The Nature of Mathematics Thingking

Let's check your knowledge! Okay, I want you to choose the correct answer from my question.
4 x 6 =  a.6+6+6+6 or b. 4+4+4+4+4+4 ???
If you choose b that's the wrong answer, yup the correct answer is a. Why? Okay, let's read the question slowly. 'four times six' it's mean we have six plus six until four times. You get it?  I hope yes. :)

In our mind we have 2 parts, there are rationality or abstracted, and idealized or experience thingking. The abstracted part to think only selected characteristic of object. It is contain about the mathematics object, and abstract object, for example number, field, cube, plus, etc. The idealized part assuming to be perfect or real characteristic. It is contain about the daily experience, value, color, price, etc. So, what happen in our mind? The information will be process in memory, then we are understand about that, we apply that, make a symbolize then we evaluate that. That process make us have willing, knowledge, attitude, skill and experience.

Volcano of Mathematics

The concrete mathematics is the object in our reality for example, there are two birds in the air. That's just for a kindergarden school. The model concrete of mathematics is about operation sign, for example there are two apples plus three apples equals five apples. This level for Primary School and Junior High School. The formal model of mathematics is a symbol for the operation, for example use point or x or y. This level use in Senior High School. And finally the formal mathematics is about the object of mathematics for example we use the number 3+2=5, a cube, why it's call cube, small, big. What is the definition of small? You cannot definite that, but you know that. So, in our level we must use our intuitive and our knowledge.

Ambition and Strunggle Make Our Dreams Come True

This motivation come from my English lecture, Prof. Dr. Marsigit, M.A.  I think he is an amazing person, because he can realize his dream to get his master in England. That is not easy, need more sacrificed. Start from Junior High School, he prefers to like Mathematics than another lesson. and he just had a little talent in art, language, and society. When first class in Senior High School, he got rank 1 althought the situatin in his era was difficult to acess internet and got more information. This good score gave the big motivation to him-self. he lived in Kulon Progo with his 'pakdhe' and grandpa. He wanted to able speak English in fluent, so he decided to go to shopping center near Taman Pintar by bike.There were a lot of second hand books, and thats very cheap. He liked to read Rainbow mini magz and read repeatdetly the interesting secyion. So, he able to speak English because he accustomed to learn it.

In the end of Senior High School, he got  rank 2 and registered to be student in Mathematics Education, FKIE, IKIP Yogyakarta. after graduated he became a lecture and wanted to go to the England to get his master. but, the minimal score of  TOEFL is 500 . When the fisrt test he got 449, in the second his score is down, and finally in the third test he got 550. Wow, his big ambition and struggle make the dream realize. So, in 1996 he go to England to get his master. he finished his thesis in 1 year, but he must waiting his friends to come back in Indonesia. Then he decided to get more experience in half of a year. he tried to go to bank alone. when he arrived the teller asked him "What note do you want?". He was upset about that, he thought what the meaning about note. The teller asked again "Which one of the money that you want to get?". So, he know the meaning about note.

In the other time, when he jogging he heard "wa e ple" that's mean "water please". In the train he got another word "oek" and that's mean all rigt. The accent in he England is very different. because waiting his friends, he got more experience. Since 2000 until now he ever to go aboard in Australian, England, Cambodia, Thailand, and Japan. So, we can learn from this story that we must have a strong foundation. then identify what the mathematics and do research on mathematics, because you can be able anything if you accustom with that.