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.

Challenging questions about Simple assessment

This question can be given to students who are learning decimal units to provide basic calculations and provide an assessment of a very large number. A simple question that challenges to stimulate simple assessment one of which is as follows.

I want to count to one million.1, 2, 3, 4, 5, ...How long does it take?

Of course, this is an open-ended question. The answer could be a variety of conditions. It could be when spell is interspersed stop, or can also be in spell the numbers constantly. In the case of simple assessment, it can be said that the number takes about one second to be spelled, and if they do not stop counting until finished it will take about one million seconds.

As a sequel, in terms of studying the decimal unit, then be directed to the state of one million seconds into a simpler form, for example by converting into units of minutes, hours, or days. These issues provide a good opportunity to emphasize the ability of the assessment.

1,000,000 seconds to change to the day we need to calculate:

For a quick calculation, round 24 to 25, so that:

Because more than 10, then a good estimate is 11 days. The real answer is approximately 11 ½ days.

Read more at:

Teaching Mathematics Third Edition: a resource book props, activities, and strategies, written by Max A. Sobel and Evan M. Maletsky, published in Jakarta by grants in 2004.

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…

Developing Mathematics Teaching Using Progressive Teaching

Friday, May 19th 2011, I got my English course. In that day, Mr. Marsigit, my lecturer, talked about “Developing Mathematics Teaching Using Progressive Teaching”. He showed the differences of traditional and progressive teaching. In showing the differences of that two methods of teaching, Mr. Marsigit difference them based on four main levels. They are spiritual level, normative level, formal level, and material level.

Mr. Marsigit explained that, “Belong to the spiritual level are spiritual, ways of life, good-bad, and functional system. Based on this level, traditional teacher gives the education as an obligation. Also the student. They study just because of an obligation, not because of their awareness. Whereas, in progressive teaching, they said that education is a need for them. So, they can be more motivated in studying, because of their awareness.”

In normative level, there’re law, decree, education system (paradigm of education and theories of education), and nature of mathematics. Based on education system, the traditional teaching, presented teaching to give, only transfering knowledge to the student. The teacher directed and controlled the student. The student just roled as empty vessel. National Examination being the final goal of this traditional teaching. Then Mr. Marsigit continued his explanation to the progressive teaching, “In progressive teaching, the paradigm of education is to construct the student’s knowledge, by themselves. So, there is a reform from traditional teaching to progressive teaching with the new paradigm. In this teaching method, the student is similar with a seed that grow and blossom out. The teacher just facilitate the student as like a farmer. The final goal of progressive teaching is classroom based assessment which is much different from national examination”. Mr. Marsigit also said that pure mathematics being the nature of mathematics in traditional teaching. Otherwise, the progressive teaching refused pure mathematics because younger learner being the learning object of this method, so it would not be pure mathematics, but school mathematics. School Mathematics, containing concret and factual problem. Ebutt and Straker (1995) defined School Matemathics as follow:

1)Mathematics is a search for pattern and relationship, enlarge the student to search pattern and relationship.
2)Mathematics is problem solving activity.
3)Mathematics is investigation activity.
4)Mathematics is a mean of communication.

That’s meaned that the nature of student learning mathematics’s motivation, collaboration, unique, and contextual. It implicated to the changing of subjective student to the objective student by input knowledge they had got, then they published it by test or other, so they would get the justification from their teacher. It made a new knowledge for them. Then, finally, they would be an objective student. It’s appropriate to the Paul Ernest opinion.

So, it could be said, that in traditional teaching the different’s only the students, because the facilites, objective, time, and result were just same with the teacher’s thinking. But, in progressive teaching, all different. Different students, different facilities, different objective, different time, and different result.

Formal level presented curriculum, syllaby, and the book as the handout of the students in learning. In Indonesia, we had known curriculum of 1975, 1980, and so on as the traditional teaching curriculum. That curriculum just orienting on content and the goal of learning. KTSP (Kurikulum Tingkat Satuan Pendidikan), one of Indonesia curriculum that had been semi-progressive, actually could reform traditional curriculum to a progresive curriculum. In progressive curriculum, students’re expected to be active learner by student competence oriented.

Class, teaching content, book, and building could be categorized as material level. In the class, expository method as the single learning method applied in the traditional teaching, because according the traditional teaching, that’s the best way for teaching. In this method, the teacher just doing the same activity repeteadly. Explaining, giving exmple, giving problem, and giving task. Text book oriented applied by the teacher. Whereas, according the progressive teaching, there’s no the best way to educate. So, just used the various method which’s contextual to the student and mathematics. It meaned teacher should be more creative to develop their knowledge and teaching method, not only based on the text book.

That’s all the differences between traditional and progressive teaching. By knowing that, we’re expected to develop mathematics teaching by using the progressive teaching method, that’s better than the tradtional one.

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.

My Impressing English Course

It was Friday, February 18th, 2011. At 1 o’clock, I had arrived in my campus, Yogyakarta State University. As soon as possible, I walked to my classroom, it was 209 room, it’s in the 2nd floor of my campus building. But, unfortunately, the room was used. So, my class should be moved to another room. After asking the Academic Staff about my classroom, I went to 107 room. On my way to the room, I met my friends, they are my classmates. Actually, they didn’t know about the changing room. Moreover, they thought that our English lecturer would not come. So, they conclude that the English lecture on that time was canceled. But, finally, we decided to wait our English lecturer in the place where I met my friends.

After waiting for a while, Mr. Marsigit, our English lecturer, came. He was leading me and my friends went to the room. Entering the room, I and my friends took a sit immediately. We had sat neatly. We had ready for our first English lecture in University. But, suddenly, Mr. Marsigit ordered us to sit around him. It’s unusual, but it’s good enough. I thought that it could make me more focus to the matters that would be explained by Mr. Marsigit. I and my friends did that first Mr. Marsigit’s instruction quickly. In a short time, we had ready to listen Mr. Marsigit introduction. He introduced himself to us. In his introduction, he often shared jokes to us. It made us laugh. Even, one of my friends laugh until her face getting red. I thought that Mr. Marsigit was a humorous person. That was supported by one of my friends words. She said, it’s Gombong people characteristic, that they’re humorous. Gombong’s a city in Central Java where Mr. Marsigit was from. After his last word of his introduction, he asked us (me and my friends) whether we had some questions about his introduction. I thought, it was the second instruction for me and my friends to speak up. But, no responses he got. For a while, I and my friends just keep silent. A moment later, one of my friends asked him about the lecture contract. Mr. Marsigit answered the question. Knowing, there’re no more question from us, he started to tell us everything about motivation that could inspiring us. Through his story that he told with smile occasionally, he gave us many inspiration and motivation. We’re impressed to him. It showed by our attention to his explanation. I looked that some of my friends faces showed that they were impressed to Mr. Marsigit when he told us about his experience in some countries, like Japan. Beside that, he told us about three important points for us. They’re Perception, Attitude, and Behaviour. He said that Perception of a person to a something could influence the person’s Attitude. Continuous Attitude could build Behaviour. So, according to me, based on the Mr. Marsigit explanation, positive Perception would grow positive Attitude. Positive Attitude would build positive Behaviour. This positive Behaviour would help us live in this life.

That’s all my story about my impressing English course. Started by room problem and lecture cancelling isue. Continued by attention and laugh. Ended by inspiration and motivation. It was impressing!