The Hermeneutic of Pure Mathematics
The figure shown expresses
the Hermeneutic of pure mathematics. Pure mathematics uses logic but not always
have the experience in life. But mathematics knowledge always has the
experience which related to life. It is true that experiences develop intuition
of pupils. Experiences sharpen the intuition because from experience we learn
more than mathematics.
The problem will come
out when teacher use traditional way to deliver the material. This is the chart
that shows the solving of traditional learning.
Teachers are required to
remain innovative in learning activities. Let the students develop according to his ability. Teachers should be glad if an
advanced student is smarter than
the teacher. In traditional
teaching, there is only material transfer from teacher to student. Pupils are not given the opportunity to argue in public. In
an innovative learning process, students compared with
seed plants. Water
and fertilizer is knowledge.
Prior to the interaction between teacher and student, the seeds do not have
roots and even leaves.
At the initial meeting
of the seed, grow roots. Until one day the seeds turn into plants that can produce fruits useful
knowledge.
Mathematics Phenomenon
From our life, of course
we can take some problems or some activities that directly or indirectly need
mathematics. This thing called phenomenon. The phenomenon that requires
mathematics inside called mathematics phenomenon. Mathematics phenomenon is available
anywhere. By idealization and abstraction, we can process the phenomenon into
new knowledge. Take some information we need to build new knowledge and then throw
away the information we don’t need to epoch.
Nature of School Mathematics
Mathematics used in
school ought to facilitate students to know and detect the phenomenon we found
in life. The nature of school has two kind of view: super serve and sub serve.
Super serve is what inside your mind. It is abstract, analytic, and coherence. For
example is the concept of number. Number has form and concept inside the form. The
number 3 has a concept, and its form can be Roman number, Arabic number, or
maybe represent with concrete objects. The form of number is sub serve, which
is outside your mind. This form is concrete.
3 -> III, ☼☼☼
The National Exam of
Indonesia is manipulative. It makes people don’t want to see the process of
learning. The National Exam has change some people mind set, they don’t really
think about the process because they think that every learning process end up
in The National Exam’s score. This kind of learning process kills pupils’
intuition. Future teacher has to have a clear picture if the nature of school
mathematics, realistic mathematics, and constructive teaching to keep pupils’
intuition alive. Teacher has to develop skill, develop various method, and
problem types.
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