THE POWER OF CATEGORY AND NETWORKING

Honestly, do you realize that Mathematics is general? It’s has very large definition and many interpretations. According to Immanuel Kant (1771), there are 4 thinks in our mind:
1. QL (Qualitative)
2. QT (Quantitative)
3. CT (Category)
4. RL (Relationship)
OK! Let’s learn those (4 thinks) relation to Mathematics itself. First is Qualitative (QL). It means that Mathematics is not only formed by numbers and formulas, but also can be stated by sentences (for example story problem in Mathematics examination). Children must read the story before to understand the problem, and then they can formulate or state the story problem into ‘mathematical sentences’ which is a Quantitative (QT) form. From this formula, they can analyze and solve the problem. Not all of that information used. We must select which is important and which is unimportant for us to solve that problem. So, we must categorize them. After that, we can find the relations of them and get the conclusion because as Mr. Marsigit said that what we say or what we think or what we see can’t represent everything.
Sometimes, children feel difficult in solve Mathematics problem. It happens because the abstract character of Mathematics itself. We, as a Mathematics teacher wannabe should motivate our children to love Mathematics and develop their happiness in studying.
According to Hudoyo (1988:3), learn Mathematics is a high mental activity then teacher should have competences to explain Mathematics well so that students understand the abstract Mathematics concepts. Hudoyo (1988:4) said that Mathematics learning process should did continuously. We, as a teacher should give the previous materials before the students learn the next materials because the materials are related each others, so that they can learn Mathematics happily.
According to Katagiri, there are three aspects in Student Mathematical Thinking in the Framework of the Nature of School Mathematics, they are:
1. Mathematics Attitudes.
2. Mathematics Methods.
3. Mathematics Contents.
Ebutt and Straker (1995) also explained about the nature of School Mathematics. Teacher shouldn’t use Mathematics axioms definitions but school Mathematics definitions. There are Mathematics realities:
a. Mathematics as an identify pattern and relation activity.
Teacher should give opportunity for their students to discover and investigate the pattern in Mathematics problem to find its relation of each others. It also can stimulate the student to do their experiments and understand the materials then make the conclusion.
b. Mathematics is a creativity that need of imaginations, intuitions, and discovery.
By applying Mathematics school, we can support students to think different and explore their curiosity. It also can stimulate them to think critically, logically, consistently, systematically and appreciate people’s opinion.
c. Mathematics is a communication way between teacher and student so that they have the same perception abiut Mathematics itself, for example the characteristics, problem stories, concepts, etc (marsigitpsiko.blogspot.com)
Now we’ll talk about Phenomenology and its Epoche. According to Edmund Husserl (1859 – 1938), phenomenology shows everything which is visible to us in our consciousness without put in some our thinking or our presupposition (rumahmakalah.wordpress.com). So, phenomenology is natural and essential. Husserl use 2 steps to get phenomenology essential, they are epoche method and eidetich vision. Epoche is a Greek language that means “postpone” the agreement or “self empty from any particular belief”. Epoche also means “bracketing” to any information without think its justice.
Epoche contains about everything else which is not too important or unused thing to think about something. For example, when we learn about formula of cube volume and its concepts, we just think about the problem and it’s solving. We only need to analyze how to get the volume formula and understand its concepts. It’s not too important for us to know the way to make the cube, from what materials of the cube made, its cost, what is the color, and etc. Automatically we knew about them and they are not really influence to the volume formula of course. So, we can say that in this case, we just had categorized the one of psychology phenomena. We can separate which is better for us, which is more important and useful to think, which is we must save in ‘Epoch Home’, etc.
There are two methods of thinking, they are Top down and bottom up. The top down method is one of the thinking methods which are use pattern from up, from general thing, some theories or references, and then we must classify or analyze it to be more simple and particular/concrete. We can get the general things from books, journal, report, research or etc.
The second method is Bottom up. It’s the opposite one of the first method. We use an inductive approach. We usually submit some facts or valid samples and then we can conclude the problem.







:
marsigitpsiko.blogspot.com
rumahmakalah.wordpress.com

MY SMALL RESEARCH

MY SMALL RESEARCH

THE POWER OF SCHOOL MATHEMATICS AND CHARISMATIC MATHEMATICS TEACHER

Every I ask some children, “Do you love Mathematics?”, we can guess what will they say. Almost of them will say, “NO…!!!”.
Yeah! I think it’s funny but so ironic. Honestly, when I was young (in elementary school) I also didn’t love Mathematics. Even, I hate Mathematics. It happens because the Mathematics materials are too difficult for us to understand and just contain from numbers and also formulas. Our teacher not really friendly with us and sometimes she got angry.
For about 10 years later, now I can understand why many children (include my little cousins) didn’t love (even hate) Mathematics. It caused from the Mathematics teacher and the materials itself. Their teacher didn’t use school Mathematics method to teach their student. They use axioms and pure Mathematics. They just give their students many of numbers, formulas, and also oriented with the ‘costs’ or final answer. They didn’t explain the process how we got that formulas or how we analyze and solve the problem, etc. They didn’t tell their student what is the function of our effort in solve Mathematics problem, so that the students couldn’t enjoy learning mathematics.
Ebutt and Straker (1995) explained about the nature of School Mathematics. Teacher shouldn’t use Mathematics axioms definitions but school Mathematics definitions. There are Mathematics realities:
a. Mathematics as an identify pattern and relation activity.
Teacher should give opportunity for their students to discover and investigate the pattern in Mathematics problem to find its relation of each others. It also can stimulate the student to do their experiments and understand the materials then make the conclusion.
It didn’t apply in school, so the students still have perception that Mathematics is difficult.
b. Mathematics is a creativity that need of imaginations, intuitions, and discovery.
By applying Mathematics school, we can support students to think different and explore their curiosity. It also can stimulate them to think critically, logically, consistently, systematically and appreciate people’s opinion.
We can apply this by giving task to our student to make some FGD (Focus Group Discussion) and command them to present their discussion result in front of the class, so the student become active learner and enjoy the Mathematics learning process.
c. Mathematics is a communication way between teacher and student so that they have the same perception about Mathematics itself, for example the characteristics, problem stories, concepts, etc (marsigitpsiko.blogspot.com)
My junior high school teacher, Mrs. Diah is so inspiring for me because they can build her student spirit in learning Mathematics and make us love Mathematics. I was falling in love with Mathematics when I was in 3rd grade of junior high school. She taught me with love and patient. She is so charismatic. She is a friendly teacher so we were not afraid to ask her for consultation or suggestion.
Mrs. Diah had a charismatic teacher who had applied the Mathematics school. She didn’t only explain pure (axioms) Mathematic but also school Mathematics.



Sources:
marsigitpsiko.blogspot.com

How to Uncover The Psychology Phenomena

Bismillah...

OK! Now, we'll talk about Psychology, -of course it's about psychology in Mathematics-.
Last Tuesday, on November 10th 2009, Mr. Marsigit entered my class and commanded my friend, Aan, the 'chairman' of my class to lead a meeting. Mr. Marsigit allowed us to dicuss about everything, about the Math psycho lesson. He gave us 15 minutes for it. Then he left us.

Of course, first we got a 'traumatics' feeling because it became an unusual treatment for us. Finally, we just discuss about our advices in studying Math psycho.

A few minutes later, Mr. Marsigit was back to my class. He explained to us that a traumatics event can caused of something that can make us shocked because we didn't know the reasons, without any explanations. Traumatics events suddenly came and it had positive or negative effects.

In philosophy, we called this with 'accident' and 'authoritarian' in politics. The solving in traumatics problems is by make a good and healthy communication. We should tell the reasons before working or doing something together with our friends and also thinking before do our task. I think it's better than we just keep silent in front of them. It can make them shocked, confused or stress with this unusual phenomena. So, let's practice to be a good leader or teacher.

In teaching Mathematics to our student, we may not to make them afraid or traumatic withourselves, especially with Mathematics itself. We must use some techniques, cultural or structural. We can approximate them by asking how their family's condition, what they feelings are, and etc. Structurally, we can prepare the appercetion before teach them, the materials, the questions or tasks, and etc. As a good and also a professional teacher, of course we not only 'teach' them and do the 'transfer of knowledge' process, but also transfer the values of life, wether it can be some advices, suggestions, annecdotes, or stories.

We also should being a friendly teacher and make closer relationship to our student. Don't let them growing up while we don't know anything. They're our children..., and we are their mother (father). So, don't make them become an object, but ask them to become a subject in the lecture.

It's so beautiful and wonderful if we, the teacher and the students, can walk harmonous together and feel the fraternity. We do our job, teaching and learning by understanding each other, so that, there wont be a 'gap' between teacher and student. They'll enjoy the lesson and become falling in love with Mathematics, insyaAllah...

_ .:. thank you for reading .:. _iDa_941

Mathematical Thinking and Scientic Works

What is Mathematical thinking?

Mathematical thinking is the way to think mathematically. Honestly, mathematics objects are in our mind and its characteristics are absolute.

How to think mathematically?

According to Mr. Marsigit, we must do two steps. A first step is idealization. We must think and assume that everything is the ‘same’ and ‘perfect’. For example, there is a basket ball (a ball which is usually use in playing basketball). For the real, the ball is not full circle in its shape. If we see it clearly and sharply (especially using microscope), we’ll find the roughness of this ball. So, the ball becomes not really ball and soft.

Secondly, we must do an abstraction. It is means that we must take a part of all the characteristics of the object we learn about. For example, the ball has many characteristics, it’s heavy, it’s hard, its shape is circle, etc. but in thinking mathematically, we don’t need all of that characteristics. We just need to take a part of them (for example the volume). So, we just concern and think to the volume of the ball. The objects in mathematical thinking are always consistence, logic and systematic.

While, the characteristics of scientific works are impersonal (objective, based on the truth) and also consider on the ethical code (the most important thing is free from plagiarism –said Mr. Marsigit-).

A. _Desil

What is Desil?
Do U know what the meaning of desil?
Refers into Ronald E. Walpole's book, "Pengantar Statistika" (3rd edition), desil is value that divide a compound of observations results into ten parts to be the same. Desil symbolized with D1,D2, etc. Now, let's see the example! --> to be continued (in the next posting), I'm sorry all, I'm sorry Mr. Marsigit for posting lately.

Exercising

On Thursday, April 2^nd 2009, Mr. Marsigit commanded us to do some Mathematics exercises. There were 5 questions that we must do.

1. Explain how to prove that the square root of 2 is irrational number!
2. Explain how to show or to indicate that the sum angles of triangle are equals to 180^o!
3. Explain how you are able to get π (phi) !
4. Explain how you’re able to find out the are of region bounded by the graph of y = x² and y = x + 2 !
5. Explain how you’re able to determine to the intersection point between the circle x² + y² = 20 and y = x + 1 !

The answers:

1. We’ll approve that the square root of 2 is an irrational number. First, we must know that an irrational number is a number that the value cannot be expressed exactly as a fraction a/b, where a and b are integers and relatively prime.

Let’s assume that the square root of 2 is a rational number, so we can state the square root of 2 equals a per b. If x is a positive integer, x² is even if and only if x is even.

Then, we can say that the square root of 2 is equals a per b. Multiply each side with b and we get new equation, a equals to b times the square root of 2. Multiply each sides by itself and we get that a square is equals to b square.

From this equation we ensure that a square is even because a square is twice of integer. Because of a square is even, so it’s sure that a is also an even. And then, we may write a equals to 2 times c (where c is an integer) and substitute this (a equals to 2 times c) in to previous equation. We get that 4 times c square equals to 2 times b square. We can divide each side with 2 and get equation 2 times c square equals to b square.

From this last equation, we get another clue that b square is also even. Why do I say that? Because as we know that b square is equals to twice square of integer, so, b is an even, of course.

Finally, it’s clear for us that a is even and b is even. As we know that the square root of 2 is equals to a per b (where a and b is even, both of them are not relatively prime) so the square root of 2 is irrational number.

2. We can draw a triangle to prove that the sum of angles of triangle is equals 180 degree.

First, let’s assume that the point angles is A, B and C (where AC is the base). From point angle C we can make a parallel line with line AB, so there is a new angle (we call it angle D) which it’s side as big as angle A, because angle A and angle D is same side ( I mean “sehadap” –sorry, I don’t know sehadap in English-). There is an angle between angle D and angle C (we call it angle E), whish has same size with angle B because angle E and angle B is angled in the opposed. Then, it shows that angle C, angle D and angle E form a straight line which is the size is 180 degree. It’s mean that the sum of angle C plus angle D (it substituted by angle A) plus angle E (it substitude by angle B) equals to 180 degree. In the other words, the sum of angle A plus angle B plus angle C equals to 180 degree. It’s enough to prove that the sum angles of triangle is equals to 180 degree.

3. As we know that π’s (phi) value is 3.14. After I read some references, now I’ll tell the history of phi. The value of phi (π = 3.14 or 22/7) found by Egyptian people in 1650 BC. We can get the value of phi by make a circle; calculate the perimeter and the diameter. If we make any circle, we’ll get that the value of the comparison between the perimeter and the diameter is always constant: 3.14. So, if we divide the circle perimeter with its diameter it is equal to 3.14 (phi). That is why the circle perimeter formula is equal to diameter time phi.
4. First step is we must draw the graph of y equals x square. We try to substitute x with a number, for example x equals 1, so we’ll get the value of y equals one or we can write it down in a table of x and y (the substitution and the result then). We can substitute x or y with any numbers. So do the equation y equals to x plus 2. So, we are able to draw the graph and get the intercept point between those two graphs. Mathematically, the interception point can be find by assume that y (in the first equation) equals to y (in the second equation. We get a new equation, x square equals to x plus 2. By reducing each side with x plus 2, we’ll get that x square minus x minus 2 equals to zero. Then we get the values of x, x is equals negative1 or x equals 2.

The area of the region bounded by the graph of y equals to x square and y equals to x plus 2 is equals to integral of x plus 2 minus x square dx from x equals negative 1 to x equals 2 (we call the region with A). After we calculate, we get the result that A equals to four half area unit.

5. To determine the intersection point between y equals x plus 1 and x square plus y square equals twenty is, first, we change the equation form x square plus y square equals twenty into form y equals square root of twenty minus x square in bracket. Assume that y equal to y, so x plus one is equal to square root of twenty minus x square in bracket. Then, square each side and we’ll get that two x square plus two x minus nineteen equals zero. We can use abc pormula to find the values of first x and second x, and we get the first x equals minus one plus square root of thirty nine per two and second x is equal to minus one minus square root of thirty nine per two: both of them are the intercept points.

Mozaic Videos

On last Thursday, March 26^th 2009 Mr. Marsigit ask me and my friends watched some English videos. Honestly, these videos are very interesting. But I want to say before that frankly, I don’t know well about the content of these videos, because the pronunciation was very good, so I just understood a little (I’m sorry Mr. Marsigit). There were 6 videos and in this blog, I’ll write what the videos about.

The first video is about motivation and the title is Death Poets Society. It told about a teacher who gave some motivations to his students. He told to his student that we must try to find our own “voice”. It’s mean that we must try to become the real ourselves and not just follow what people do. We also have to look at thing in different point, different way. Don’t overcome a problem just with a solution, but we must open our mind to find the others solution. Try to get the better ones.

The second video told about a boy (+ 8-10 years old) who stand up on the stage, in front of thousands of adult people and he said wonderfully in front of them. The boy motivated the audience about a trust. He asked the audience to believe themselves. We must believe in ourselves, to dream anything, do anything. I think it was the most interesting video because it was very amazing. Imagine! What a wonderful presentation! It done by a small children, in front of thousands people, and the audiences claps their hands when the boy said something powerful and “magic” for them. I’m very proud to that child. He could show up his ability to influence the people with his said. I doubt that this powerful presentation could be presented by every child. Excellent!

Next video was a song about Mathematics. Maybe the title was “What You Know about Math?” because the face lyrics was “…what you know about Math, what you know about Math,,,”. It’s a hip hop music, I think and it’s contain about everything in Mathematics, about trigonometry, logarithm, numbers, exponents, dividing, etc.

The fourth video is about how to solve differential equation. The example is dy per dx equals 4 x square dx. The way is integrate each of side and calculate, so we get the result. Next video is about solving linear inequality. We can get the value of a variable (for example x) by add or reduce each sides with a same numbers. So, we get the result for final. The last video was about the explanation of logarithm equation and it’s solving.