My small research

Most junior high school students think mathematics is the most difficult lessons. They tend to prefer to learn other subjects in the comparative study mathematics. They learn mathematics considers only makes them dizzy with the formula-the formula is complicated. They also considered the formula too much given, they do not quite understand the previous formula, but was given a new formula is more complicated, because so many formulas that they had been increasingly reluctant to start learning. When given the task by their teachers prefer cheating friends than doing the job themselves.
Seventh grade math class consisting of junior integer, fraction, algebra and application, one-variable linear equation, linear inequality and 1 variable ratio

In small research I took respondents my brother Muhammad Fathoni Nurrohman. He is students of the junior high N 2 KARANGANYAR RSBI class. In grades last semester, he had scored 88. And on the mathematics test which given RSBI provincial education office and central java math score of 93. In the first semester Mathematics subjects that he received yesterday consists of an integer, fraction, algebra and application, one-variable linear equation, linear inequalities with one variable and comparison. According to the last semester of the most difficult chapter is a comparison.

In this research I want to identify why he did not master the chapter comparisons. The purpose of this research is to know how to think she and her understanding of the extent to which the comparison. To find out we need to know mathematical thinking. According to mathematical thinking katagiri has three parts of this. The first is Mathematical Attitude. We must suit our attitude in mathematics attitude to get it .

In this study I provide a few questions to see how understanding he was on the comparison.
Problem one: find the value of at equation
(x-3)=(x+2)/6
The first problem in doing this, he worked with the methods of commutative and distributive, so he managed to find the value of x in equation
Answer:
6(x-3)=x+2
6x-18=x+2
6x-x=2+18
5x=20
X=4

Problem two:
A project finish approximate 25 days when the project will be build 12 persons. Done after 15 days, stopped 4 days. The project must be finished at 25 days, so how much added many person?
Answer:
In his work he wrote
time that should be done = 25 days
Time left = 21 days
Workers start = 12
Workers end = 21/25 *12

He stopped working because the answer is fractional, whereas the number of workers cannot be fraction. In working on this second question, he still difficulties in mathematics realistic. so that the necessary understanding about the practice, in order to better understand the problems the application of the comparison.

The power of category and networking

Kant(1771) said that our mind consists of intense, idealism, abstraction, and epoche. The source of intense is awareness. There isn’t something perfect in the world, so we only assume that something is perfect. Assume something perfect is called idealism. When we learn about something we must not learn all characteristics of this object,we only learn some characteristics of this object. When we learn about a cube, we must not learn about the color, the material and the age, but we only learn about the shape and the size. Learning about important characteristic is called abstraction. Epoche consists of characteristic which is not important.

When we think about something, we must categorize the characteristic of the object. What is characteristic concluded abstraction? And, what is characteristic concluded aphoce? By category we can easier learn about the object.
There are phenomena and neumena . phenomena is something which realistic. something which unrealistic is called neumena.

There are two strategy to learn mathematics bottom up and top down. Study form bottom is called bottom up. Study from top to bottom or study from theories by read references from journal ,book or essay is called top down.
There are three learn system routine, intensive and extensive. Routine is learn by schedule. Learning from general object to special object is called intensive. Extensive is opposite intensive, so extensive is learn from special object to general object.

The nature of school mathematics is pattern, problem solving, investigation and communication. The instrument is observation, question, analysis than conclusion.

How to uncover the psychological phenomena

An event which is not understood is called traumatic. Let you give some money for your mother, but you don’t tell her what your reason, so you can make your mother feel traumatic. When a mathematics teacher gives some formula, but he doesn’t explain his students, the students will be traumatic. In politic, traumatic is called authority. A person who can’t explain her/his reason do something is called authority. But in philosophy, traumatic can be accident. So we must make communication to decrease traumatic. The component of communication is sender, constant and receiver. Sender is people who send messages. Constant is messages. Receiver is people who receive the messages. Effective communication is dynamic communication. Effective communication must be flexible and contextual. Starting from sensation will be apperception, then apperception will be readiness, and readiness will be awareness. Some sensation can make a perception and some perception can make a concept. There are two kinds of concept, a-priori concept and empirical concept. A-priori concept contain of assumption, pure sciences, definition, axiom, theorem and concept. Assumption is undefined term. Pure sciences are arranged for senior high school and students which level highest. The world is traumatic, so don’t be afraid to solve traumatic.

Limit tolerance can be measured and measure can be compared. So it will be characteristic of phenomena. Characteristics of phenomena consist of quantity (universal, partial, singular), quality, category, and relation (subject, predicate). Theory of mind says that mathematics is student’s mind.

Structure of teaching: introduction, transfer knowledge process and closing rework. The schema of interaction is classical, group discussion, and individual. The schema of competencies achievement is the nature student and the nature subject. The natures of student learn mathematic need motivation and application, individual, need collaboration, and learn in context. The nature of school mathematic is pattern and relation, problem solving, investigation, and communication.

Mathematics Thinking and scientific work

The definition of Mathematics from some lecture:
•mathematics is problem solving
•mathematics is investigation
•mathematics is creation
•mathematics mean of communication
pure mathematics is formal mathematics. The characteristic of formal mathematics is axiomatic, axiomatic mathematics different mathematic.
There are some definition of deduction mathematics is concept, definition, theorem, proof, axiom, procedure to proof theorem.
To starting point mathematics is system we should have assumes. The assumes can be a concept or definition of formal mathematics. The formal mathematics have base axiom, theorem and definition. Before definition you have clear picture or concept of object mathematics. Object mathematics can be your main or idea from the possibility object meta mathematics.
How to get mathematics object from the object concert:
1.idealism
idealism is assume that something is perfect, but perfect is God’s. We assume that something is sharp, but truly there is nothing which is sharp perfectly. We assume that line is straight. But truly there isn’t a perfect straight line.
2.Abstraction
A concert object have a lot of characteristic. In mathematics we just learn a few of the characteristic. Let : to learn about plane, we just learn about the shape and the size, to learn number, we just learn about the value. Mathematics is easy because just learn a few of the characteristic.


- Characteristic of mathematic thinking
1.Consistent
same with the first formula
2.Logic
We can know about the difference of big and small, relationship, mathematic separation or arithmetic, if than statement, the table of proof, how to get conclusion (premise), thesis, antithesis, hypothesis, let, etc.
- Scientific work
Example: report, proposal, text book, etc.
The characteristic of scientific work:
1.objective
2.have criteria or standard.

The characteristic paper:
1.abstract
2.recommendation
3.free from plagiarism
4.reference

exercise

exercise I

1.we will proof that square root of two is irrational number

• square root of two is irrational number because two is not perfect square number.
• So two is irrational number.

2. we will show that the sum of angels of triangle is equal one hundred and eighty.36

• Draw a triangle between two parallel line which one of triangle side coincide in one of the parallel line. Label your triangle using ABC. The vertex of triangle is A.
• Let: angle B is interior angle which the arm is one of the parallel line and the other arm is triangle side. Angle A exterior angle of the triangle top. Angle B and angle A are called alternate interior angle, so angle B and angle A have the same degree measurement.
• Angle C is the other interior angle. So angle C and the other exterior angle of the triangle top are called alternate interior angle.
• So the sum of angle A and two exterior angle of the triangle top is one hundred and eighty degree measurement because angle A and two exterior angle are supplementary angles.

3. we will explain how to get phi

• draw a circle with radius one centimeters. Put string and place in circle.
• Find the length of string
• The length of string is circumference of a circle
• We know that circumference of a circle is two times phi times radius,
• We have number of circumference of a circle with radius one centimeter, so we can find phi.
• Phi equal perimeter over two times radius
• Substitution the perimeter and the radius, so we get phi.

4. we will find the area of region bounded by the graph of y equal x square and y equal x plus two.

• We find the intersect of two graph by find x from equation x square equal x plus two. And than add two side with negative x minus two. So we get x square minus x minus two equal zero.
• Than we can find the factor. The factor is x minus two in bracket times x plus one in bracket equal zero. So we get x equal two and x equal negative one.
• The area of region bounded by the graph is define integral over boundary negative one and upper boundary two of x plus two minus x square dx.
• The area equal open square bracket a half times x square plus two times x minus one third times x cubeb close square bracket from x equal negative one to x equal two.
• The area equal open bracket a half times two square plus two times two minus one third times two cubeb close bracket minus open bracket a half times negative one square plus two times negative one plus one third times negative one cubeb close bracket.
• The area equal two plus four minus eight third in bracket minus a half minus one minus one third in bracket.
• So the area equal four and one sixth.

5. we will find the intersection point between the circle x square plus y square equal twenty and y equal x plus one.

• Substitution y equal x plus one to the circle x square plus y square equal twenty
• We get x square plus open bracket x plus one close bracket square equal twenty
• Than find the equation, x square plus x square plus two times x plus one equal twenty.
• Add two side with negative twenty, so two times x square plus two times x minus nineteen equal zero.
• Than find the value of x with ABC formula, first x or second x equal negative b plus or minus square root of open bracket b square minus four times a times c close bracket all over two times a
• First x or second x equal negative two plus or minus square root of two square minus four times two times negative nineteen in bracket all over two times two
• First x or second x equal negative two plus or minus square root of one hundred fifty six all over four
• Square root of one hundred fifty six equal two times square root of thirty nine, so first x or second x equal negative two plus or minus two times square root of thirty nine all over four.
• So first x equal negative one plus square root of thirty nine all over two and second x equal negative one minus square root of thirty nine all over two.

Exercise II

A.Triangle
- Definition : triangle is plane figure with three straight sides.
- Pythagorean theorem,” the square on the hypotenuse of a right triangle is equal to the sum of the square on the other two sides”.
- On the basis of size of triangles, there are three types of triangles:
1. Equilateral triangle
An equilateral triangle is one with all sides equal in length
2. Isosceles triangle
An isosceles triangles is a triangle with two sides equal in length.
3. Scalene triangle
A scalene triangle is a triangle with no sides equal in length.

• On the basis of the measures of the angles, there are three types of triangle:

1.Obtuse triangle
An obtuse triangle is a triangle which has one obtuse angle and two acute angles.
2.Acute triangle
An acute triangle is a triangle which all of angle is acute angles.
3.Right triangle
A right triangle is a triangle which has one right angle and two acute angle.
- The sum of angels of triangle is equal one hundred and eighty.
- the area of triangle is a half times the length of base times the height.
Problem solves:
1.We have right triangle with hypotenuse seventeen centimeters and height fifteen centimeters.Find the area of right triangle!
Solution:
•According to Pythagorean theorem, the square on the hypotenuse of a right triangle is equal to the sum of the square on the other two sides.
•So we can find the length of base. The length of base is square root of open bracket hypotenuse square minus height square close bracket.
•The length of base equal square root of seventeen square minus fifteen square in bracket. Seventeen square equal two hundred and eighty nine. And fifteen square equal two hundred and twenty five.
•So the length of base is square root of two hundred and eighty nine minus two hundred and twenty five in bracket.
•The length of base equal square root of sixty four. Square root of sixty four equal eight.
•So the length of base is eight.
•the area of triangle is a half times the length of base times the height.
•The area equal a half times eight times fifteen
•a half times eight times fifteen equal sixty
•so the area of square triangle is sixty.
2.Find the perimeter of triangle in number one
Solution:
•The perimeter of triangle is the sum of all sides.
•The perimeter of triangle equal seventeen plus fifteen plus eight
•seventeen plus fifteen plus eight equal forty
•so the perimeter of triangle is forty.

B.Parabola
•Definition : a parabola is the set of point in the plane that are equidistant from a point (the focus) and a line (the direction)
•We can draw parabola graph from square equation
•How to draw parabola graph??
-First find the x intercept of curve, we can find the x intercept of curve when the value of y is zero so the equation equal zero. Than we calculate the factor of the equation, if we can not find the factor, we can use ABC formula. ABC formula,” first x or second x equal negative b plus or minus square root of open bracket b square minus four times a times c close bracket all over two times a. so we can find the x intercept of curve.
-Than find y intercept of curve, we can find the y intercept of curve when the value of x is zero. Than substitution the value of x in the equation so w can find the y intercept of curve.
-We also find point of the top. Let point of the top is (x,y). Value of x is negative b over two times a and value of y equal b square minus four a times c all over negative four times a in bracket.
-Than draw the x intercept of curve, y intercept of curve and point of the top, and draw curve which contain the points.
•Characteristic of parabola:
Let: the equation is a times x square plus b times x plus c
-Above open parabola, when the value of a ( coefficient of x square) is negative.
-Bottom open parabola, when the value of a (coefficient of x square) is positive.

C.Exponent equation
•exponent equation is equation which the base or the power contain x variable.
•let: a to the m, a is the base and m is the power
•the formula of exponent equation:
-if the value of the base more than zero and m,n is rational number.
a.a to the m times a to the n equal a to the m plus n in bracket.
Example: calculate four to the six times four to the three !
four to the six times four to the equal four to the six plus three in bracket, so the solution is four to the nine
b.a to the m over a to the n equal a to the m minus b in bracket
example: calculate seven to the eight over seven to the two!
seven to the eight over seven to the two equal seven to the eight minus two in bracket, so the solution is seven to the six
c.a to the m in bracket to the n equal a to the m times n in bracket.
Example: calculate three to the four in bracket to the three!
three to the four in bracket to the three equal three to the four times three. So the solution is three to the twelve.
d. a times b in bracket to the m equal a to the m times b to the m
e. a over b in bracket to the m equal a to the m over b to the m
f. if a not equal zero than a to the zero equal one
g. if a more than zero and m is rational number than a to the negative m equal one over a to the m
h. if m,n is integer, n more than one and m over n is rational number, than a to the over n in bracket equal n-th root of a to the m.
•thorem:
1. a to the f(x) equal one
if a more than zero, a not equal one and a to the f(x) equal one, than f(x) equal zero
example: find the value of x in equation three to the open bracket x square plus three times x minus ten close bracket equal one!
Answer: if three to the open bracket x square plus three times x minus ten close bracket equal one, so x square plus three times x minus ten equal zero. The factor of x square plus three times x minus ten equal zero is x plus fife in bracket times x minus two in bracket. we get x plus fife equal zero, so the value of x is negative fife. And we get x minus two equal zero, so the value of x is two. The solution x equal fife or x equal two.
2.A to the f(x) equal a to the p
If a more than zero, a not equal one and a to the f(x) equal a to the p, than f(x) equal p
Example: find the value of x in equation: two to the x square minus fife times x in bracket equal two to the six.
Answer: two to the x square minus fife times x in bracket equal two to the six mean x square minus fife times x equal six. Than add two side by negative six. Than we get equation x square minus fife times x minus six equal zero. Factor of the equation is x minus six in bracket times x plus one in bracket. So the value of x is six or negative one.
3.A to the f(x) equal a to the g(x)
If a more than zero, a not equal one and a to the f(x) equal a to the g(x), than f(x) equal g(x)

Reflection of video

Video 1
Someone has many character. Everyone has positive side and negative side. We should look at someone from many different point of view. So we can understand the character of someone. Start look at something in our environment from many different point of view.

Video 2
A faith is very important and influence self of someone. If we believe someone and someone believe me so we can do everything better. So faith is very interest. If someone believe me we must keep the faith by doing everything which is our responsibility. So someone will believe me.

Video 3
What you know about math
There are a lot of knowledges in mathematics. Everything in our environment contains mathematics. By learn mathematics we can do everything in our life easier. In mathematics we can learn algebra, trigonometry, curve, logic, line, linier equation, etc.

Video 4
Solving deferential
We will find dy over dx equal four times x square to get the equation y.
• Dy over dx equal four times x square
• Dy equal four times x square dx
• Integral two side, so integral of dy equal integral of four times x square dx
• Integral of dy is y and integral of four times x square dx is four third times x cubeb plus Constanta.
• So y equal four third times x cubeb plus Constanta.

Video 5
Problem solving:
1. We will find the value of x in equation x minus five equal three.
• X minus five equal three
• Add two side with five, so we get x minus five plus five equal three plus five
• x equal three plus five
• so the value of x in equation x minus five equal three is eight.

2. we will find the value of a in equation seven equal four times a minus one
• seven equal four times a minus one
• add two side with one, so we get seven plus one equal four times a minus one plus one
• eight equal four times a
• multiply two side with a quarter , so we get a quarter times eight equal a quarter times four times a
• a quarter times eight is equal two, and a quarter times four times a is equal a
• so the value of a in equation seven equal four times a minus one is two

3. we will find the value of x in equation two third times x equal eight
• two third times x equal eight
• multiply two side with three second, so we get three second times two third times x equal three second times eight
• three second times two third times x is equal x, and three second times eight is equal twelve
• so the value of x in equation two third times x equal eight is twelve

4. we will find the value of x in equation five minus two times x equal three times x plus one.
• Add two side with negative three times x, so we get five minus five times x equal one
• Add two side with negative five, so we get negative five times equal negative four
• Multiply two side with negative one fifth, negative one fifth times negative five times x is equal x, and negative one fifth times negative four is equal four fifth.
• So the value of x in equation five minus two times x equal three times x plus one is four fifth.

5. We will find the value of m in equation three minus five times open bracket two times m minus five close bracket equal negative two
• three minus five times open bracket two times m minus five close bracket equal negative two
• three minus ten times m plus twenty five equal negative two
• so negative ten times m plus twenty eight equal negative two
• add two side with negative twenty eight, we get negative ten times m equal negative thirty
• divide two side with negative ten , we get negative ten times m over negative ten equal negative thirty over negative ten
• negative ten times m over negative ten is equal m and negative thirty over negative ten is equal three
• so the value of m in equation three minus five times open bracket two times m minus five close bracket equal negative two is three.

6. We will find the value of x in equation a half times x plus a quarter equal one third times x plus five forth
• Multiply two side with twelve, so twelve times a half times x plus a quarter in bracket equal one third times x plus five forth in bracket times twelve
• We get six times x plus three equal four times x plus fifteen
• Add two side with negative four times x, we get two times x plus three equal fifteen
• Add two side with negative three, so two times x equal twelve
• Divide two side with two, so two times x over two is equal x and twelve over two is equal six
• So the value of x in equation a half times x plus a quarter equal one third times x plus five forth

7. We will find the value of x in equation oh point three five times x minus oh point two equal oh point one five times x plus oh point one
• Multiply two side with one hundred, we get thirty five times x minus twenty equal fifteen times x plus ten
• Add two sides with twenty minus fifteen times x, we get twenty times x equal thirty
• Divide two side with twenty, twenty times x over twenty is equal x and thirty over twenty is equal three second
• So the value of x in equation oh point three five times x minus oh point two equal oh point one five times x plus oh point one is equal three second

Video 6
We will prove that C times logarithm base x of A equal logarithm base x of A to the C in bracket.
• C times logarithm base x of A equal logarithm base x of A to the C in bracket
• We know that if logarithm base x of A equal B, so X to the B equal A,
• So x to the B in bracket to the C equal A to the C
• X to the B times C in bracket equal A to the C, so logarithm base x of A to the C equal B times C. its second equation
• Substitution second equation in first equation, we get C times logarithm base x of A equal logarithm base x of A to the C in bracket. Its shown

We will prove that logarithm base x of A minus logarithm base x of B equal logarithm base x of A over B in bracket
• If logarithm base x of A equal m, so x to the m equal A
• If logarithm base x of B equal n, so x to the n equal B
• If Logarithm base x of A over B in bracket equal p so x to the p equal A over B
• We know that A equal x to the m and B equal x to the n, so x to the p equal x to the m over x to the n
• X to the p equal x to the m minus n in bracket, we get p equal m minus n
• So logarithm base x of A over B equal logarithm base x of A minus logarithm base x of B. its shown.

My reflection in learning English

To know our ability in English lesson, it was done English test. And the result can be used as our reflection. Is our competence in English good or not. So we can know what we must to do for the next step.

The English test result in the last week was very surprised. My result is not good. It means my ability is not good and must be increased. And so is my application.
English lesson is very important in our life to face this global era. Someone who have a little ability in English will have difficulties to face the competition in the future. Someone who is good in English will be easy to win the competition in work world. So, from this time we must optimize our competence in English language.

To increase my ability in English can be done with many ways, some of them are:
• Getting data from blogs
• Access from internet
• Find TOEFL test CD
• Use English in our daily
• Etc

How is the way to make us more competence than our friends?
1. Competence in English
The way to increase our competence in English is like: train our ability in
communication,express idea, understand English language, etc.
2. Competence in Mathematic
What is the really mathematics?
a. Have assumption what is the really mathematics.
b. Understand mathematics concepts.
T here are a lot of concepts in mathematics. Some of them can be definition of a
sentence concept, can define number, line, angle etc.
c. Axioms
Mathematics is analysis.
The truth in Mathematics experiment must based on logic (must be consistent or
there is no contradiction).
That is my reflection in learning english, i hope i can be better in english and mathematics.

The meaning of mathematics

The object of mathematics is abstract object. There are 2 ways to get the abstract object.

1. Abstraction

Abstract and abstraction is different. Example abstract: the price of thing, the value of thing, the material of thing, etc. what happen in mathematics? In mathematics, abstraction means the value of something.

2. Idealization

Nothing is perfect . We always assume that something is perfect, but perfect is God’s. We assume that something is sharp, but truly there is nothing which is sharp perfectly. We assume that line is straight. But truly there isn’t a perfect straight line. Mathematics is an art.

What is the object of mathematics?

The object of mathematics is structure, system, formula, pattern, etc. Mathematics is a science which is formed deductively and contains theorems.

The characteristic of mathematics is logic and consistent.

Based a professor from Melbourne University, the characteristic of mathematics is conjecture (thinking, predict) and conviction( to communicate the thinking)

Based from Prof Katagiri from Japans, mathematics consist of 3 aspects:

1. Mathematical attitude

Mathematical attitude is positive thinking, have a question, have a critical when study mathematics.

2. Mathematical method

The mathematical method is :

a. Deduction

Deduction is a method to take a conclusion from general to specific.

b. Induction

Induction is a method to take a conclusion from specific to general.

c. Syllogism

example:

Premise 1 : I am a UNY student

premise 2 : all UNY student have a student card

conclusion : I have a student card.

d. Logic

logic is a knowledge to learn the principle of reflections and take the valid conclusion.

e. Prove

3. Mathematical content

Kinds of the object of mathematics:

a. Formal object: deductive method, inductive method, syllogism method, logic, prove

b. Material object: thinking object, learning based on the ages.

The power of mathematics is critical thinking.

The meaning of mathematics is realistic mathematics:

1. Horizontal mathematics

2. Vertical mathematics

It is my writing about mathematics and its characteristics. I hope I will be useful for the readers. I hope you can see that mathematics is not a simple thing.

AN INTRODUCTION TO BAHASA INGGRIS II

Last week I had a first meeting English lesson II. For this semester the lecturer is Mr. Marsigit. He is very interesting and nice. He graduated from London university in 1996. He went to Japan at the first time in 2000. Now, he can go to Japan to join some meetings annually.

Last week, he explained that this semester’s exercices must be written at our blogs. Because it is formal blog, so we must fill our blog with formal photos and writings. And the most important thing is don’t make any plagiatism. Our blog must be his blog’s follower at http://marsigitenglish.blogspot.com. But it’s his second blog. His main blog is http://powermathematics.blogspot.com. In his main blog, he wrote elegies/sad songs about students, lecturers and teachers’ condition. But this writing can’t be understood easily by common people.

There are 5 points to study English well:

1. Motivation

Motivation is very important. If we don’t have motivation, we can’t understand the lesson well. From right now, we must love English language and don’t be afraid to start to do something. Motivation is not only willingness, but also our feeling, happiness, our focus and our belief that we can. Motivation can help us to love English and make us more bravier to practice our ability.

2. Attitude

Our attitude to English must be good. We must think that English is very important.so, we should make some tactics to study English.

3. Understanding

Knowing English is needed to built our ability. With knowing, we can learn English easily. We can start from knowing the structures, grammars etc. We also must be responsible with our way. If we understand others, we can work with other friends easily.

4. Skill

Our speaking skill influence English learning. Skill can be increased with using it in our daily life.

5. Experience

Experience can make us better. It can help us to learn the wrong and the right. So, we must try to practice our skill. Then we will be experienced with English.

Those are some tips to reach your success in learning English. It’s enough and sorry for my mistakes.