A. INTRODUCTION
Most of students think that mathematic
is the difficult subject. Almost of the subject in mathematic is abstract, it
makes student become scary before they learn mathematics. The result of the
National examination especially for mathematics subject show that the student’s
capability in mathematics still lower. This reality make all of the component
start from the students, the teacher and the parents become anxious when the
National examination will be done by the students.
The teaching learning process of
mathematics is moved from time to time so that the teacher must use all of the
facilities to make the teaching learning process of mathematics become enjoy
and fun. Become a teacher or candidate of the teacher, especially for
mathematics teacher, we must prepare all of the things that will be used when
we teach our students. To achieve good teaching learning process we must manage
all of the preparation like manage the lesson plan, apperception, various
method of teaching, various media/ teaching aids, various interaction, small
group discussion, students presentation, students worksheet and assessment. All
of that, must be prepared well.
We know that our students have the
various characteristics and we must facilitate all of the students as well as
we can. To reach the best teaching learning process of mathematics not only
needed a smart teacher or a good teacher but also the method from the teacher
also decide the success of teaching learning process.
B. CONTENT
To developing
the design of innovative teaching learning process of mathematics. We have to
consider about the Curriculum. The curriculum that be used in Indonesia is
KTSP. This curriculum emphasize the student’s capability. And the teacher only
as a facilitator in teaching learning process.
In this curriculum we know about the Standard of competences and Basic
Competences. Standard of competences and basic competences is made by
government, in this case is the Educational ministry. Then, the task of the
teacher is to decide the objective learning and then arrange the indicators as
a standard achievement.
Then, after all
of the indicators are defined well the teachers must design the type of the
teaching learning process. There are some types of the design : constructivism,
realistic mathematics, problem based learning, cooperative learning, and
contextual learning. What’s the meaning of all of the type of the teaching
leaning models?
1.
Realistic Mathematics
Mathematics
must be close to children and be relevant to every day life situations.
However, the word ‘realistic’, refers not just to the connection with the
real-world, but also refers to problem situations which real in students' mind
(Zulkardi, 2006). For the problems to be presented to the students this means
that the context can be a real-world but this is not always necessary. De Lange
(1996) stated that problem situations can also be seen as applications or
modeling. The idea of mathematics as a human activity is stressed. Mathematics
education organized as a process of guided reinvention, where
students can experience a similar process compared to the process by which
mathematics was invented. The meaning of invention is steps in learning
processes while the meaning of guided is the instructional environment of the
learning process. Moreover, the reinvention principle can also be inspired by
informal solution procedures. Informal strategies of students can often be
interpreted as anticipating more formal procedures.
Two types of mathematician which were
formulated explicitly in an educational context by Treffers, 1987, in Zulkardi,
2006, are horizontal and vertical mathematician. In horizontal mathematician,
the students come up with mathematical tools which can help to organize and
solve a problem located in a real-life situation. The following activities are
examples of horizontal mathematician: identifying or describing the specific
mathematics in a general context, schematizing, formulating and visualizing a
problem in different ways, discovering relations, discovering regularities,
recognizing isomorphic aspect in different problems, transferring a real world
problem to a mathematical problem, and transferring a real world problem to a
known mathematical problem (Zulkardi, 2006). On the other hand, vertical mathematician
is the process of reorganization within the mathematical system itself.
2.
Problem
Based Learning
Problem
Based Learning exists as a teaching method grounded in the ideals of constructivism
and student-centered learning. When using PBL, teachers help students to focus
on solving problems within a real-life context, encouraging them to consider
the situation in which the problem exists when trying to find solutions.3 The
majority of research examining Problem Based Learning focuses on its use in
medical schools, with the key features being (a) the use of collaborative
small-group work, (b) a student-centered approach, (c) the teacher as
facilitator and (d) the use of real-life problems as the organizing focus.
3.
Cooperative
Learning
The
purposes and aims of cooperative learning need to be elaborated within certain
domains of study. Cooperative learning is not a technique for its own sake but
needs content in order to be useful. The specific content or subject
matter is not a result of arbitrary choice, without any consequences for the
design of a curriculum in which cooperative learning takes place. Content has
its own characteristics, which can be utilized in the designing process and in
the classroom in order to facilitate the development of thinking as a human
activity. Mathematics education, for example, offers specific opportunities for
cooperative learning with this purpose in view. To put it differently and to
make the general idea more specific, the content of mathematics allows for specific
models of cooperative learning in order to accommodate individual differences between
students. Mathematical problems can be situated in real-life contexts and
designed in such a way that solutions can be reached along different routes and
at different levels. This makes cooperative learning in mathematics different
from cooperative learning in other domains, such as languages and world
orientation. Each domain has their own opportunities for teaching and learning
with regard to individual differences among students.
4.
Contextual
Learning
Contextual
learning is a proven concept that incorporates much of the most recent research
in cognitive science. According to contextual learning theory, learning occurs only
when students (learners) process new information or knowledge in such a way
that it makes sense to them in their own frames of reference (their own inner
worlds of memory, experience, and response). This approach to learning and teaching
assumes that the mind naturally seeks meaning in context—that is,
in relation to the person’s current environment—and that it does so by
searching for relationships that make sense and appear useful. Building upon
this understanding, contextual learning theory focuses on the multiple aspects
of any learning environment, whether a classroom, a laboratory, a computer
lab, a worksite, or a
wheat field. It encourages educators to choose and/or design learning environments
that incorporate as many different forms of experience as possible—social, cultural,
physical, and psychological—in working toward the desired learning outcomes.
The teacher determine the approach in teaching
learning process then the teacher determine the methods in the process. There
are some methods to be used in teaching learning process. There are : Discussion
Methods, Inquiry Methods, Investigation Methods, Practical work, Small Group
Discussion, Problem solving
The teacher must consider about the teaching
materials. Teaching materials can be obtained from lesson plan, students
worksheet, module, handout, textbook, and teaching aids. Providing
books or textbook is one of the crucial policies to improve the quality of
teaching learning processes. The ideal program for providing the needs of large
scale of the books should not in the means of monopoly by one or some
institutions, but let the schools to choose their own needs of textbook to be
used at schools. It was also to be suggested that the students have their right
to select and by their own books without much intervention by the teacher or by
the school. However, the situation is that it is still far away for the
teachers to produce their own books. The main reason is lack of skill to write
and produce good quality of textbooks. In the case of providing textbooks, we
face with the large number of students who could not buy the books because of
the very low on its social economical background. So, there is an expectation
from the teachers, the students and the society that the government is able to
provide the books with the lower prices.
After all of the preparation is prepared well then
we enter the implementations step. The teaching learning process must be observed.
In teaching learning process there are some things that must be implemented
like apperceptions, small group discussion, various methods, various media,
various interaction, lesson plan, student worksheet, students reflection,
cognitive scheme, conclusion by the student, assessment (record). Then, we
continue in reflection step. In this step, it is divided in teacher’s
reflection, observer’s reflection, and summary. Then, like in the classroom
based there is continued in the next cycle.
C. CLOSING
To developing
the design of innovative teaching learning process of mathematics there are
some preparation that must be prepared. After the preparation do well then it
must be implemented in the real teaching learning process of mathematics.
Actually, in a reality there is some problems that must be reflected to find
the best way in teaching learning of mathematics. Observation in the class is
needed to find the problem in teaching learning process and then it must be
found the solution and to get the best way in teaching learning process. All of
the preparation must be prepared well. We know that to get success in teaching
learning process it not only need a good teacher but, the process is very
determine the teaching learning process to be get success.
Sources :
Marsigit.
2010. The Iceberg Approach of Learning
Fractions in Junior High School: Teachers’ Simulations of Prior to Lesson Study
Activities. Yogyakarta: Yogyakarta State
University.
Marsigit. 2010. Developing Teacher Training Textbooks for
Lesson Study in Indonesia. Yogyakarta: Yogyakarta State University.
