Referring to an article “*The Didactical Use of Models in Realistic Mathematics Education: An Example from A Longitudinal Trajectory on Percentage*” written by Marja van Den Heuvel-Panhuizen, I would like to share my understanding about general theory of RME and the role of models within this theory.

Realistic Mathematics Education (RME) conceptualizes Freudenthal’s (1971) thought of “mathematics as a human activity”. It means that mathematics is an activity of organizing problems from real situation or mathematical matter – which is called **mathematization**– rather than just the body of mathematical knowledge. Treffers (1978, 1987), furthermore, distinguished the perspective of mathematizing into “horizontal” and “vertical” mathematizing. Mathematical tools, in term of horizontal mathematizing, are used to organize or solve a problem related to daily life. In the other hand, vertical mathematizing indicates for all kind of re-organization and operation within the mathematical system itself.

Regarding to mathematizing, the characteristics of RME is also historically related to the levels of *Van Hiele theory* and Freudenthal’s *didactical phenomenology*. As a result, those theory compose the five characteristics (tenets) of RME (de Lange, 1987; Gravemeijer, 1994) which is generally described as follows.

*1. The use of contexts in phenomenological exploration*.

The starting point of mathematics learning in RME should use mathematics concept appearing in reality, such that pupils become immediately connected in contextual situation.

*2. The use of models or bridging by vertical instruments*

In this case, the term of “model” refers to situational and mathematical models developed by pupils themselves.

*3. The use of pupils own creations and contributions*

Using students’ own constructions and productions. Students’ own constructions and productions are meaningful for them, and so should be used as an essential part of instruction

*4. The interactive character of the teaching process or interactivity*

The interactivity principle of RME signifies that learning mathematics is not only an individual activity but also a social activity. Therefore, RME favors whole-class discussions and group work offering students opportunities to share their strategies and inventions with others. In this way, students can get ideas for improving their strategies. Moreover, interaction evokes reflection that enables students to reach a higher level of understanding.

*5. The intertwining of various learning strands or units*

The intertwinement principle means mathematical content domains such as number, geometry, measurement, and data handling are not considered as isolated curriculum chapters, but as heavily integrated. Students are offered rich problems in which they can use various mathematical tools and knowledge. This principle also applies within domains. For example, within the domain of number sense, mental arithmetic, estimation and algorithms are taught in close connection to each other

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