Mathematics
is for all people whether there are younger student, older student, very old
people, or very young baby.
When Mr.
Marsigit visited his grand daughter at Jakarta, he had a chance to make
experiment with his grand daughter (named Queen). He try to understand his
grand daughter and differentiate the concept of short and long time.
He has
a battery (flashlight) with three modes. If we click the battery one click the
battery will iluminate continually and then double click it will iluminate blinkingly,
but if we push it for a long time compared with just one click, the battery
will turn off. Then he gives example to his grand daughter. For the first
experiment his grand daughter could not turn off the battery. Then he gives her
an example, in the second time his grand daughter was able to do, but then she
forgot and could not do that again. So Mr. Marsigit found that his grand
daughter was learning about the concept
of short and long time. It is very difficult for his young grand daughter, she
bored and want to change activity. From this activity he can learn that very
young baby learn mathematics by doing experiment and following the adult
activity,and copiing. This is not exactly the point that can be differentiate
absolutely whether it is mathematical concept or not.
When you
are at junior or senior high school, you learn about the relationship between
the distance and the speed, and alo the time. Example: Mr. Marsigit went to
Jakarta at 9 P.M and arrived at about 9 A.M, so it took about 12 hours. We can
conclude that the longer the time, the distance will be farther. That is the relationship
between time and distance. So from the experience, Mr. Marsigit’s grand
daughter was learning about the concept of time. How long time that is needed
to turn off the battery. So by having experience it will imerge intuition. That
is the importance of intuition.
Mathematics
need to be learned for all people. What is the basic mathematics that need to
le learned by younger student? The answer are the concept of numbers,
mathematics basic operation (like addition, substraction), any kind of
geometrical shape. How to learn numbers for young student? By make and sing a
song about numbers, by look at the picture and playing games.
Mr.
Ilham said that according to the deffiniton of intuition, we agree that student
have to learn from what they already know and it is impossible if we learn
something that is not have any connection with our life. It is good idea to
search what is student really know about something, what they already have and
make the connection between that with what they will learn, and related to what
very young student could learn in that ages.
It is
good to learn Mathematics with game, for example traditional games. From playing
traditional games we could learn a lot of thing, we can learn how to count, if
we play with friends and we could not remember what is the number after nine
maybe, so our friends will help us, and then we could remember again, the
number after nine is ten. The game that teach us how to count for example is
marbles game. We can start to add one by one the marbles that we get if we can defeated
our friends. So by intuition, eventhough we not yet learn about counting at
school, we have learn about numbers and how to count by playing games.
They could
also learn about measurement by using a kind of game, for example Patok Lele,
traditional games in Javanese. Who could hit the stick farther they will be the
winner. How could they know the winner? They have to measure informally using
the stick. The more stick so the distance is farther and they will be the
winner. So they could learn about measurement eventhough they not yet learn
that at school.
Actually
what is measurement? Measurement as a connection between our real world with
the world of numbers. For example if we have real world thing like a pen, and
we have a set of numbers, we can connect the numbers and the pen with measurement.
We can measure the length or the width of a pen with the numbers, like 7 cm, or
else. But for the first, in the measurement activity, they do not yet use
formal scale. They use what they have around them. Example they measure something
using pen, span, etc.
In Netherland
there is a game that never be found in Indonesia. The name of the game is
Rummikub.
There is about 40 floortile with 4 different colours and
with numbers from 1 until 13. The game is very simple. It could be played by
minimum 2 people and maximum 4 people.
Every player at the beginning, they have 14 tiles, but the
others will not know what kind of numbers and colours that they have. The remainder of the tiles will be “pool”. Then the person
who could have tiles that could sum up to thirty could go first. If you the one
who has 10,11,and 9 tiles could go first, but it has to in the same colours. So
whoever has tiles with the sum thirty could go first, and the player next to
him/her could go next.
But if
you don’t learn formally in the school, how could you know that thesum of the
tiles are thirty, maybe the player have to explain that 10+11+9 is thirty by
adding one by one. So from this game they could learn additional.
The next step is you have to make an arrangement at least in
three tiles which have numbers in a series like 3,4,5. Not only to learn about
numbers in a series, you can also learn about shape recognition. You choose 3
tiles which have same colours or same numbers, example 4,4,4 and you can bring
the tiles to the table. So the one who finished first is the winner.
The keyword
about contextual learning are related to and ready for. So whatever you learn,
it has the aspect of relation and ready. Why should be related to? In order
that you are ready.
Let’s continue to the mathematics terminology in the junior
and senior high school
8=8 eight
is equal to eight
8=4+4 eight
is equal to four plus four
This is example of linear equation : 2x+1=0
2 is coefficient, x is variable, and 1 is constanta
In each equation, the problem is to find the value of
variable.
Procedure : 2x+1=0
both sides is substracted by 1, then we get
2x+1-1=0-1,
we get
2x
= -1, both sides is divided by 2, then we get
(2x)/2
=-1/2
X=
-1/2
So the solution set is {x|x=-1/2}
Find the formula of finding the roots of ax2+bx+c=0
We as the person who has already learn about mathematics can
measure the width of the classroom by intuition, but if we don’t learn intuition
of mathematics we can’t do that.
We have many geometrical object
around us. For example tv, window, door, etc. So we can learn mathematics from
resources that coming from our surrounding of our life. That is contextual of
learn, related to and ready for. So that is very important for teacher to dig
up potential that came from our surrounding to learn mathematics. Including our
habit, product of society and the culture. We have very popular and important
resources to learn mathematics in the form of artefak in Prambanan and
Borobudur temple. So if you go to the temple make use your time to learn
mathematics in the temple with artefak. That is the responsibility to develop
learning resources and also teaching resources in order that the student can
learn mathematics naturally based on the characteristic of the student nd it’s
society. In the present time, we have many kind of technological product to
develop teaching learning process. As a candidate of teacher, we can start to
identify what kind of technology that capable to support our mathematics
teaching, including the computer, software, flash, etc. so learning can be from
surrounding to technology.
