The Aspect of Mathematics

            From time to time since you born, you have many experiences about the aspect of Mathematics. From the daily life to the academic life in the university you can identify many aspect of Mathematics. But sistematically maybe inference about the different of the aspect of Mathematics for example the application of Mathematics, the concept of Mathematics. So probably it is better for us to think first about the concept of Mathematics than to implement. In our daily life, there are so many question that we could not answer it directly, for example :

1.      Since when you are able to calculate?

2.      Since when you understand about the concept of numbers? Since when you understand about the concept of one?or two?

None of you who are remember since when and where you start to understand the numbers.

The others question are when did you start to understand about the distance? Did it when you are in the second grade of school?

The concept of the distance and numbers is Mathematics concept. If you now understand about something but you don’t remember when you start to understand, that what we called Intuition.

There are so many concept that we can’t answer since when we understand about it, for example : sad, love, missing somebody, etc. we understanding it using Intuition. The amount of the concept that we can’t explain it and when we start to understand it is unlimited. Intuition is very important. So don’t we ignore the intuition.

Intuition is not dominated only by the children but the older people also using intuition to do something. Example : why are you wake  up in the morning?

In order to empower your intuition, you need to have many experiences like experiences about mathematics, personalize, or daily life at house.

            Inside the definitionof Mathematics concept (example : limit) there are elements of intuition. Most of your life dominated by intuition. Intuition imerge from experiences. Learning is not as obligation, but as a need. You will be a successfull student if you understand the psicology of learning.

            In the university you will find the different concept about Mathematics. You  are using different approach to understand axiomatic Mathematics. You need to read and understand the definition first and then the theorema and problem example.

Learn Mathematics by Playing Games

                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.

My Effort to Improve My English Abilities
English is very important language, because it is an international language. English is life, so from the characteristics that English is life, I need to learn English continually. I have various method and activity to learn English. There are four factors which influence my effort to learn English.
The first factor is motivation. Motivation is very important, after I hear some story from Mr.Marsigit and Mr.Ilham it motivated me to learn English continually, because I want to be like them, study abroad. In the educational world, there is very competitive, so I think that I have to had more skill than the others. And if I have English skill, maybe I will get point plus, so I can win from the others in the competition to get job as teacher or lecturere.
The facilitator that support me on learning English is my lecturer (Mr.Marsigit and Mr.Ilham) on UNY. I can learn English with the supporting facilitation, for example there are recording to record my convertation wih native speaker from England, flashdisk to save all my data about English, and maybe laptop for watching movie in English and listening to what the actors say to sharp my English skill.
Learning English also can be from various resources, the resources can be coming from the internet, I can download many kind of English test especially vocabulary test. So I can improve my English ability. If there is no internet, I can learn by reading book in library or from magazine or newspaper, then I cut the article in English, I stamp it on my notebook and I translate it to Indonesian and I write it down so I can easily remember the words that I wrote on my notebook.
Learning English also pass through smartphone, I can download dictionary applications on my smartphone so I can easily searching the word that I don't understand without opened the dictionary book, which is so thick. The other way to improve my English ability are I can joined English course and also practice to speak English with my friend. So my English ability can be better than before.