concept, generalize, and apply it into the other aspects of life.

**2. The use of models**

In order to bridge the students from horizontal to vertical mathematics, RME applies 4-level emergent modelling (situational, referential, general, and formal) concepted by Gravemeijer (1994).

a) Situational, students work within the context of situation

b) Referential (model of), students employ models and strategies regarding the situation given in the problem

c) General (model for), students use math-related strategies to solve the problem

d) Formal, students apply conventional procedures and notations to solve the problem

**3. The use of students’ creations and contributions**

Streefland (1991) argued that students would be more creative when they are encouraged to solve the problems with their own way. In RME, the students be the center of learning, in which, the teacher guides them to reinvent the concept by themselves.

**4. Interactivity
**Interactivity, between pupils and either the teacher or other pupils, is so important in RME-based learning that it dominates and characterizes the whole process. This allows students to argue, explain, describe, and reveal their ideas to others. Hence, their confidence could be built as well as their reasoning skills.

**5. Intertwining
**Solving real life problems, which is connected to mathematics either directly or indirectly, sometimes requires more than a single concept. Thus, the relationship among the concepts is absolutely needed.

**B. Designing RME Curriculum Materials
**Once we design an RME materials, the five aforementioned characteristics should be encouraged. In addition to that, according to Streefland (1991), there are three steps to design RME based learning materials, that is:

1. Classroom level

2. Course level

3. Theoretical level

**C. RME Exemplary Lesson Materials
**A good example of RME learning material should contain content materials, learner and techer activities, and assessment.

PS:

The article is based on my own understanding to the reading. For more detail, you may have a look at its origin.