The Story Puzzle of Sliced ​​Bread

At that time in a bakery there is a mother with a son. The owner of the bakery seems already quite familiar with this customer. When the mother is busy talking about his order to the owner of the store, the boy kept staring at a big carrot cake with a mature crust and a layer of vanilla in it. Apparently the store owner memperhatika the child. Then he filed a tempting offer.

"I will give the tart for you if you can solve this little puzzle," said the shopkeeper. "How can so I can cut this round tart into 16 pieces are exactly the same only with four slices straight?"

The child immediately said, "How many ways Mr. want?"

"Just one way. But remember, all the slices must pass vanilinya layer. "

"Oh ... yes, you were right. Indeed, there's only one kind of way. With two slices perpendicular, Mr. will acquire four pieces. Then lined up all four pieces before and iris once again be straight in the middle row. Well, Mr.'ve got eight pieces. Furthermore, these eight pieces lined up again. The fourth straight slices will produce 16 pieces of the same. How ... right? "

"Exactly, Jake. Here, tart it now belongs to you all. "

The mother insisted to pay the tart, but the shop owner refused.

The boy and his mother thanked the owner of the shop and hurried home (of course, along with the tart).

Read more at:

Puzzle adventure Dr. Ecco, written by Dennis Shasha, published in Jakarta by grants in 1995.

Just Math: Math for All

Bismillah ...

Just Math?

Is this expression impressed underestimate mathematic? Definitely no, it’s not! This is an expression of hope that many people do not feel horrified by mathematics. The phrase "Just Math" is also intended to demonstrate that a variety of information, stories, and whatever is in my writings are essentially turns on only about mathematics, whether related to basic mathematics, logic, or whatever they are called. Essentially "Just Mathematics", but if from reading these writings gain other than math lessons, then that is a bonus!

Starting from the field of mine who is a college math, I want everyone from all fields of life to know various information about mathematics. Quite a lot of information about this math simple but very interesting, impressive and unexpected, in addition to interest on the math is daunting, complicated, tedious, and so on. Through the medium of this simple, I will refer to that share some knowledge and information I have about mathematics. Science and this information comes from various sources: my notes during the education of elementary, junior high school, to college, including my notes when ever the race and the like, or from what I've heard and I've read. Most reference books listed as the source of my writings is my favorite books. I can confirm that these books have a good enough quality to be enjoyed by fans of mathematics, but also did not rule out the possibility of these books can be easily understood by everyone. Therefore, with my share through my writings is later expected to be more interested in reading this kind of books, and also can be used as a source of information to support other references related. At least my writings could be read your leisure time.

I say thank you to all the viewers who took time to visit and read, may be able to feel the benefit of these writings. Aameen .. I would like to apologize profusely when writing in this media is nothing that makes you less pleasing. I begged the correction of viewers over my writings, if there is something wrong or inaccurate. Please criticism and constructive suggestions to be submitted to me. Thanks for all your attention and cooperation.

Hope it is useful…

As Mathematics Education Student, We are Proud !

Friday, May 13th, 2011, I and my friend got our English course. In our English course, Mr. Marsigit, our lecturer, told about anything. In that meeting, he said that in his point of view, we should be very happy as mathematics education student. Why?

Then, he told us the reason : We should be very happy as mathematics education student because only few of young people who concerning to the mathematics education. However, as mathematics education student, we need to empower ourself. We should not to be hesitate and disappointed. We had to wake up and make sure that we’re in the right track. We should support our competence. We could use many facilities thats’s available to support our competence. To gain our goal as the mathematics teacher, we also need support from our family. And the most important’s getting understand. We should understand ourselves and everythings around us. If we didn’t understand, we could be blind and empty. Blind meaned there’s no destination. To know our life destination, we had to know the inside of ourselves and the world outside. Then, we could find the destination of our life. Whereas, empty’s, we had not anything in our life. So, we had to fill it by hard struggling in our life. Then, we would not get blind and empty.

Mr. Marsigit said that life could be defined as a character. For example, “What are you?” he asked. “You are a character who want to transform yourself to a certain characteristic. You are aware of characteristic, again and again.”
Continuing his explanation, Mr. Marsigit said, “As the adult student, you must not depend on your lecturer. Doing anything by understanding and self-awareness, not by other influence and other compulsion. You can do some exercises by your self as the adding supplement to support your goal beside the lecturer teaching. Because there are various source in learning English. Even, you can benefitted the internet facilitate that provide youtube as the video provider. From youtube, we can download many learning material video that is usefull for you.”

We, as the candidate of mathematics teacher should be proud. We had an important role to break the old paradigm about the old way on teaching. We had to renew our paradigm. Because the most difficult thing’s to show the different function of traditonal teacher and modern teacher. As the modern teacher, we had to know the different thingking of younger student and the adult student. It could be explained from the nature of mathematics iceberg. It showed some grade of mathematics learning types. They’re formal mathematics for adult student (learning postulates), model, scheme, and physics for younger student.

Teacher should prepare something to teach. The preparation of teacher could be Lesson Plan (RPP) and Student Work Sheet (LKS). Teacher also need to know the role of interaction. Interaction could make transformation from subjective knowledge of mathematics to objective knowledge of mathematics. This meaned that teacher should guarantee to improve their knowledge about mathematics from the subjective mathematics to objective one.

That’s all Mr. Marsigit explanation about mathematics education generally.

In Deep Thinking About Mathematics Education

In my English course meeting last Friday, April 8th, 2011, Mr. Marsigit, my English lecturer, told us (me and my classmates) about “In Deep Thinking About Mathematics Education”. He said that, “All of you should be very happy in studying mathematics. Why? Because you can develope your mathematics ability by making the best anything that is available in this faculty, Mathematics and Natural Sciences Faculty, especially is Mathematics Education Study Program which is your study program. Studying in this program, you get more lesson subjects about mathematics, and it is continuously until higher semester. “

Mr. Marsigit continued his explanation by making us understand about the student position in Mathematics Education Department. He asked us about the difference of study program in the Mathematics Education Department. They’re Mathematics Study Program and Mathematics Education Study Program. Then he continued. “Mathematics Study Program and Mathematics Education Study Program are two different study program. Firstly, the lesson. In Mathematics Education Study Program, you will be teached how to teached mathematics well, whereas in Mathematics Study Program you will study mathematics subject which is very complex, so you can hold the complex mathematics. Secondly, the people of the Mathematics Study Program and Mathematics Education Study Program have different background. As Mathematics Education Study Program person, you will face younger student, which is pre-elementary, kindergarten, primary school, junior high school, senior high school, or university student. How it can be a problem? In learning mathematics, older people and younger people are different. Psychologically, they are different. For example in facing problem as like below :

•A plastic ball radius is 7 centimetres. The ball being broken after it’s falled from certain place (height 15 metres). Find the volume of the ball!
•Given a teak from Blora (Central Java), colorful painted, has radius 20 centimetres. Find the area of the teak!

From two problems above, we can test younger people and older people to answer. Most of the younger people will find the solution of those problems by material thinking. Whereas, the older people will do that by abstract thinking.According to the older people, mathematics is only a thinking object, not factual/material object. Clearly, this is explained as below :

•Given two numbers 4 and 7. 4 is written in bigger size than the 7 number. Then, which is the bigger number?

To solve this problem, the younger people will think materially. They will answer that 4 is bigger than 7, because it looks like that. Whereas, the older people will think abstractly. They will answer that 7 is bigger than 4, because of the value.
From the explanation above, we can conclude that in abstractional thinking, people just take certain properties which is interesting for them, and they want to study more about it. They are also idealize, think that all properties in mathematics are perfect. There is not ‘agak’ (Indonesian language) word in mathematics.
Because of the different thinking ability of younger and older people, mathemathics divided in three, they are University Mathematics, School Mathematics, and Pure Mathematics.

a.University Mathematics, contains proving problem, axiom/postulate, and other.
b.School Mathematics, contains concret and factual problem.
Ebutt and Straker (1995) define School Matemathics as follows:
1)Mathematics is a search for pattern and relationship, enlarge the student to
seacrh pattern and relationship.
2)Mathematics is problem solving activity.
3)Mathematics is investigation activity.
4)Mathematics is a mean of communcation,
c.Pure Mathematics is studied by pure mathematicians.

That’s all about three kinds of mathematics level study based on thinking ability”.
Ending the course, Mr. Marsigit explained one more lesson. That’s the characteristic of the student who learned mathematics as follow :
•The student will learn effectively if the student have a good motivation and a good perception.
•The student learn mathematics individually, the nature of individual creature.
•The student learn mathematics in collaboration with others, the nature of social creature.
•The student learn mathematics in context.