Conception of Learners and Learning
The conception of Learning in RME is in line with the conception of learners. The starting point in the learning process in the realistic approach is emphasized on the conception that the students are familiar with. Each learner has a preconception or a set of alternative conceptions about mathematical ideas. After a student is involved meaningfully in a learning process, the student develops the conceptions to a higher level. In this step, the student actively acquires new knowledge. The construction of knowledge is a process of change that proceeds slowly from the first to second and then to the third. In this process the student is responsible for his own learning.
The conception of Learning and Learning that relevant with RME are:
- Each learner brings his or her preconception to the educational experience. These preconceptions are highly influential on subsequent learning. Learners possess a diverse set of alternative conceptions about mathematical ideas that influence their future learning.
- Each learner actively constructs meaning. Learners acquire new knowledge by constructing it for themselves.
- Each learner is ready to share his or her personal meaning with others, and based on this negotiation process, reconceptualizes the initial knowledge structures. The construction of knowledge is a process of change that includes addition, creation, modification, refinement, restructuring, and rejection.
- Each learner takes responsibility for his or her learning. The new knowledge learners construct for themselves has its origin in a diverse set of experiences
- Each learner is convinced that success in learning with understanding is possible. In other words, all students regardless of race, culture, and gender are capable of understanding and doing mathematics.
Conception of the teacher and teaching
The tenets of RME reflect the role of the teachers in mathematics teaching. Ideally, the teachers developed 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. 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 the authority by way of selecting instructional activities, initiating and guiding a discussions, and reformulating selected aspects of students’ mathematical contributions.
In the conception of the teacher an teaching, the tenets of RME are:
- The starting points of instructional sequences should be experientially real to students so that they can immediately engage in personally meaningful mathematical activities.
- 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.
- Instructional sequence should involve activities in which students create and elaborate symbolic models of their informal mathematical activity.
- 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 alternative, reflecting.
- Real phenomena in which mathematical structure and concepts manifest themselves lead to intertwining of learning strands.