Mathematics
as a branch of science that is structured and systematically
organized is considered playing
an immense role in
optimizing the ability of human thinking. Therefore, mathematics
learning in schools is expected to
be a media of establishment
thinking skills particularly for students. There are, nonetheless, some major problems in
mathematics education in Indonesia, such as: quality of curriculum materials,
teaching methods and assessment strategies, emerging a gap between the intended
and the implemented curriculum. It is,
therefore,
necessary to design the integrated learning
which is expected can reduce such gap, namely Realistic Mathematics
Education or so called Pendidikan Matematika
Realistik Indonesia (PMRI).
RME
is a theory of teaching and learning in mathematics education that was
initially developed in Netherland. It stressed the idea that mathematics is a
human activity as Hans Freudenthal’s concept (Freudenthal, 1991). According to
him, pupils should not be treated as passive recipients of ready-mathematics,
but rather that education should guide the pupils towards using opportunities
to discover and reinvent mathematics by doing themselves. There are five
characteristics (tenets) of RME (de Lange, 1987; Gravemeijer, 1994):
·
The use of context in phenomenological exploration
In
RME the instruction should not be started with the formal system, but its
starting point should be experientally real to the students, allowing them to
become immediately engaged in the contextual situation.
·
The use of models or bridging by vertical instruments
Model
virtually refers to situational models and mathematical models that are
developed by the pupils themselves. Level of models in RME (Gravemeijer, 1994)
are;
o Situational level, where domain-spesific and situational
knowledge are used within the context of the situation.
o Referential level or ‘model-of’, where models and
strategies refer to the situation described in the problem;
o General level or ‘model-for’, where a mathematical focus on
strategies dominates over the reference to the context;
o Formal level, where one works with conventional
procedures and notations.
·
The use of pupils own creations and contributions
Pupils
should be asked to be active and initiative by creating concrete things,
reflecting on their learning process. They might be asked to do an experiment,
collect data, draw conclusions, or write an essay.
·
The interactive character of the teaching process or
interactivity
Pupils
should be motivated to develop their confidence by making good interaction in
instructional process. They are encouraged to discuss their own thinking rather
than focusing on whether they have the right answer.
·
The intertwinning of various learning strands or units
Those five tenets of RME then should be represented in designing or redesigning curriculum materials using realistic approach. Streefland (1991) used three levels of construction in this case: (i) The classroom level. Based on the characteristics of RME, instructional activities are designed in this level. Materials used are started from meaningful context and then intertwinned with other strands or units. Tools such as symbols or diagrams are produced to support the materials. Then, making interactive class by encouraging students to interact with others and giving them assignment leading to free productions. (ii) Course level. At this level, materials are expanded to other contents and context in order to develop the instructional sequence of the topic. (iii) The theoretical level. `All activities in two previous levels form the source of theoretical production for this level. In addition, a local theory is constructed, revised, and tested again during additional cyclic development.
RME Exemplary Lesson Materials refers to learner materials
and teacher guides used as a learning trajectory for teachers in the RME
classrooms. Generally they consist of three components, namely: (i) Content materials. RME material should
be associated with
the students’
environment so it is real experientally for students. (ii) Learner and teacher activities. In
classroom, the RME teacher’s roles are as facilitator, organizer, guide and
evaluator, whilts students should be active in constructing their own idea.
(iii) Assesment. It can be conducted
in the classroom using strategies both during the interaction process
(formative), and products of their solutions (summative).
