Idea
means a design that is arranged inside a human mind, can include opinion and ideals.
Construct means build, helping to improve something. Construct the ideas means
helping to improve a design that arranged in a human mind that makes a real
idea.
Basically
the idea is not easy to build. Moreover, developing ideas in mathematics
learning. Not as easy as we imagine. In solving mathematical problems there is
need for the development of ideas that allows us to solve the problem. Before
we begin to work on problems in mathematics, we must understand a few important
steps before we start.
First,
we have to develop ideas related to the problem. This is useful to find all the
possibilities that will appear when we solve the problem such as a double
meaning or a hidden purpose in it. Developing an
idea related a problem, never make us doing wrong the steps in our
works.
The
second is crafting ideas that have been developed into a draft of mind. So it
becomes a whole design idea. Through constucting the ideas we can determine
which steps we will take to resolve the problem.
Next
is to solve the problem. In solving the problem, we can use the design idea that
was conceived and developed before so that we'll find easier way to find the
right answer.
By
using the steps above, hopefully we can solve Mathematics problems better and get a correct answer. In learning mathematics the
most important is the process towards the right result, not on the final result
regardless of the process. The processes that we do, can build our own ideas
and can build up our knowledge. This process will add our experience in solving
the math problems correctly. So that we build a world, ideas, and knowledge of
our own without realizing it. And it would be easy to stick in our minds than
solve out the problem without regard to the process.
In
Indonesia, mathematics learning still focuses on teachers, so that students
only be described as an empty barrel that every day continues to be filled and
refilled. Students are difficult to grow, especially in developing their ideas,
because every day they just accept, never do something.
Then,
learning system in Indonesia is too open minded, still searching for the
identity. So that the teaching methods sometimes adopted from other countries.
In
mathematical problem solving in Indonesia, is still dominated by the teacher.
Because they assumed that teachers teach as a professional obligation in
accordance with government regulations and have to achieved all learning
indicators of competency standards that have been applied.
However,
many schools are implementing student center. Student center is a method of
student-centered learning, students become a major role in the learning process,
and the teacher only as a facilitator who facilitates the students when faced
with learning difficulties. By applying this method of student center, students
are expected to be able to develop ideas and construct their own ideas to solve
mathematical problems according to their ability and their own way. Teachers
are not allowed to impose a method to students. That way they can build their
own knowledge, without being forced.
In
Japan, the mathematical problem solving do not know "contstruct".
They do not construct ideas before solving problems, but they are directly to
solving the problem. It is can be said that students can not develop properly.
Besides that, problem solving is also used as a character study. So that
learning becomes semi-authoritarian and contstructivis not go well. Students
are not given the opportunity to build their ideas and solve problems in their
own way, so here the teacher took a leading role in the learning process. It is
also influenced by the culture in Japan too.
While
in Australia, they applied Mathematical Modelling method. Mathematicals
modeling is a method of learning mathematics that uses models as a tool in the
learning process. This method is used for teaching mathematics in primary
schools. Due to the use of models or props students will be more easily aroused
and easily capture the point that the teacher has been submitted. This model
will facilitate students in learning mathematics. They can develop their skills
by using models or learning aids.
According
to Max Stephens, models used in the learning of mathematics should be varied
and not monotonous, so students are more interested and not get bored Modelling problems
need to be designed so that multiple solutions of varying mathematical
sophistication are possible and such that students with a range of personal
experiences and knowledge can participate In this way, the mathematical
experiences of students become more challenging, authentic and meaningful.
. A
good teacher in the learning does not focus on text books. Rather they should
be able to develop a medium of learning for students. Learning mathematics in
pattern-making is required. Because the pattern gives us the ability to find
something we have not understood so that we can understand the meaning of the
pattern. Involvement of students in the learning process of mathematics provide
more knowledge and experience for them. So that they can easily capture the
intent conveyed.
Mathematics
can not be separated from the numbers. The number is mathematical knowledge.
Function of the numbers is to measure the quantity, to decide, to the make something
more specific, make a definition. Number is one of the pattern. The number is
also often used to construct the problems in mathematics.
As a teacher we need to rationalize in teach mathematics to the
students. It’s means that we have to be able to explain the phenomenom of
mathematics education as a reference in teaching mathematics. Teacher
personality is desperately needed in teach mathematics in class. Because
teacher personality in teach mathematics is very influental to the students’
mental developing.
In
addition, in constructing the ideas, teachers also need to know about the
theories and international paradigm in learning mathematics. So that they can
apply them appropriately in learning process at school. Teachers also must be
able to see the difference between students' competence, so that they can
deliver the right system to their students. Cultural differences are also very
influential in the teaching of mathematics in schools.
Mathematics
has links with the science of religion. Some concepts in mathematics are also
used for religious purposes such as the construction of a Borobudur temple in
Central Java, the level and shape are using the concept of a complex geometry
and the construction is perfect. Religion has the highest position in life. It
is effective if religion and mathematics knowledge can runs together and
ballance.
Sources:
General
lecture on Monday, 12 March 2012 by Prof. Mohan Chinnappan, PhD.
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