A
lot of people give opinion that teacher is a person who teach student. Not only
teach the subject but also teach about moral, social, etc. Teacher as parent of
students in school, so teacher must make students feel comfortable to study in
the school. If students feel boring, teacher must know how to make them feel
comfort again.
We
know that there are two paradigms about teaching; they are old paradigm and new
paradigm. The old or traditional paradigm called teacher-centered where the teacher supposed
that the students as empty vessel and be passive students, the teacher transfer
of knowledge, give and direct. Make students will always follow teacher’s
instruction. For the new paradigm called student-centered, make creative
students where suppose that each of students as a seed, who if we give it opportunity,
it will grow and develop and on uncertain time will product the fruits. The teacher
as the facilitator and the task of teacher is making the students’ active and improve their skills. Students
must interest in finding solutions of problems.
For make
students become like mathematics according to (Ebbut and Straker, 1995)
teachers should not use axiomatic mathematical definition, but defines
mathematics as school mathematics. Because
the nature of students learn Mathematics are :
1. The student learn Mathematics effectively if they have
good motivation and perception
2. The student will learn mathematics individually
3. The student can learn Mathematics in collaboration with
others
4. The student learn Mathematics contextually
And here is the essence of
school mathematics:
1. Mathematics
is the search activity patterns and relationships
By give
students opportunity to discovery and determine patterns of relationships, to
show their experiments premises in various ways. Support the students to
develop the sequence, difference, comparison, grouping, and so on. Support the
students to make general conclusion and help them understand to find a
relationship between understanding one another.
2. Mathematics is the creativity that requires
imagination, intuition and invention
Support
the students to get their initiative, to think different.
By worm out of their curiosity, then they desire to ask. Appreciate their question. Encourage students to think reflexive. Don’t recommend them to use particular method.
By worm out of their curiosity, then they desire to ask. Appreciate their question. Encourage students to think reflexive. Don’t recommend them to use particular method.
3. Mathematics
is problem solving activities
Teacher
must stimulate students’ learning mathematical problem. Help students solving
mathematical problem using their own way. Help students find the information
which need to solve mathematical problems. Make students think logically,
consistently, systematically and develop a system of documentation / records.
Develop the ability and skills to solve problems. Helps students learn how and
when to use various visual aids / media mathematics education such as: term,
calculator, etc.
4. Mathematics
is a main of communicating
Give
information to students about the nature of mathematics. Encourage students to
justify the need for mathematics activities. Invite them to discuss mathematics
problems, to read and write mathematics. Respect the students' mother tongue in
talking about mathematics.
We know that the problems of teaching are always different. The
innovative teaching or progressive are consist of system, curriculum, syllabus,
lesson plan and student worksheet. Principles of teaching mathematics are effective mathematics
teaching requires understanding and knowledge students need to learn to attract
and sustain them for a good learning, effective learning requires knowledge
and understanding of mathematics, students as
learners, and education
strategies, effective learning requires a class challenging and supportive learning
environment, effective learning requires a continuous search for improvement.
Science
is process of thinking and social activities. Based on Paul Ernest the aims of
teaching mathematics are socially and societally embedded. There are five interest groups and their aims
for mathematics teaching. They are :
1.
Industrial
Trainers
The elements are
:
-
Politics
: radical right
-
Mathematics
(Opinion about the nature of mathematics) : body of knowledge
-
Moral
value: good vs. bad
-
Theory
of teaching: transfer of knowledge
-
Resources:
white board, chalk, anti calculator
-
Evaluation:
external test
-
Diversity:
monoculture
-
Social
location: radical ‘New Right’ conservative politicians and petty bourgeois
-
Mathematical
aims: acquiring basic mathematical skills and numeracy and social training in
obedience (authoritarian, basic skills centered)
2.
Technological
Pragmatists
The elements are:
-
Politics:
conservative
-
Mathematics:
science of truth
-
Moral
value: pragmatism
-
Theory
of teaching: external motivation
-
Resources:
teaching aid
-
Evaluation:
external test
-
Diversity
: decentralization
-
Social
location: Meritocratic industry centered industrialists, manager, etc., New
Labour
-
Mathematical
aims: Learning basic skills and learning to solve practical problems with
mathematics and information technology (industry and work centered)
3.
Old
Humanist Mathematicians
The elements are
:
-
Politics
: conservative / liberal
-
Mathematics
: structure of truth
-
Moral
value : Hierarchies Paternalistic
-
Theory
of teaching : expository
-
Resources
: visual teaching aid for motivation
-
Evaluation
: external test
-
Diversity
: competent based curriculum
-
Social
location : conservative mathematicians preserving rigors of proof and purity of
mathematics
-
Mathematical
aims : understanding and capability in advanced mathematics, with some
appreciation of mathematics (pure mathematics centered)
4.
Progressive
Educators
The elements are:
-
Politics
: liberal
-
Mathematics
: process of thinking
-
Moral
value : humanity
-
Theory
of teaching : construction, development
-
Resources
: various resources
-
Evaluation
: Porto-folio, assessment
-
Diversity
: multiple solution, local culture
-
Social
location : professionals, liberal
educators, welfare state supporters
-
Mathematical
aims : graining confidence, creativity and self expression through mathematics
(child centered progressives)
5.
Public
Educators
The elements are:
-
Politics
: democracy
-
Mathematics
: social activities
-
Moral
value : justice, freedom
-
Theory
of teaching : discussion, investigation
-
Resources
: social environment
-
Evaluation
: Porto-folio, social context
-
Diversity
: heterogeneous
-
Social
location : democratic socialists and radical reformers concerned with social
justice and inequality
-
Mathematical
aims : empowerment of learners as critical and mathematically literate citizens
in society (empowerment and social justice concerns)
From
the different social groups we know that the industrial trainers, technological
pragmatists, and old humanist mathematicians are placing their aims in
curriculum. In the progressive educators give name the processes of a personal
knowledge-application dimension by ‘using and applying mathematics’, which is
the National Curriculum attainment targets. For the public educators’ aim, about
the development of critical citizenship and empowerment for social change and
equality through mathematics (has no part in curriculum development).
Based
on Paul, the appreciation of mathematics consist of understanding and having an
awareness of its nature and value, as well as understanding and being able to
give critic about its social uses. The breadth of knowledge and understanding
involved is potentially immense, but a lot of students leave school without
ever having been exposed to apply it. The empowered learner will not only be
able to pose and solve mathematical questions, but also be able to address
important questions relating to the broad range of social uses of mathematics.
Mr.
Marsigit, said no matter where and no matter when, we need scheme as container.
If we not feel comfort when live in foreign country it means we don’t have
scheme. Based Mr. Marsigit, the opinion about nature mathematics as body of
knowledge, science of truth, and structure of truth and diversity of
monoculture, decentralization, and competent based curriculum is traditional
paradigm or teacher centered. National exam is one example of external test in
Indonesia, and it’s also traditional. But evaluation like Porto-folio, assessment,
social context is innovative. Because can improve students’ ability to be
responsible about their learning activity by write down in the porto-folio or
called record their working. Social context also make students’ share their own
work to their friend. Assessment for evaluate their work, are their answer,
process true or false. Example of moral value in industrial trainer is from
puppet show, which shows the good and bad value. In the end of the show the
good/kind person will win. Then the example from justice freedom of moral value
in public educators is social justice for all Indonesians (5th of the
five basic principles of the Republic of Indonesia).
The teachers need to change the paradigm of teaching from traditional
paradigm to new paradigm. The teacher as the facilitator and the task of
teacher is making the active students. In new
paradigm, there are a lot of ways for students to improve the students’ skills
and to be active students. The nature of learning mathematics is
interaction among the students and the teachers. Development of mathematical learning has a
good impact for students, but in the implementation of teachers found several
problems. It was a task for the teacher to solve the problem of
learning mathematics through improving the competence of teachers, resulting in
students who are really smart and high quality.
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