“MY SMALL RESEARCH ON THE PSYCHOLOGY OF TEACHING LEARNING MATHEMATICS: THE RESPON OF STUDENTS IN SIXTH ELEMENTARY SCHOOL IN MATHEMATICS”
A. ABSTARCT
Many assumptions that Mathematics is a difficult subject and make bored. And that had doctrine until nowadays. Even, Mathematics is always had assumed as a ghost, also the student of Elementary school. Given a describe that Mathematics is a interesting subject is a must for us, even though to Students of Elementary School. Because, they had touch in a basically. So, is a must to eliminate the assumed that Mathematics is a difficult or bored subject, we must a built a means to them that Mathematics is interesting and Mathematic is a basic of the other knowledge. And the teachers must teach clearly, so the student can get what the teacher says.
B. OBSERVATION
In this small research, the writer had observed the student of sixth elementary school in a village where the writer lives. And to complete the data, the writer is also had interview one of Mathematics teacher in a elementary school which is different with that the student. The observation had with proposed some questions which relevance with this topic is the respond of student in sixth of elementary school in Mathematic. Those are such as:
1. How Mathematics in themselves?
2. How to see Mathematics in school?
3. Is Mathematics difficult like what in their mind until nowadays?
4. What the method had used the teacher to teach Mathematics in sixth of Elementary School?
5. What the material which forced by the teacher in Mathematics is relevant to the content of Mathematics?
6. Are the teacher us the other relevance dictate or not to support the teaching learning process?
7. What is the respond of the student if they can’t do the work of Mathematics, are they to be lazy following the subject or study hard to do it?
8. What are the factors caused the students happy to study Mathematics and what the factors which make the student to be bore?
9. What the media had used the teacher to communicate the subject or just to teach them?
C. INTERVIEW
With his opinion, Mathematics is not difficulty subject for him, because he can do it more and always get a good result. Many factor which make he have a trustworthy in himself, such as his parents is always support him to can do the work without be give up, and basically he like Mathematics more than other subject. The teacher in his school not use a more media to learn Mathematics to their school, it just use the dictate which there are in there and sometimes, the teacher adding the relevance book to support them. He like study Mathematics, and sometimes his parents support him with buy things which related in Mathematics. That is which make him happy to study Mathematics. So, he judge that Mathematics is easy not difficult like his friend judging Mathematics up to now. He feel so happy in Mathematics, and he has a motivation to study hard in Mathematics because he was has a basic in Mathematics. If he can’t do the homework, he would answer to his mother, or sometimes he do with his friend. Sometimes, he and his friend make a group to study in group. It use for do the homework or just study together. Even, in his school his teachers establish private less to up grown their student match. In there, formed any group so, the student be happy if in there because except study Mathematics, they can meet can play with their friend. He always studying Mathematics in night, because in evening he also follow an Islamic school in his village. Sometimes, if he be lazy to study his parents press him to study with direction which can received him.
With the teacher opinion, he said that Mathematics is not had basically yet in his student. And also the district of their student’s lives is not supported. And his school can be in category not updating school yet. And then, the teachers in there are not high quality teacher yet, because some of them just school until D3. So it also influence how their student studying Mathematics in school. Except that, many activities of the student in there except school. They are helping their parents to survive their live.
D. EXAMINATION
A positive motivation will support the child or students happy study Mathematics. Ebbutt and Straker in Mr. Marsigit’s blog, gasp that it have implication for teacher, whereas a teachers are necessary to do something to grown up the motivation of their student to study Mathematics, such as:
1. Serving the material of Mathematics interest. That means, a teachers must prepare everything for serve the material of Mathematics. So, the student not be bore if the teaching learning process which interest created. Except that, study Mathematics mustn’t just in class, but also can do in outdoor, everywhere. And, the teachers better give an application of the material to rill live. So, the students not think that Mathematics is abstract and just make a bore.
2. Attend the student activities. Except as a teacher who teaching the material of knowledge, a teacher have a role as a controller the student activities, so their student’s attitude and activities can be bridle.
3. Build the direction with describe where the student can understand. Don’t be pressing the capability of student to understand what we serve, because it just makes the student be pressed. Each child has different capability to understanding something. So as a teacher, we must be patient. And the teachers don’t use a method which the student can’t understand with the material which will transfer to the students.
4. Make interesting condition which can support and simulate the student to study Mathematics better. In teaching learning process in Mathematics, can doing with use any learning media such as, use the audiovisual aids, video which have a same theme with the material and etc which can upgrade the capability, creativities, critics’ of the student in Mathematics.
5. Give an activity which supports the purpose of learning. The teachers hoped not give a work or activity to the students which complicate the purpose of learning. Better if a teachers give exercises and applications of Mathematics in live days, so they can spirit to study Mathematics and the assume that Mathematics is difficult, abstract, and make a bore can eliminate.
THE POWER OF CATEGORY AND NETWORKING
The philosophic of Immanuel Kant, said that the power of category there are some point, such as: Qualitative, Quantitative, and category Relationship. Each of that has capacity in basic area. First, the basic of Quantitative are Plural, partial and singular. Second, the Qualitative of category is according of universal, partial and unique. And the last, Category Relationship according with the basic principal, like the law of if only if or the relation of cause and effect.
We can see many references in the power of category and networking, in nomena or phenomena. In nomena, there are two criteria category, that is category (categorization) and networking. Where the Categorization, we must know the definition, the function, the purpose, and the component of the reference.
And in phenomena, there are many step to be a real dream. We must know the category of highlighting ideas in our work, such as: the title, the abstraction, the introduction, the power of category, the power of networking, the relationship, the conclusion, and the reference.
The power of the network can create a bigger, national, global, or local presence than you could create on your own. This categorization has been important to us and helped us develop a much better methodology on how best to utilize our network. It has helped us develop an understanding of when we can rely on a contact to help us and when the request for help is unlikely to bear fruit. Having said that, we also realize that if our never ask, we will never know and we just never know who might know whom, for it is a small world. To restate the obvious not everyone in the network is equally able or willing (or a combination of both) to help in times like this. This leads to the next step on how to best utilize the network to get to the next opportunity. Network can be divided into three categories or four if we include friends.
There are four predefined relationship categories:
Hierarchical: Relationship types that are used to connect objects that have a hierarchical relationship.
peer to peer: Relationship types that are used to connect object that have a peer relationship.
Support: Relationship types that connect supporting objects to another object (for example, you can connect a News object to a Spreadsheet object).
Precedence: Relationship types that connect precedence objects to data resources (for example, you can connect a Precedence object to a File object). Objects that are connected with this category of relationship are displayed in the Information Catalog Center Show Lineage Tree window.
There are eight predefined relationship types:
Attachment: Attaches objects to other objects. Comment objects can only be attached to other objects as a support object.
Cascade: Connects two precedence objects.
Contact: Identifies a reference for more information about an object. More information might include the person who created the information that the object represents or the department responsible for maintaining the information.
Contains: Identifies Information Catalog Center objects that contain other objects. For example, use contains to denote objects in a hierarchical relationship, where one object is the parent and the other is the child.
Dictionary: Associates a glossary entry object type with another object. You can use a glossary entry object type to define terminology that is associated with the object.
Input: Connects objects that transform to their input data resource.
Linked: Connects two or more objects in an information catalog. Objects in a linked relationship are peers, rather than a hierarchical relationship.
Output: Connects objects that transform to their output data resource.
Supported: Provides additional information about your information catalog or enterprise.
TO UNCOVER THE PSYCHOLOGY PHENOMENA
The last week, our class of Mathematic Studying Psychology, Mr. Marsigit had made a phenomena where he go out for some minutes and at time he like be angry to us, we be afraid. He give an instruction that one of us as be the leader to handle all of us who in there to do something, and he had requested one of us to pinch him if we was get an idea or a concept to studying with him. We would to perform a Seminar, and Mr. Marsigit to be the speaker. And do you know what happened at the moment at one of us will pinch him? In the fact, Mr. Marsigit just simulate for explain about psychology of phenomena. And the material of that such as:
Traumatic is a phenomena without a cause, Where traumatic is related with the importance of communication. But, in my experience traumatic is always interlaced with the negative phenomena in our live, such as the phenomena caused of disaster, and etc. Maybe, that had been because of doctrine in our live since a long time. The traumatic psychology is a type of damage to the psyche that occur cause of the traumatic phenomena. When the traumatic to be damage stress posttraumatic, it can influence the psychic of brain, and etc.
Readiness where it tested us how we prepare anything in that condition. In psychology, readiness interlaced with a apperception. It also related with how we identity the situation and then we prepare to solve the problem in there. The high readiness will be escaped from traumatic. So, to escaped from traumatic we must have a will of alternative solution of any problem, so if we get a situation which it can be candidate make us trauma, we can have a more readiness.
Motive is a will of an intention something or someone, where it can be causes the people who are trauma. Such as, Mr. Marsigit in last week has a motif when he had leave us in our class. In fact, he has a motif that he wants to explain how to uncover the psychology phenomena.
Implementation is a part how to realize something which in our mind or something which had got from the other to our live company. In school, implementation can to realize to the teacher and the students. Such as, a material of linear algebra, from the material we can apply it to our live. Better, the teacher can implementation the material to a concrete problem of our live, so the student not be abstract to see the problem of Mathematic.a
Prediction is the any mind from the phenomena which had happened. The prediction sometime can be right but also can be wrong statement, hanged the minder. From the phenomena last week in or class with Mr. Marsigit, we get any prediction, such as some of us had predicted that Mr. Marsigit be angry because we be noisy in class not attended him, and some of us are also predicted that Mr. Marsigit be angry because we are not preparing the media to studying learning process, such as LCD and etc. And in fact, our predictions are wrong.
Attitude interlaced with how we must placed ourselves with any situation. Our attitude is also influence to our readiness to opposites the phenomena.
Except the points above, there are any point which interlaced about how to uncover the psychology phenomena such as, feeling, determine, subject, object, relation, explanation, and etc. which not be presented by me now day, maybe soon.
Monday, November 8th 2009
By: noka setya maharani
IT IS A MUST I HAVE COMPETENCE IN ENGLISH FOR MATHEMATIC EDUCATION
Many situation where I must have a competence in English for Mathematic Education, even though I am as a college in Mathematic Education of Yogyakarta State University who demanded to be a teacher afterwards and to follow the develop of the world in many aspect. I am not only must have a competence in Mathematic Education, but also I must have a competence in English for balancing and support my knowledge and my skill for teaching Mathematic to the students afterwards. Except that, with have a competence in English for Mathematic, hoped I can compete with many other candidate Mathematic teachers in Mathematic Education world. Many reasons why English is very important commanded me and I have a competence more in it, such as:
First, English is an International language where for communicate in International, surely we must use English. We demanded to command English well as an International language. If I haven’t a competence in English, so I sure overdue and can’t compete in this world and how I can communicate with others.
Second, Mathematic is one of important subject in the world. In each country surely learn Mathematic to their students, because other subject grounded by Mathematic to solve the problem, such as: Physic, Chemistry, Economic and etc are need Mathematic counting and many aspect why Mathematic is also important and very influence many subject in this world. Because Mathematic is important in this world, so I must for can communicate English well. It can be easily for me for communicating Mathematic and I can compete in the world. If I haven’t a competence in English, how I can communicating Mathematic to other people in the world or how I can have knowledge more about Mathematic from other people in the world. So, except I must have a competence in Mathematic Education, I also must have a competence in English for increase my skill in many aspects afterwards.
Except it, I must have a competence in English for Mathematic Education, because in Yogyakarta State University Mathematic Education is in World Class University where English had used for communicated in teaching and learning process. As a college of Mathematic Education, it is a must I follow this development. Where afterwards hoped I can compete well in there. And then, it supported by many school which follow the International Standard School, where also use English for communicating in teaching and learning process. As a college in Mathematic Education and surely also as a candidate of Mathematic teacher afterwards, is a must for me to have a competence English in Mathematic Education for easily communicate in teaching and learning process afterwards. Indirectly I must into in this reality. So, I must always up to date my knowledge and my skill not only how to teach Mathematic to the students, but also I must always increasing my skill in English, where it can help me for teach in International Standard School, because I hope I can teach and can serve in International Standard School afterwards, even though in this semester I follow the bilingual class in Mathematic Education of Yogyakarta State University. So, I have a will to always increasing my knowledge and my skill in many aspects, in English for Mathematic Education especially to being my dreams. So, it is a must I have a competence in English for Mathematic Education. Not only for my private a needs, but also can make Indonesia and Yogyakarta State University especially not overdue from other country or other university in Mathematic Education to go International.
Work I Have Done and Work I Will Do About English for Mathematic
As a college student, while in Mathematic Education it surely that I must know more about Mathematics. Because, this after indirectly I must teach Mathematics to children. So, to be not being confused if teach the children. I must know Mathematics more and always study hard, while the development of this world is very fast. English is also important to increase my knowledge and my skill, while now many school which have standard of International, where as a candidate of teacher, I must follow the development in this world, so I not be a behind the times people.
In English for Mathematics, I had increased my word about Mathematic in English, where before I don’t know, nothing! Because, before I really lost in English. But, now I have a will to can communication with English well. While, now I follow the bilingual class in Mathematic Education of Yogyakarta State University. So, indirectly my word about English Mathematics is added. And now, I try use English communication if I communication with my friends. Such as, send English message and he/she replay use English word, too. So, we communicate with English. I also use English word to expressing my inspiration, such as in facebook and friendster, express my condition with English. Even thought, it not always I do. But I am always tying it. I think that, with trying something begin little thing, it can develop our self of knowledge. Slow but sure! Maybe, I just can do it now, but I will increase my English Mathematic words. Now, I feel that English is very interesting for me. While, I can be appointed if I can communicate English well. For Mathematics, surely as a college student of Mathematic Education everyday I always study Mathematic. No day without mathematics! Mathematics is in my world and always in my heart forever. In English II now, my lecturer Mr. Marsigit is always give me something which very important for us generally. He give us about knowledge about Mathematic, Mathematic Education, Mathematic in English while role of mathematics education with a work which given to us. Maybe, it make us lazy to do it, but if we know more, it very useful and important for development our knowledge as a candidate teacher. With written the word of Mr. Marsigit said and we must post it to our blog, written our difficult word of mathematics, nature make our word about mathematic in English is increasing. I sure that Mr. Marsigit have a purpose for us with give us that work and it sure is useful for us and maybe we have skill more. I am so happy if I can do it well. So, now I always try everything which connected about mathematics in English. I hope I can do more than before. I sure that I can do it, well. And the last, I want to increase my skill more of English with follow a les of English.
I. The Nature of Logarithm
a. a to the power of m times a to the power of n equals a to the power of m plus n in bracket.
b. a to the power of m over a to the power of n equals a to the power of m minus n in bracket
c. Logarithm base a b equals n, so b equals a to the power of n
From the third nature of logarithm, so we can make the other equality:
a. logarithm the base g a equals a, so a equals g to the power of x
b. logarithm the base g b equals y, so b equals g to the power of y
If we have logarithm the base g a times b in bracket equals x, so it means that logarithm the base g a times b in bracket equivalent a times b equals g to the power of x.
Example:
Showed: - logarithm the base g a equals x, so a equals g to the power of x (as the first equality)
- logarithm the base g b equals y, so b equals g to the power of y (as the second equality)
• we can find the problem solving of a times b with that equality
From the first and the second equality, we get that:
a equals g to the power of x
b equals g to the power of y
So, a times b equals g to the power of x times g to the power of y
Equivalent with a times b equals g to the power of x plus y in bracket (the first nature of logarithm that a to the power of m times a to the power of n equals a to the power of m plus n in bracket)
Equivalent with logarithm the base g a times b in bracket equals logarithm g g to the power of x plus y in bracket
Equivalent with x plus y in bracket times logarithm the base g g
Remembered that logarithm the base g g equals one
Equivalent x plus y in bracket times one
So, logarithm the base g a times b in bracket equals x plus y
And remembered the equality that x equals logarithm the base a and y equals logarithm the base g b
So, logarithm the base g a times b in bracket equals logarithm the base g a plus logarithm the base g b
• we can find the problem solving of a over b with that equality
from the first and the second equality, we get that:
a equals g to the power of x
b equals g to the power of y
So, a plus b equals g to the power of x plus g to the power of y
Equivalent with a over b equals g to the power of a minus b in bracket (the second nature of logarithm that a to the power of m over a to the power of n equals a to the power of m minus n in bracket)
Equivalent with logarithm the base g a over b equals logarithm the base g g to the power of x minus yin bracket
Equivalent with logarithm the base g a over b equals x minus y in bracket times logarithm the base g g
Remembered again that logarithm the base g g equals one
Equivalent with logarithm the base a over b equals x minus y
And remembered the equality that x equals logarithm the base a and y equals logarithm the base g b
So, logarithm the base g a over b equals logarithm the base g a minus logarithm the base g b
Logarithm the base g a to the power of n equals logarithm the base g times open bracket a times a times a times…times a to n factor close bracket.
Equivalent with logarithm the base g a to the power of n equals logarithm the base g a plus logarithm the base g a sum of logarithm the base g a until n factor
So, logarithm the base g a to the power f n equals n times logarithm the base g a
II. Find the Value of Phi
The area of a circle showed equals eight over nine times the diameter of circle in bracket square, and the volume of aright cylinder is equals the area of the base times the altitude of cylinder. So, we can explain it:
The circle area equals open bracket eight over nine in bracket times diameter close bracket square
We know that diameter of circle is equals two time the radius of circle. So, we can get:
The circle area equals open bracket eight over nine in bracket times two times the radius of circle close bracket square
Equivalent with sixty four over eighty one in bracket times four times r square (r as radius)
Equivalent with two hundred fifty six over eighty one in bracket times r square
Equivalent with tree point sixteen times r square
So, Egypt had found the value of Phi, it is tree point sixteen.
III. Find the Formula of abc to Solving the Problem of Mathematics
The general form of square equality is a times x square plus b times x plus c equals zero
Then divided all with a
So, a over a in bracket times x square plus b over a in bracket times x plus c over a in bracket equals zero
Equivalent with x square plus b over a in bracket times x equals negative c over a in bracket
We complete the equality with perfect square
So, equivalent with x square plus b over a in bracket times x plus open bracket b over two times a in bracket close bracket square equals negative c over a in bracket plus open bracket b over two times a in bracket close bracket square
Equivalent with open bracket x plus b over two times a in bracket close bracket square equals b square minus four times a times a in bracket all over four times a square
Equivalent with x plus b over two times a in bracket equals plus minus the square root of b square minus four times a times c in bracket all over four times a square
Equivalent with x equals negative b plus minus the square root of b square minus four times a times c in bracket all over two times a in bracket
The value of x is negative b plus minus the square root of b square minus four times a times c in bracket all over two times a in bracket
We ever call this pattern as abc pattern.
IV. The Square Root of Two is Irrational
If we will approve that the square root of two is irrational, firstly we instance the square root of two as rational. It means that the square root of two equals a over b which a and b as prime. So, the square root of two equals a over b
Equivalent with a equals b times the square root of two or a equals b square times two
Because a square equals a integer so, a is also even number
If we instance a equals two times c, o the equality to become:
Four times c square equals two times b square
Equivalent with two times c square equals b square
So, b square is even number and b is even number, too. But it is impossible, because a and b is imposable as even number because a and b is relative prime. So, the assumption that the square root of two is rational had bought us to the impossible anything and it must canceled. So, we can see that the square root of two is irrational has approved.
V. The Point Intersect from Two Equality
y equals x square minus one as the (first equality)
x square plus y square equals thirty (as the second equality)
The first equality:
y equals x square minus one
Equivalent with y square equals x square minus one in bracket square
Equivalent with y square equals x to the power of four minus two times x square plus one
The second equality:
x square plus y square equals thirty
Equivalent with y square equals negative x square plus thirty
The first and the second equality joined:
y square equals y square
equivalent with x to the power of four minus two times x square plus one equals negative x square plus thirty
equivalent with x to the power of four minus x square equals twenty nine
equivalent with x square times x square minus one in bracket equals twenty nine
so, x square equals twenty nine or x square minus one equals thirty
for x square equals twenty nine, so x equals plus minus the square root of twenty nine, it means that x equals the square root of twenty nine or x equals negative the square root of twenty nine.
For x square equals thirty, so x equals plus minus the square root of that, it means that x equals the square root of thirty or x equals negative the square root of thirty
We had got the value of the x, then for get the value of y we input the values of x to the equality. In here, we use the first equality to find the value of y.
For x equals the square root of twenty nine
The first equality:
y equals x square minus one
input x equals the square of twenty nine to the equality
so, y equals the square root of twenty nine in bracket square minus one
equivalent with y equals twenty nine minus one
equivalent with y equals twenty eight
So, the first intersect from two equality above is x equals the square root of twenty nine and y equals twenty eight
For x equals negative the square root of twenty nine
The first equality:
y equals x square minus one
input x equals negative the square of twenty nine to the equality
So, y equals negative the square root of twenty nine in bracket square minus one
equivalent with y equals twenty nine minus one
equivalent with y equals twenty eight
so, the second intersect from two equality above is x equals negative the square root of twenty nine and y equals twenty eight
For x equals the square root of thirty
The first equality:
y equals x square minus one
input x equals the square of thirty to the equality
so, y equals the square root of thirty in bracket square minus one
equivalent with y equals thirty minus one
equivalent with y equals twenty nine
so, the third intersect from two equality above is x equals the square root of thirty and y equals twenty nine
For x equals negative the square root of thirty
The first equality:
y equals x square minus one
input x equals negative the square of thirty to the equality
so, y equals negative the square root of thirty in bracket square minus one
equivalent with y equals thirty minus one
equivalent with y equals twenty nine
so, the fourth intersect from two equality above is x equals negative the square root of thirty and y equals twenty nine
The word from the video which I had learned in English II lesson last week with Mr.Marsigit
1. Do you believe me
I believe in me. Do you believe in me? Do you believe there I am in here? That’s right. They do because here the real. I can do anything, be anything, and cry anything, become anything. Because of you believe me. Let’s me as your questions. Do you believe at my classmates? Do you believe that every single. You better because next week where also in up your school. One six tee seven hundred is over. And what we needs from you assembly that we carried or have… no marry where we came from. What it is? A way ever you be nice, because true know is same kazoos your...guides. You’re the wines to finders how weep a tiers. Who hound our hand? You’re the wine who loves when something if feels like a known else’s. To give my classmates. Do you believe and your calyxes? Do you? I hope so, because they can to your school because they want it make a different, too. Believe in there, swarthier and line on there when times gets off. We are know, we kits in sometimes my kit off. I am right? Can I get up? Can’t learn. All library, a teacher sixteen, and friend office. What you surf a milk and cappuccino, my foods. What your teachers or principle? We need you. Please believe in your calyxes and we believe in you. Do you believe in your self? Do you believe that what your doing shipping. Not it just, but that my children am I children student. It probably it way make a living, but I want to tell you a behavior all the students in dailies. We need you. We need you now want over believe in your self. Finally, do you believe that every child daily this is ready on the world place? Do you believe that daily for college students can be active; we need you ladies and gentleman. We need to know that what you doing in the most important jobs in this today. We need you to believe a nice in your calyxes, in your self. If you long believe. I want to thank you for what you do for me? And you help to me get today. Thank you…thank you… thanks you…
2. Do you know about math?
What you know about math …what you know about math…what you know about math…what you know about self math. Travel bag. What you know about math. I know all about math. Significant figure. Fourth five. Memories key. Trigonometry. Exponent line to declaim.
3. Trigonometry
Welcome to be presentation on basic of trigonometry. Trigonometry is from triangle and metry. Trigonometry’s story is right triangle. Relationship between the sides to the angles. So, let’s make a right triangle. The angles we call theta. The side of line is 3, 4 and 5 in the hypanus.
Sin theta equals?
For solve the problem on the school, for remember every times other the trick is:
Soh cah toa
It means that:
Soh: sin is opposite over hypannus
Cah: cos is adjust over hypannus
Tao: tan is opposite over adjust
So, sin theta equals 4 as opposite over 5 as hypannus
Cos theta equals adjust over hypannus. It means cos equals 3 as adjust over 5 as hypannus
Tan theta, is also use tao: tan theta equals 4 as opposite over 3 as adjust
Then, we call the other angle is x
So, tan x is also opposite over adjust, tan x equals 3 as opposite over 4 as adjust. It means that tan x is inverse of tan theta.
4. properties of logarithm
1. basically, if you have logarithm to the base b so the number be it’s call they base x. so log base b x equals y really the you logarithm.
2. if you have log base b ten x equals log x, log base e which e irrational number, log base e x equals ln x, its call natural logarithm .
Example:
log base ten one hundred is some number who called x. So, the base reason to the power and equals b reason y is equals x. so ten x to the power equals one hundred. Exponent of ten square equals one hundred. So, that means the value of x is two. So, log base ten one hundred is some number is two. Same ways, if we have log base two something number x equals tree. So, two the third power equals x. so, eight equals x. so, log base two eight equals tree.
Log base seven one over fourth nine equal x. whit same way
Seven to the x power equals one over fourth nine. We make a recognize the power of seven. Fourth nine equals seven square. And we remember the exponent. So, one over seven square is to be seven negative two to the power. So, the value of x is negative two.
If we have log base b M times N equals log base b M plus log base b N
Log base b M over N in bracket equals log base b M minus log base b N
Log base b x to be n equals n times log base b x
5. pre calculus
Will discussion about graph of a rational function. Can be discontinuities. why? Because the function has a polynomial in the denominator.
Example, if the function of f is equals x plus two equals x minus one. When x equals one so the function of f to be tree over zero and the zero as the denominator, its bad idea. Its break in function graph for example. The function of f equals x plus two over x minus one, then insert zero to the x so the function of one equals of two over negative one ore negative two. The graph is so far so good. Then insert one to the x. so the function of one is equals one plus two in bracket over one minus one in bracket with equals tree over zero that we know that is impossible, really bad. Now, rational function doesn’t always work with this way. Not all rational functions will give zero in denominator. In function of negative one equals one over negative one square plus one, never zero because of the positive one. Don’t forget rational functions denominator can be zero. For polynomial, smooth unbroken curve, rational function x to zero in the denominator. There is no value for the function, brake in the graph. Missing point, example: y equals x square minus x minus six in bracket over x minus tree in bracket. if we insert tree to the x, so the result is zero over zero. It not possible, not feasible and not allowed. It example for missing point syndrome zero over zero is factor top and bottom. Example y equals x square minus x minus six in bracket over x minus tree is equals x minus tree in bracket times x plus two in bracket over x minus tree in bracket, so it mean y equals x plus two. And it no problem if we insert tree to the x. Missing point is a loophole.
6. lets the function f be defined by f (x)=x+1
if 2 f(p) = 20, what is the value of f(3p)?
f(x)=x+1
2 f(p) = 20
f(p)=p+1=10
p=9
f(3p) is mean x=3p
so, x= 3 times 9
x= 27
so, f(3p)=27+1=28
if the xy coordinate plane the graph of x equals y square minus four intersect line at (0,p) and (5,t). What is the greatest possible value of the slope of graph.
My difficult word to express Mathematical idea
Part I (Print Storming)
- Intercept
- Proportional
- Sphere
- Tangent
- Point of tangency
- Chord
- Secant
- Inscribe angle
- Concentric
- Circumference
- Circular region
- Sector
- Set solve
- Equality
- Integer
- Lateral surface
- Boundaries
- Altitude
- Lateral edges
- Oblique cylinder
- Isosceles triangle
- Right angled triangle
- Squared
- Cubed
- Multiplied
- Divided
- Plane
- Whole number
- Addition
- Subtraction
- Number line
- Numerator
- Denominator
Part II ( meaning and application of my difficult word)
1. Two sphere or more are concentric if the both of them in a same center of sphere
- sphere = bola
- concentric = sepusat
2. A circle have radius of 5 cm, so the circumference of that circle 220/7 cm
- radius = jari-jari
- circumference = keliling
3. The solution of linear equality one variable only one problem solving. So, if there is a equality :
X + 5 = 6
<=> x = 1
So, the set solve that linear equality one variable is {1}
- equality = persamaan
- set solve = himpunan penyelesaian
4. Integers are the number of whole number and negative number
- integer = bilangan bulat
- whole number = bilangan cacah
5. Addition on integers can be interpreted as a directed distance
- Addition = penjumlahan
6. Subtraction operation on integers is to find out the difference between two integers. We can use a number line to indicate subtraction
- subtraction = pengurangan atau selisih
- number line = garis bilangan
7. The form of a/b where a and b are integers, a and b are not equal as with 0. a is called the numerator and b is called denominator
- numerator = pembilang
- denominator = penyebut
8. A isosceles triangle have two of same edges
- isosceles triangle = segitiga sama kaki
- edge = sisi
9. A cube have twelve of lateral edges
- lateral edge = rusuk
10. One of the angles of right angle triangle have 90
- right angle triangle = segitiga siku-siku
11. A tube with 7 cm of radius and 4 cm of altitude have 176 cm of lateral surface
- altitude = tinggi silinder
- lateral surface = luas selimut
What is mathematics and how to learn mathematic
A part of us was know what is a mathematic, but another hand a part of other us are don’t know what is mathematic. Basicly, mathematic can’t be far from our live, because in each our activitys, without conscious we always using mathematics to solving our problem, such as to know how square our land, how to build our haouse and etc. mathematics is very complete. The learn of mathematics such as Geometry, Calculus, Arithmetic, eventhough mathematics is also a pattern, communication, investigation and problem solving.
How mathematic can be pattern, communication, investigation and problem solving? Let’s we learn together about it. Firstly, mathematics is a pattern.. anything needs apattern to be better, mathematics is also, such as triangle, square, rofm, construction, structure needs a pattern to be usefull things. Second, mathematics is communication. From article was I read in Mr. Marsigit blog about “ Elegi Menggapai Hakekat Matematika ke Satu”, that the begining the mathematics is a phenomenon which at last the phenomenon can be communication for communicate to human. So, mathematics is communication, too. Third, mathematics is investigation. Mathematics also can used to investigation anything which happened in this world. And the last, mathematics is a problem solving. Each problem can solve with mathematics, such as how to know the square of our land, in bussiness is also use mathematic for account the surplus and many other. So mathematics is very complete. Anything can’t be far from mathematics, because basicly, mathematics be a basic for another knowledge.
Because now we study in mathematic education and we had hope to be a teacher, we must know how to learn our student afterwards. Before it, we also must know the basic character of our students generally. Firstly, basicly students needs motivation and spiri, even when our student be droping because there are many problem which to give audience them. We must know how oyr student have trusted to themselves again. Possible, we can aswered them about their problem and we be care them, and etc. Second, students is unique. Each student have different character to another students, because in this world is impossible that there are two child have identic character. So, we must patient to give audience our students when we learn them. Third, students have competence. Each student have competence and each student have a remainder and diminish, because no body perfect in this world. So, we don’t be angry if our students less in a lesson, possible in other lesson he/she lost. And the last, student os contexluality. As a social human, we can’t live alone. Our students are too. So, we must can help them if they have a problem.
So, we as a candidate of a profesional teacher of mathematic must always study how to give audience to our students and attitude to learn our students. Not only it, we also must know about mathematics generally and always surplus our knowledge about mathematic and how to learn our studen. May, we can be a profesional teacher of mathematic who not only learn mathematic, but also can become friend for our students. So we are be usefull teacher. Amien…
good evening Mr. Marsigit,,,
I was read your article about elegi pangakuan orang tua berambut putih,,,I like it...from your articles in this blog I more like this article because it make me have a will to know who am I more as the way of white hair old man to know him self in your article,,,,
I want to answer to you, how to know our self more obey your opinian, Mr. Marsigit?
the last,, I want to thank you to mr. marsigit for all your gift.
MY PREPERATION IN PARTICIPATING MARSIGIT’S LESSON IN ENGLISH II
Firstly I will introduce my self. My name is Noka Setya Maharani. I come from Pacitan city,
And My preparation in participating Mr. Marsigit’s lesson in this English II is preparing anything. Began read anything about English, although I still felt difficultly to understood all. Except it, I also tried to communicate with English well, example I tried to talk with my self, although it’s felt crazy, I don’t’ mind…more important I can speak English better. I tried to write something with English, too. Although, sometimes I just wrote one or two line in my book. I tried….tried and always trying to be can communicate with English well, because since I studied in Elementary School until now I lost in English, but now I have a will to be can communicate English well, because I conscious that English is very important for increasing my self and my knowledge especially. Many information from any sources, I know that English is also used for getting a work, so I must can communicate English well. I believe that I can communicate English better…better…and well if I always trying it seriously.
And now, I thank God that I began can study English better, because as little as possible I can write English only open dictionary least to preview.