To improve our ability in mathematics
education, we need to learn a variety of mathematical learning systems from
different countries. That way we will have a broad view of mathematics education
and we can apply the appropriate learning system when we become a teacher someday.
One way is watching a video about the lesson
study in Japan. This video is about mathematics learning in grade 3 elementary
schools in Japan about the multiplication algorithm.
The
video shows how
to solve a mathematics problem on
the multiplication of numbers.
First time, the teacher writes a problem
on the blackboard and explained the problem to the students. Students are
left to guess the intent of
the question and let them started to think.
Then, the teacher gives an illustration by using a paper containing the image
of circle in three rows,
and each row contains
23 circles. They
were asked to count the number of
the existing circle. Then the teacher provided the illustrations for
each student. Students are required
to solve these
problems in their own way and they were
given a few minutes to complete.
Teachers not only stay waiting their work,
but also he went
around the classroom to check and help
them.
After a few minutes, the
teacher provides the opportunity for students to present their
work. One by one they put forward
their work. While the students' talk, the
teacher wrote their work on the board so that all
students in the classroom can be
more clearly what is their
friends talk about.
They
do many ways
in finding the answers to multiplication 23 to 3.
The first way, they were devides
the first line into two parts, the
20 circles and 3
circles. Then multiply
each part by 3, so
20 times 3,
and 3 times 3.
Then the result of
the multiplication are summed to get 60 +9
= 69.
The
second is to likens
the number
2 at
23 as
a 10-yen
coin,
so
2
multiplied by
3
and we get the
6,
and 3
multiplied by
3
equal to 9.
Then,
because two
are assumed as 10-yen
coin,
so
6
is multiplied by
10
and the result
is 60.
Finally,
add
60
with
9 and
get
69
as the results.
Most of students doing their works
by using the first approach. They assess the first approach is more effective
in multiplying 23 times 3. But some students are arguing with each other even
though they are the same answers. There is also another way to approach the
answer but instead to explain the confusion.
Some of students use the way that
has been given by a teacher at a previous meeting. So, there are no a lot of
difficulties. The arguments they made were grounded on the concept that they
have received at previous meetings.
After several minutes of discussion,
and some students have submitted their work. Blackboard was already full with
the results of their work. Finally, the teacher gives the conclusions of the
problems that have been granted. The teacher explains the correct and effective
steps and appropriate solutions to these problems.
From
the video,
it can
be concluded
that the
learning
of mathematics
at
grade
3
elementary schools in
Japan
is use a
system of learning
with
problem-solving
methods.
There
are many
positive
and negative
values
that we can take
from
this
video. The positive values that we can take from
this video are teachers provide opportunities for students to find solutions of
by their own way , train the thinking skills of each student, train speech ability
and express their statement to the other student, train the confidence of each
student, and student become more active in the classroom. While the negative
side of this footage is the teacher does not allow students to explain their
answers in front of the class. So they
just talk not do something. Sometimes the teacher is also confusion with their
answers, so that often cut their conversation. Maybe in a way like it will save
time and learning process do not take a long time.
Although
done
in that way,
the learning system
was considered
appropriate
in the learning
of mathematics
in
primary schools.
Because the teacher was
actively involve
students
in the learning
process.
The teacher
is seen as a
facilitator
who
is ready
to facilitate
students
in learning.
The learning process
is no longer
centered
on teachers,
but
student-centered.
Students
must be
active
in the learning process.
Students are
expected to
solve
math
problems
in their own way
without
any
compulsion
to use
a
particular method.
There is no
compulsion in
learning,
so that
they
can
construct
their
own
knowledge
in
their
own
way.
In
addition students
also need
to be
given a challenging
problem,
but
not too
difficult,
so that
students
have
a strong will to
solve them.
According
Hermenberger
&
Reichel
(in
Posamentier,
1996:201):
“Students must have various opportunities to
get down to easier problems themselves
so that they get a chance to think about them and to develop solutions themselves (maybe with some minor hints).”
If
we
do not
provide
a big
opportunity for
students, it
would mean that
we are
still
of the view
centered
teachers.
If so
the atmosphere of
the class will be
dominated by
teachers and
students do not
understand the
lesson.
It is
reminded by
Umran
Inan
(in
Plooster,
1997:1)
says:
"The worst thing that can happen is to go
along through a full hour without any
questions. That might mean two things: a very remote possibility that you are extremely clear, but more often
than not that you are not clear
at all."
Sources:
Plooster,
N. 1997. Teaching Tips for TAs: 10 Suggestions for Teaching Problem Solving.
California: TA Development Program, University of California.
Posamentier,
A. S. & Stepelman, J. 1996. Teaching Secondary School Mathematics,
techniques & enrichment units. New Jersey: Prentice-Hall, Inc.
