Conception of the teacher and teaching in Realistic Mathematic Education

Cobb (1994) states that the theory of RME constitutes a highly compatible, domain
specific instructional theory that relies on real world application and modeling.
compatibility between constructivism and RME is due, in large part, to the similarity in the characterization of mathematics and mathematics learning. Both contend that
mathematics is a creative human activity, and that mathematical learning occurs as
students develop effective ways to solve problems (de Lange, 1996; Streefland, 1991;
Treffers, 1987). Using the description by Cobb (1994), de Lange (1996) addresses the
tenets of RME:
1. The starting points of instructional sequences should be experientially real to
students so that they can immediately engage in personally meaningful
mathematical activities.
2. In addition to taking into account the students' current mathematical ways of
knowing, the starting points should also be justifiable in terms of the potential end
points of the learning sequence.
3. Instructional sequences should involve activities in which students create and
elaborate symbolic models of their informal mathematical activity.
4. The first three tenets can only be effective if they are realized in interactive
instruction: explaining and justifying solutions, understanding other students’
solutions, agreeing and disagreeing, questioning alternatives, reflecting.
5. Real phenomena in which mathematical structures and concepts manifest
themselves lead to intertwining of learning strands.
The tenets of RME reflect the role of the teachers in mathematics teaching. Ideally, the teachers develop highly interactive instruction, give opportunities to the students to actively contribute to their own learning process, and actively assist the students in interpreting real problems. De Lange (1991) describes RME teaching as unteaching.
In order to be a successful RME teacher, one has to learn the 'art of unteaching' which is not easy to realize. Unlike traditional interpretation of teaching as an activity carried out mainly by the teacher, in RME the teaching is more complex than just a well organized sequence of introduction – explanation – exercise – conclusion (like PKG teaching model).
In RME the teacher is not supposed to teach anymore. His or her role is emphasized
on being an organizer and a facilitator of the students' reconstruction of mathematical
ideas and concepts. He or she needs to make his or her own personal adaptation.
Gravemeijer (1994) similarly describes that since students are no longer expected to
simply produce correct answers quickly by following prescribed procedures, but have
other obligations such as explaining and justifying solutions, trying to understand the solutions of others, and asking for explanations or justifications if necessary, the role of the teacher is changed. According to Gravemeijer (1994) the authority of the teacher as a validator is exchanged for an authority as a guide. He or she exercises this authority by way of selecting
instructional activities, initiating and guiding discussions, and reformulating selected aspects of students' mathematical contributions.