Mathematics is the mother of
science, so it is studied and applied by all of the lesson. All of the people
also studied it, from the younger people until the older people. Every level of
schools studies about it, since entering elementary school, junior high school,
senior high school, until university. After we graduate from university, we
still need mathematics. We cannot escape from mathematics because mathematics
is so important to be study.
Let’s start with the question
about the nature mathematics! First, we must know about the nature of
mathematics. What is it? Start with the meaning of mathematics. The
mathematician can define the meaning of mathematics through the history.
Philosophers define mathematics to the simple mathematics and prove it, and it
builds systematically as the system that develops as formal mathematics.
Mathematics for university consists of system, axiom, definition, n making
theorem. Moreover, the nature of mathematics is how to make someone not bore
with it and it can plant mathematics for mathematics.
Many problem that showed for us
as the teacher, the problem is how to develop or to build communication with
the students. Mathematics for the younger student and older student is
different. Younger student think about something concrete and the older people
think about something abstract. It is so different between mathematics in
university and mathematics in school. In university, they learn about something
abstract and it developed with the axiom and a lot of proof. In contrast to
mathematics in school, they learn not to prove, they learn about something
concrete, daily objects, and example.
The other problem is if we are a
teacher and we must teach about mathematics, we need to adapt or to know the
psychology of our student. As a teacher, we must adapt the student’s world.
This is some example why we must know the student’s world, if parent say like
child, so it’s caused the parent want to understand the children’s world, or
the designers must know about girl’s fashion to know the girl’s world so they
can design some thing that girl like. If the teachers cannot adapt, they will
be avoided.
According to Ebutt and Straker
(1995), teachers do not use axiomatic mathematics definition, but they must use
mathematics as school mathematics. With this definition, the student will like
mathematics. The following is the nature of School Mathematics by Ebutt and
Straker :
1.
Mathematics is a search of pattern or
relationship
In this point,
the student should be motivated to determine their pattern or relationship
between in material to the other material. Therefore, the students have a
freedom to determine their own pattern or relationship with their method. In
the last, the student will be more understanding with the teacher’s
explanation.
2.
Mathematics is problem solving activity
What is the
goal learn mathematics? The goal of learning mathematics is to find the
solution of each problem. As we know that mathematics happen in daily life
situation, inevitably and in real life situation, pencil and paper do not
always come in handy. So learning must be meaningful, so number should be make
useful and sense. But remember when the students solve the problem, they have
another way to solve it. So these activities is useful to develop the student’s
thinking.
3.
Mathematics is investigation activity
What do you
think about mathematics as investigating activity? It means that to solve the
problem of mathematics, we must investigate it. When investigating it, the
students have many ways to solve the problems. They use their pattern or
relationship that it depends of their understanding about the material. So this
activity will develop the student’s creativity, so many ways that they can use.
These activity can make the student think that mathematics is so easy and not
rigid or limited with one ways, but mathematics can be solve with many ways.
4.
Mathematics is learning of communications
Mathematics as
learning of communications works to:
a. Encourage students to make examples of the nature of mathematics
b. Encourage students to explain the nature of mathematics
c. Encourage students to justify the need for mathematics
d. Encourage students to discuss mathematical problem
e. Encourage students to read and write mathematics
1.
Mathematics students learn effectively is by good motivation and
perception
How can the
student get a good motivation and perception? It depends of the teaching
method. The teacher must inspire, challenge and stimulate the students by the
teaching method. However, we must know the psychology of our student
because students have different character so the teacher must different way to
be motivated each students.
To encourage
students to become self-motivated independent learners, the teacher can do the
following:
a. Give frequent, early, positive feedback that supports students' beliefs that they can do well.
b. Ensure opportunities for students' success by assigning tasks that are neither too easy nor too difficult.
c. Help students find personal meaning and value in the material.
d. Create an atmosphere that is open and positive.
e. Help students feel that they are valued members of a learning community.
2.
Students learn mathematics individually
Students
examine their own mathematics. He studied according to his understanding.
Sometimes he is abstracting events in everyday life into the concept of
mathematics. Every student has different ways of learning mathematics. It can
be seeing directly when the students solve with a case of mathematics. It will
be looked different way of solving the problems between students with the other
students. This is not blame for mathematics is essentially investigative
activity.
3.
Students learn mathematics in collaboration with
the other
Learning
mathematics with the other can make us more expected to understand math.
In-group, the students can exchange their ideas and if they have some problem,
they can solve it together.
4.
Students learn mathematics contextually
that bound by space and time
Students will
be better understand math if teachers pass them contextually. Young student
learn about something concrete and daily living that close to them. With the
experience, they develop their ability to understand abstract concept, axiom,
prove, reason logically, manipulate symbol and generalize. Teacher can give the
example that close to daily live so the student know the application of
mathematics in daily live not only just calculate the formula.
So what the teachers need to
teach their student? They need the paradigm of teaching
The old paradigm of teaching
©
transferring knowledge from teacher to student
©
filling passive empty vessels with knowledge
©
classifying students by deciding who gets which
grade and sorting students into categories
©
conducting education within a context of impersonal
relationships among students and between teachers and students
©
maintaining a competitive organizational
structure
©
assuming that anyone with expertise in their
field can teach without training to do so
Constructivism : constructing
meaning and making sense of numbers
The new paradigm of teaching
©
knowledge is constructed, discovered,
transformed, and extended by students
©
students actively construct their own knowledge
©
teacher effort is aimed at developing students’
competencies and talents
© education is a personal transaction among
students and between teachers and students as they work together
©
all of the above can only take place within a
cooperative context
©
teaching is assumed to be a complex application
of theory and research
©
that requires considerable teacher training and
continuous refinement of skills and procedures
The differences between the old
paradign and the new paradigm is like the table below
Factor
|
Old paradigm of teaching
|
New paradigm of teaching
|
Knowledge
|
Transferred from faculty to
students
|
Jointly constructed by students
and faculty
|
Students
|
Passive vessel to be filled by
faculty’s knowledge
|
Active constructor, discoverer,
transformer of own knowledge
|
Faculty purpose
|
Classify and sort students
|
Develop students’ competencies
and talents
|
Relationships
|
Impersonal relationships among
students and between faculty and students
|
Personal transactions among
students and between faculty and students
|
Context
|
Competitive/individualistic
|
Cooperative learning in
classroom and cooperative teams among faculty
|
Assumption
|
Any expert can teach
|
Teaching is complex and
requires considerable training
|
With the differences, we can know
that the new paradigm is more effective that the old paradigm, so what do you
think again. Let's to use the new paradigm.....
References :
