Realistic Mathematics Education
(RME) Theory as a Guideline for Problem-Centered, Interactive Mathematics
Education
(Koeno Graveimeijer)
Over
the last decades, there has been a huge alteration in mathematics education in Indonesia;
instruction which has been widely believed as transmission of knowledge has
turned into learning as the construction of knowledge. In line with this case,
there has been a shift away from teacher-centered class toward
problem-centered, interactive mathematics education. This shift surely will
require a change in how instruction is conceptualized. RME so called as
Pendidikan Matematika Realistik is a domain-specific instruction theory which
can support teachers in the incarnate of a problem-oriented classroom
condition.
Turning
into this such new classroom culture certainly requires a different didactical
contract as well by adopting classroom social norms for students, such as the
compulsion to construct their own idea, explain and justify their solution,
understand other students’ reasoning, and ask the unclear explanation. It is
realized, however, that implementing those new didactical contracts takes a
significant amount of effort. It is not easy to encourage students construct
their own idea, start sharing their thinking and no longer rely much on the
teacher, since students are likely accustomed to being passive information-recipient
in the learning process.
Reforming
mathematics education virtually rests on two pillars: the ability of the
teacher to create a problem-oriented classroom culture and then engage with
students in interactive instruction as well as the design of instructional
activities that allow for the reinvention of mathematics together with the
ability of the teacher to support this reinvention process.
Relating
to that case, RME is a domain-spesific theory that can offer guidelines for
instruction aiming at supporting students in constructing, or reinventing
mathematics in problem-centered interactive instruction. RME further requires
the teacher to play an active role in orchestrating productive whole-class
discussions and in selecting and framing mathematical issues as topics for
discussion. RME then would refer to mathematics instruction based on practical
problems in an everyday life context. The ‘real’ in ‘realistic’ has to be
understood as real in the sense of being meaningful for the students. According
to the RME theory, instructional starting points have to be experimentally real
for the students.
In
elaborating and applying RME approach, of special focus will be the role of
concrete materials, context problems, and the cultivation of mathematical
interest. To begin with, concrete materials can help students bridge the gap
between their informal knowledge and the more formal abstract knowledge they
need to acquire. Considering this case, RME alternative is to provide
manipulatives to students as a means for scaffolding their own thinking. Manipulative
can be a powerful means to support students in building upon their own ideas
and scaffolding their thinking. It allow
abstract mathematical knowledge become more concrete and easier to understand
for students.
As emphasized before, the instructional
starting points in RME have to be experiantally real for students. Therefore,
one of its focus is using context problem which has two goals; to offer the
students a motive concerning the intention to create a situation in which it
makes sense for the students. Students are supposed to be able to image
themselves in the situation how the problem is cast. Another objective is to offer students footholds
for a solution strategy, in which students have to build upon their own
thinking.
A
further issue of corcern with context problem is that RME aims to eventually
surpass the level of just finding solutions to practical problems. Rather, it
also aims to teach students to start thinking mathematically. In RME,
reinvention requires a combination of horizontal and vertical mathematization. Horizontal
mathematization is mathematizing activity applied to a subject matter of
reality whilst when it applies to a mathematical matter, it’s called as
vertical mathematization. To solve the the practical problems, horizontal
mathematization actually is sufficient to perform by students. Nevertheless, to
invent new mathematics as well as enhance students’ mathematical skills and
insights, students also have vertically mathematize their own mathematical
activity. To help students in this process, teachers will have to cultivate the
mathematical interests of students.
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