Observation’s result about Mathematical Method, Mathematical Attitude, And Mathematical Content Hold by Katagiri’s version, in teaching Learning Mathematic about Learning Area of Triangle, Rectangular, and persegi to Grade IV of Elementary School Year 2009.
Observer: Ety Antikasari
Prof. Katagiri from Japan when his presentation in Sapporo-Tokyo in said that mathematics is mathematical thinking consist three aspects, and I conclude that:
1. Mathematical attitude.
It is very important in determining student’s behavior in mathematical thinking. A good attitude is always asks to be perfection. Mathematical attitude is very important affective factor in determining student’s behavior in mathematical thinking depend on how interested, they are in problem solving on the lesson. Student’s expectation that mathematic will be useful and their personal attitude such as confidence, persistence, and organization are mentioned by Stacey (2006) as some of the skill and abilities required from problem solving.
2. Mathematical method.
Why we prove that? We can study from the specifics to general is called inductive thinking, from general to specifics is called deductive thinking, logical mathematics, or syllogism is one choice to it. We also use preposition. What is preposition? Preposition is sentence which consists true or false. We use conjunction, disjunction, implication (if then), or if then if. Beside that, we use direct or indirect prove.
3. Mathematical content.
Mathematical contents include ideas of set or unit operation, algorithm, or approximation. These can be compared to mathematical skill (as well as estimation mental computation) or deep mathematical knowledge as stated in Stacey’s requirement from problem solving.
Interview’s Result with one of the student grade IV of Elementary School:
A. Mathematical Method
1. What are the students do abstraction?
Abstraction is search similarity to get form or characteristic is very simple can make object of mathematical thinking. For example: with abstraction, let circle just is learning about just form and size does not color, material, prize, an characteristic others.
Answer:
- The students do abstraction to model of triangle, rectangular, and square.
- The students do abstraction that a rectangular is formed from fours line which first line and second line have same in long, but third line and fourth line also have same in long. For example: in every day, we can get model of rectangular such surface of table, surface of book, black or white board
- The students do abstraction that a square is formed from fours line which the fourth line have same in long. For example, the thing in our life which have form as square such paper which side has same in long.
- The students do abstraction that triangle is formed from three points was related with lines so when the student have two points, they can not make a triangle. For example, the thing in our life which has form as triangle is three wheel pictures on cover or packet cement. In teaching learning, the students do abstraction from triangle with unite tip of forefinger our hand and tip of our thumb.
2. How step or process to do abstraction and what term is used to it?
Answer:
The method to do abstraction:
• The students take instrument or thing in our life every day which has form such rectangular such book, paper; square such the paper has same in long of side it; triangle such picture on cover cement Gresik with merk “tiga roda”.
• The students use paper, pencil, eraser, ruler, and scissor to make form of rectangular, square, and triangle then they direct to me. So the form of triangle, rectangular, and square; the students must understanding it.
• The students use term on unsure that square has point side, side, and area of square. Rectangular has side, point side, and area of rectangular. Triangle also has base, high, side, point of side, and area of triangle.
• The students give definition of model with our sentences every day so more easily to understanding. Square is model was formed from fours line which the fourth line have same in long Square is such floor of home so it side has same. Rectangular is model was formed from fours line which first line and second line have same in long, but third line and fourth line also have same in long Rectangular such surface of door which second side same and second side other also same. Triangle is formed from three points was related with lines so when the student have two points, they can not make a triangle such picture on “pagoda pastilus” candy.
3. What the students do to represent it so easy to understanding?
Answer:
- The students represent area of rectangular with long time width so notasion to it that p x l
- The students represent area of square with side time side so notasion to it that s x s
- The students represent area of triangle with (base time heigh) divide two so notasion to it that (a x t) :2
4. What are the students do idealization?
Answer: Yes, so every rectangular, square and triangle, are formed from straight line there are not crooked lines. The student has assumption that to make rectangular, square, and triangle must use straight lines.
B. Mathematical Attitude
Mathematic learn with students honesty, consistent, absolute, etc. We can see it when the students do examination from their teacher. That time, I give my students question as examination in end month. The students imitate student other’s answer so I see that the student does trust. From observation it, we can see that the student have not honesty so the student must trust and believe with themselves. The student’s assumption that mathematic is difficult, so when they do exercise of mathematic although just several minute but they were bored and feel lazy to do it.
Observer : “Every time, how long you study mathematic?”
Student : “Average approximately an hour sister.”
Observer : “Why just an hour? We know that mathematic need much time to do exercise or solve problem?”
Student : “ Oh no,,,,,,mathematich is difficult so when we long time to it we will was bored.”
Observer : “Ok, I will give you exercise.”
Student : “I like do question if it from yourself does not from my book.”
From dialog above, we can give conclusion that the student assumption that mare and more difficult mathematic to learn it. The student like exercise question from our then from book. The students often do not hear my explanation, but far-out when I give some question to the student, they can give answer with true. They do not hear explanation but in end explanation, they ask several questions and in my opinion their question is brilliant. The student looks for apathetic but they give critical and active when there are several question. Sometimes, along teaching learning in class, the student request to rest because they tired with mathematic.
C. Mathematical Content
On above discussion about triangle, rectangular, and square so this explanation it, I more emphasize on comprehension student with my concept about:
What is rectangular, square, and triangle?
How form from rectangular, square, and triangle?
When the student understanding about two problem above so I will explanation what is side, point of side to square; base and high for triangle; long and width for rectangular. I will start to count area of rectangular, square, and triangle when the student understanding unsure of rectangular, square, and triangle. The student can learn to use formula if they can write it with notation. For side of square can be notation s, for long of rectangular can be notation p, for width of rectangular can be notation l, for base of triangle can be notation a, for high of triangle can be notation t. The students have assumption that mathematic is very difficult so I more why the student love with mathematic. I more emphasize so that the student few material but understanding than they much material but don’t understanding with it. Useless if I give much material but my student zero about it. So, I teach with several methods in this bottom:
1. Giving material so in every meeting, I more explain concept.
2. When the material reach finish, I will repeat or just review it to remember again so does not forgot.
3. Exercise question and I discussion the question with student.
4. Do evaluation pass trough examination in
Conclusion:
So, mathematical thinking has three component are mathematical method, mathematical attitude, and mathematical content. Mathematical thinking is very important to teaching learning mathematic. Every student has different mathematical thinking to understanding what mathematic. Different student has different paradigm, so a teacher has to can identify characteristic their student.
Senin, 28 Desember 2009
Minggu, 27 Desember 2009
The Power of Category and Networking
If was was asked about what is category? So, what is our answer? Many people can give several definitions about category. But hold by Kant, 1771 that in our mind there is a something and we can called are category and relation. In category, we must can to chose to do and we must enter so save in epoche’s house and which still phenomena form. In Kant's philosophy, a category is a pure concept of the understanding. A Kantian category is a characteristic of the appearance of any object in general, before it has been experienced. Such a category is not a classificatory division, as the word is commonly used. It is, instead, the condition of the possibility of objects in general, that is, objects as such, any and all objects, not specific objects in particular. Meaning of category that the word comes from the katēgoria, meaning that which can be said, predicated, or publicly declared (describe) and asserted (explain), about something. A category is an attribute (characteristic), property, quality, or characteristic that can be predicated of a thing. Kant said, "I remark concerning the categories that their logical employment consists in their use as predicates of objects." So Kant called it ontological predicates.
For example, we will discus about mathematics from definition of mathematics, characteristic of mathematics, and type of mathematics. There are difference between school mathematics and university mathematics. In university mathematics, study pure mathematics and applied mathematics. But in school mathematics, study general mathematics. The object of mathematics is abstract while abstract is our mine. There are two steps to get mathematics concept are abstraction and idealization. Abstraction is search similarity to get simple form and simple characteristic so it will to can be object of mathematical thinking. When we will discuss about teaching and learning of mathematics in front of class so our students will take notice our. Let, we will describe a cube so they will think about shape and size. When we think about cube, in our memory or our brain, there are many points which mixed in our mind such think our family in home or our lovely. Consequently, we must make a grouping everything which enters in our mind because it is very important to ours. When we can not grouping points it so our mind will was boxes. Everyone has to priority or accentuate several points on their mind. Brain always was used human to think, work, and study so was trained to grouping everything. If our brain over long time to rest, it means vacuum to think so it will cause we lazy to grouping everything.
”What is mathematical thinking?” Prof. Katagiri from Japan when his presentation in Sapporo-Tokyo in said that mathematics is mathematical thinking consist three aspects, and I conclude that:
1. Mathematical attitude.
It is very important in determining student’s behavior in mathematical thinking. A good attitude is always asks to be perfection. Mathematical attitude is very important affective factor in determining student’s behavior in mathematical thinking depend on how interested, they are in problem solving on the lesson. Student’s expectation that mathematic will be useful and their personal attitude such as confidence, persistence, and organization are mentioned by Stacey (2006) as some of the skill and abilities required from problem solving.
2. Mathematical method.
Why we prove that? We can study from the specifics to general is called inductive thinking, from general to specifics is called deductive thinking, logical mathematics, or syllogism is one choice to it. We also use preposition. What is preposition? Preposition is sentence which consists true or false. We use conjunction, disjunction, implication (if then), or if then if. Beside that, we use direct or indirect prove.
3. Mathematical content.
Mathematical contents include ideas of set or unit operation, algorithm, or approximation. These can be compared to mathematical skill (as well as estimation mental computation) or deep mathematical knowledge as stated in Stacey’s requirement from problem solving.
In Ebbut and Straker, 1995 the nature of school mathematics has four aspects are pattern or relation, problem solving, investigation, and communication. From Katagiri’s idea and Ebbut’s idea so we can write it in a table in this bellow:
pattern problem solving investigation communication
atitude √ √ √ √
method √ √ √ √
content √ √ √ √
If the people think from top to down so we use reference such book, journal, or research report. We have a reference to grouping everything in our memory. So, for example when we will write essay with title “Student’s Mathematical Thinking in the Framework of The Nature of School Mathematics of Geometry” we has reference so we can grouping everything. We must to think extensive, intensive, and routine as a spiral dynamic. The people must group everything in our mind so they are habitual to it.
For example, we will discus about mathematics from definition of mathematics, characteristic of mathematics, and type of mathematics. There are difference between school mathematics and university mathematics. In university mathematics, study pure mathematics and applied mathematics. But in school mathematics, study general mathematics. The object of mathematics is abstract while abstract is our mine. There are two steps to get mathematics concept are abstraction and idealization. Abstraction is search similarity to get simple form and simple characteristic so it will to can be object of mathematical thinking. When we will discuss about teaching and learning of mathematics in front of class so our students will take notice our. Let, we will describe a cube so they will think about shape and size. When we think about cube, in our memory or our brain, there are many points which mixed in our mind such think our family in home or our lovely. Consequently, we must make a grouping everything which enters in our mind because it is very important to ours. When we can not grouping points it so our mind will was boxes. Everyone has to priority or accentuate several points on their mind. Brain always was used human to think, work, and study so was trained to grouping everything. If our brain over long time to rest, it means vacuum to think so it will cause we lazy to grouping everything.
”What is mathematical thinking?” Prof. Katagiri from Japan when his presentation in Sapporo-Tokyo in said that mathematics is mathematical thinking consist three aspects, and I conclude that:
1. Mathematical attitude.
It is very important in determining student’s behavior in mathematical thinking. A good attitude is always asks to be perfection. Mathematical attitude is very important affective factor in determining student’s behavior in mathematical thinking depend on how interested, they are in problem solving on the lesson. Student’s expectation that mathematic will be useful and their personal attitude such as confidence, persistence, and organization are mentioned by Stacey (2006) as some of the skill and abilities required from problem solving.
2. Mathematical method.
Why we prove that? We can study from the specifics to general is called inductive thinking, from general to specifics is called deductive thinking, logical mathematics, or syllogism is one choice to it. We also use preposition. What is preposition? Preposition is sentence which consists true or false. We use conjunction, disjunction, implication (if then), or if then if. Beside that, we use direct or indirect prove.
3. Mathematical content.
Mathematical contents include ideas of set or unit operation, algorithm, or approximation. These can be compared to mathematical skill (as well as estimation mental computation) or deep mathematical knowledge as stated in Stacey’s requirement from problem solving.
In Ebbut and Straker, 1995 the nature of school mathematics has four aspects are pattern or relation, problem solving, investigation, and communication. From Katagiri’s idea and Ebbut’s idea so we can write it in a table in this bellow:
pattern problem solving investigation communication
atitude √ √ √ √
method √ √ √ √
content √ √ √ √
If the people think from top to down so we use reference such book, journal, or research report. We have a reference to grouping everything in our memory. So, for example when we will write essay with title “Student’s Mathematical Thinking in the Framework of The Nature of School Mathematics of Geometry” we has reference so we can grouping everything. We must to think extensive, intensive, and routine as a spiral dynamic. The people must group everything in our mind so they are habitual to it.
Minggu, 15 November 2009
How to Uncover the Psychological Phenomena?
Last week in psychology class, Mr.Marsigit asked the students to reflex along three months after learned psychology of mathematics. One of my friends walked in front of class to write critics, suggestion, and impression about psychology lesson. We said that in learn psychology, we had not book as reference, the matter didn’t clear and we difficult to understand, lesson make confused, the students didn’t readiness to follow lesson and the students gave negative responds. From explanation it, Mr.Marsigit gave a conclusion that we were traumatic. In my opinion, traumatic are one of spikiest condition where someone felt bottle up with one condition, event, or incident. Traumatic had relation with kind of work and grade of competence. Traumatic can recover by effective communication. The communication can be form by dynamic spiral. The components of dynamic spiral are flexible and contextual. Flexible is simple, easy to adapt every time and every where. Next, communication must contextual; it means that communication must suitable with space and time. Flexible and contextual on psychology will establish readiness, on philosophy will establish awareness, but in education will establish appreciation. Someone who living in the world must brave to traumatic and afford come at traumatic because everyone certain come trough but we don’t know when the time it. For example: in our house, our father is very authoritarian and protective. He His instruction must we do it without hear from our answer. Often in our heart, we complain about it but our father exactly angrier with ours. In this problem, I believe that we confuse and appear many question why our father easy to angry and like to necessitate? What is our mistake? We can give conclusion that our father ever traumatic about something so he apply it with ours. Traumatic need long time to recover because traumatic left injury which very poignant. The peoples in around must help to recover it. Good interaction from environment very important in this problem. I ever read article that to recover traumatic by TAT (Tapas Acupressure Technique) is a new technology, simple and effective to construct peaceful, relax, and health on short time. TAT is kind of form therapy on group Energy Psychology. We do it with touch several akupuntur points at head. If traumatic doesn’t recover so it can disturb every human activity. Traumatic can appear when different event resemble with now event. Consequently, the people must ready to traumatic because this problem will happen to ours.
Rabu, 29 April 2009
Mathematical Thinking and Scientific Work
Last week on April 23rd,2009 Mr.Marsigit told about mathematical thinking and scientific work in my class. Different mathematician has different definition about science. There is said that science is mathematical thinking, but there is said that science is establish with deductive method contain concept, definition, theorem, axiom, etc. Pure mathematics has characteristic more formal that mathematics is axiomatic mathematics. Before we describe about mathematics, we need strengthen object mathematics. What is mathematical object? Mathematical object is our mind; mathematical object is our idea and abstract and it doesn’t concrete object so we can’t manipulation using our sensory tool. And now, how we get mathematical object? We can get mathematical object from everything being our around.
There are two wise to get mathematical object:
1. We use abstraction
What is abstraction? Abstraction is looking for similarity to get form or simple characteristics to be object of mathematics. For example: “What do you think about the number five?” Every students giving various answer but in English class, the lecture and the students have similar characteristics so they discus about the value of number five. Why? Because this very minute, the lecture explain about English for mathematics so it is abstraction because we just learn several characteristic which we really dispersed.
2. We use idealization
“And what is idealization?” Idealization is straight or don’t taper because straight just for SIROTOL MUSTAQIM. For example, we have plan so it doesn’t really flat because absolutely right just Allah SWT, one other the teacher make question to their student don’t direct so the students must try to solve this problem and then it is called idealization.
And know, what is the characteristic of mathematical thinking? Mathematical thinking has many characteristics among others:
a. Consistent, it means that mathematical thinking must accord with the first requirement. For example we said A so can permanent A.
b. Mathematical logic, it blankets daily logic and formal logic. In mathematical logic contain ma thematic operation, if then statement, relation, etc.
c. There are thesis and antithesis. Thesis is sentence contain rightness but antithesis is opposite from thesis. So, before thesis and antithesis we need write hypothesis which temporary presumption.
Scientific work has standard or criteria inside writing them. Many people do some research or experiment to can write scientific work. A book about Mathematics for Senior High School include inside scientific work. It has systematical among others:
1. Introduction
Introduction contain about background why we write scientific work. Inside it, we can also give some problems to get solution.
2. Discussion
In discussion we said about problems and the solution it. In there, we take in some theory and material others which support it.
3. Conclusion
In this part, we must resume about problem solving in discussion part. We also give recommendation about problems above.
4. Reference
We can get reference from whatever such the books in library, dictionary, internet, etc. References create as source in our scientific work.
If we will write scientific work so we must to know about ethical code scientific work such:
a. Impersonal
It means we forbid to put emotional unsure. For example, we write book about Mathematical for Senior High School and in end page, we write “good luck and success” so we admit personal unsure inside it.
b. Has standard or criteria
It means if we write scientific work must know how arrangement writing, contain inside it is whatever.
c. Objective
Objective has means that suit with topic, so it doesn’t subjective. We write suit our material and it must coherent.
There are two wise to get mathematical object:
1. We use abstraction
What is abstraction? Abstraction is looking for similarity to get form or simple characteristics to be object of mathematics. For example: “What do you think about the number five?” Every students giving various answer but in English class, the lecture and the students have similar characteristics so they discus about the value of number five. Why? Because this very minute, the lecture explain about English for mathematics so it is abstraction because we just learn several characteristic which we really dispersed.
2. We use idealization
“And what is idealization?” Idealization is straight or don’t taper because straight just for SIROTOL MUSTAQIM. For example, we have plan so it doesn’t really flat because absolutely right just Allah SWT, one other the teacher make question to their student don’t direct so the students must try to solve this problem and then it is called idealization.
And know, what is the characteristic of mathematical thinking? Mathematical thinking has many characteristics among others:
a. Consistent, it means that mathematical thinking must accord with the first requirement. For example we said A so can permanent A.
b. Mathematical logic, it blankets daily logic and formal logic. In mathematical logic contain ma thematic operation, if then statement, relation, etc.
c. There are thesis and antithesis. Thesis is sentence contain rightness but antithesis is opposite from thesis. So, before thesis and antithesis we need write hypothesis which temporary presumption.
Scientific work has standard or criteria inside writing them. Many people do some research or experiment to can write scientific work. A book about Mathematics for Senior High School include inside scientific work. It has systematical among others:
1. Introduction
Introduction contain about background why we write scientific work. Inside it, we can also give some problems to get solution.
2. Discussion
In discussion we said about problems and the solution it. In there, we take in some theory and material others which support it.
3. Conclusion
In this part, we must resume about problem solving in discussion part. We also give recommendation about problems above.
4. Reference
We can get reference from whatever such the books in library, dictionary, internet, etc. References create as source in our scientific work.
If we will write scientific work so we must to know about ethical code scientific work such:
a. Impersonal
It means we forbid to put emotional unsure. For example, we write book about Mathematical for Senior High School and in end page, we write “good luck and success” so we admit personal unsure inside it.
b. Has standard or criteria
It means if we write scientific work must know how arrangement writing, contain inside it is whatever.
c. Objective
Objective has means that suit with topic, so it doesn’t subjective. We write suit our material and it must coherent.
Rabu, 15 April 2009
Exercise before English Examination
Last week, on 2nd April 2009 Mr. Marsigit gave English examination in my class. I and my friends very surprised because Mr.Marsigit didn’t say anything in before meeting. So we do it during thirty minutes and finally Mr.Marsigit said that it is just exercise to do English examination next week. Immediately, our profile change becomes very happy and we felt relieved.
Exercise I:
1. Explain how to prove that square root of 2 is irrational number!
2. Explain how to show or to indicate that the some angel of triangle is equal to 180 degree!
3. Explain how you are able to get phi!
4. Explain how you are able to find of the area of region foundered by the graph of y equal x square and y equal x plus 2!
5. Explain how you are able to determine the intersection point between the circle x square plus y square equal 20 and y equal x plus 1!
Answer:
1. To prove that the square root of 2 is irrational number so for example we have assumption that the square root of 2 is rational number. It means the square root of 2 equal a over b, which a and b as prime so the square root of 2 equal a over b. a over b can be writing with a equal b times the square root of 2 or a square equal 2 times b square because a square equal 2 times of integer so a square even so a also odd. Example equal 2c so the equation because four c square equal 2b. So, be square even and b also even. But, it's impossible because a and b impossible even because they are relative prime. So, assumption that square root of 2 is rational number is impossible. So, the conclusion that the square root of 2 is irrational number.
2. To show or to indicate that the some angels of triangle are equal to 180 degree so we can cut all of angel of triangle. Then, we adhere become one so three angel that will configured straight supplementary angel. We also prove it with we draw a line pass one of point angel from triangle which parallel with side in front of it. For example we have triangle ABC and we draw MN line pass point angel B and parallel with AC. Attention that size supplementary angel on B equal size sides of triangle ABC are a degree plus b degree plus c degree equal 180 degree. Every pair angel congruent is pair angel inside opposite on lines parallel.
3. To get phi we must do exercise. We can make a circle has radius of one cm from wire. Then, we wrap wool accord form of that wire. Then, we measure the length of wire with rule. For example, really we get 6 coma 28 it means 6 coma 28 is round of the circle. We know that the round of circle is phi time’s diameter or phi times two times of radius so phi equal round divide two times of radius. So, we can write that 3 coma 14 equal phi times two times of radius. And know phi equal 6 coma 28 divide two equal 3 coma 14.
4. To find of the area of region foundered by the graph of y equal x square and y equal x plus 2 so we must draw of each curve. After draw it, so we look for intersection point between two equations above. So, we get value of x and x as interval of integral to account the area of region it. If, y equal x square and y equal x plus 2 so we can write that x square equal a plus 2 and we get that x square minus x minus two equal zero. So, x minus two in bracket times x plus one in bracket equal zero. So, we get value of x with x equal two and x equal negative one as interval of integral it. Now, we can account the area of region it with integral x plus two minus x square in bracket to x with an equal negative one until x equal two. If we integral the equation so we get half x square plus two x minus one over three x cube with interval x equal negative one until a equal two. So we must substitution x with negative one and two and we get four half. So, the area of region foundered by the graph of y equal x square and y equal x plus two is four half.
5. To determine the intersection point between he circle x square plus y square equal 20 and y equal x plus 1 so we must substitution y equal x plus 1 inside x square plus y square equal 20. And we get x square plus open bracket x plus 1 close bracket square equal 20, so x square plus x square plus two x plus 1 equal 20, so two x square plus two x minus 19 equal zero. To get value of x, we must use the formula abc that x one or x two equal negative b plus minus the root of b square minus four times a times c divide angel negative 4a. So, x one or x two equal negative 2 plus minus the root of 2 square minus 4 times 2 times negative 19 divide negative 4 times 2. After we account it so we get that value of x one equal negative 1 coma 291 or x two equal 1 coma 791.
Exercise II:
1. High line
High line from a triangle is segment line which perpendicular correlates a point angle with a point on side in front of point angle. The theorem high line on hypotenuse a right angle establishes two triangles which uniform and also uniform with right angles.
2. Percentile
Percentile is value which divide batch of data becomes 100 part same.
Formula of percentile:
Pi equal TB Pi plus open bracket (i divide 100) N minus fk divide f P10 close bracket times p.
TB is limit under percentile i
i is number of percentile
N is sum all percentile
f is frequentation class percentile i
fk is frequentation cumulative class percentile i
p is interval class
Exercise to percentile:
Table frequentation and frequentation cumulative score
Score (x) Frequentation (fi) Frequentation cumulative
0-9 3 3
10-19 67 70
20-29 205 275
30-39 245 520
40-49 213 733
50-59 147 880
60-69 77 957
70-79 34 991
80-89 8 999
90-99 1 10000
sum 10000
P10? To get it, so we look for class which contains P10 is we account 10 divide100 in braked N equal 10 divide 100 times 1000 equal 100.
P10 equal 19 coma 5 plus open bracket 100 minus 70 divide 205 close bracket times 10 so we get that P10 equal 20 coma 96.
3. Relation
• Definition of relation is making a pair from element of compilation A to element of compilation B.
• Domain relation R from A to B is subset compilation from A while range E is subset compilation from B. Example A={1,2,3,4,5} and B={a,b,c,d}
Relation R= {(1,b), (3,b), (4,c), (4,d)}
Domain from relation R from A to B={1,3,4}
Range from relation R from A to B={b,c,d}
• Kind of relation
a. Reflective relation
Relation R called reflective relation if to every a element S, (a,a) element R is every element S is related with their self. Example relation R inside G is same and uniform relation
b. Symmetry relation
Relation R called symmetry relation if to every a,b element S (a,b) element R so (b,a) element R. Example G is parallel relation.
c. Transitive relation
Relation R called transitive relation if to every a,b element S if (a,b) element R and (b,c) element R. Example Q is relation minus from.
d. Equivalent relation
Relation R called equivalent relation if relations R are reflective relation, symmetry relation, and transitive relation.
Exercise I:
1. Explain how to prove that square root of 2 is irrational number!
2. Explain how to show or to indicate that the some angel of triangle is equal to 180 degree!
3. Explain how you are able to get phi!
4. Explain how you are able to find of the area of region foundered by the graph of y equal x square and y equal x plus 2!
5. Explain how you are able to determine the intersection point between the circle x square plus y square equal 20 and y equal x plus 1!
Answer:
1. To prove that the square root of 2 is irrational number so for example we have assumption that the square root of 2 is rational number. It means the square root of 2 equal a over b, which a and b as prime so the square root of 2 equal a over b. a over b can be writing with a equal b times the square root of 2 or a square equal 2 times b square because a square equal 2 times of integer so a square even so a also odd. Example equal 2c so the equation because four c square equal 2b. So, be square even and b also even. But, it's impossible because a and b impossible even because they are relative prime. So, assumption that square root of 2 is rational number is impossible. So, the conclusion that the square root of 2 is irrational number.
2. To show or to indicate that the some angels of triangle are equal to 180 degree so we can cut all of angel of triangle. Then, we adhere become one so three angel that will configured straight supplementary angel. We also prove it with we draw a line pass one of point angel from triangle which parallel with side in front of it. For example we have triangle ABC and we draw MN line pass point angel B and parallel with AC. Attention that size supplementary angel on B equal size sides of triangle ABC are a degree plus b degree plus c degree equal 180 degree. Every pair angel congruent is pair angel inside opposite on lines parallel.
3. To get phi we must do exercise. We can make a circle has radius of one cm from wire. Then, we wrap wool accord form of that wire. Then, we measure the length of wire with rule. For example, really we get 6 coma 28 it means 6 coma 28 is round of the circle. We know that the round of circle is phi time’s diameter or phi times two times of radius so phi equal round divide two times of radius. So, we can write that 3 coma 14 equal phi times two times of radius. And know phi equal 6 coma 28 divide two equal 3 coma 14.
4. To find of the area of region foundered by the graph of y equal x square and y equal x plus 2 so we must draw of each curve. After draw it, so we look for intersection point between two equations above. So, we get value of x and x as interval of integral to account the area of region it. If, y equal x square and y equal x plus 2 so we can write that x square equal a plus 2 and we get that x square minus x minus two equal zero. So, x minus two in bracket times x plus one in bracket equal zero. So, we get value of x with x equal two and x equal negative one as interval of integral it. Now, we can account the area of region it with integral x plus two minus x square in bracket to x with an equal negative one until x equal two. If we integral the equation so we get half x square plus two x minus one over three x cube with interval x equal negative one until a equal two. So we must substitution x with negative one and two and we get four half. So, the area of region foundered by the graph of y equal x square and y equal x plus two is four half.
5. To determine the intersection point between he circle x square plus y square equal 20 and y equal x plus 1 so we must substitution y equal x plus 1 inside x square plus y square equal 20. And we get x square plus open bracket x plus 1 close bracket square equal 20, so x square plus x square plus two x plus 1 equal 20, so two x square plus two x minus 19 equal zero. To get value of x, we must use the formula abc that x one or x two equal negative b plus minus the root of b square minus four times a times c divide angel negative 4a. So, x one or x two equal negative 2 plus minus the root of 2 square minus 4 times 2 times negative 19 divide negative 4 times 2. After we account it so we get that value of x one equal negative 1 coma 291 or x two equal 1 coma 791.
Exercise II:
1. High line
High line from a triangle is segment line which perpendicular correlates a point angle with a point on side in front of point angle. The theorem high line on hypotenuse a right angle establishes two triangles which uniform and also uniform with right angles.
2. Percentile
Percentile is value which divide batch of data becomes 100 part same.
Formula of percentile:
Pi equal TB Pi plus open bracket (i divide 100) N minus fk divide f P10 close bracket times p.
TB is limit under percentile i
i is number of percentile
N is sum all percentile
f is frequentation class percentile i
fk is frequentation cumulative class percentile i
p is interval class
Exercise to percentile:
Table frequentation and frequentation cumulative score
Score (x) Frequentation (fi) Frequentation cumulative
0-9 3 3
10-19 67 70
20-29 205 275
30-39 245 520
40-49 213 733
50-59 147 880
60-69 77 957
70-79 34 991
80-89 8 999
90-99 1 10000
sum 10000
P10? To get it, so we look for class which contains P10 is we account 10 divide100 in braked N equal 10 divide 100 times 1000 equal 100.
P10 equal 19 coma 5 plus open bracket 100 minus 70 divide 205 close bracket times 10 so we get that P10 equal 20 coma 96.
3. Relation
• Definition of relation is making a pair from element of compilation A to element of compilation B.
• Domain relation R from A to B is subset compilation from A while range E is subset compilation from B. Example A={1,2,3,4,5} and B={a,b,c,d}
Relation R= {(1,b), (3,b), (4,c), (4,d)}
Domain from relation R from A to B={1,3,4}
Range from relation R from A to B={b,c,d}
• Kind of relation
a. Reflective relation
Relation R called reflective relation if to every a element S, (a,a) element R is every element S is related with their self. Example relation R inside G is same and uniform relation
b. Symmetry relation
Relation R called symmetry relation if to every a,b element S (a,b) element R so (b,a) element R. Example G is parallel relation.
c. Transitive relation
Relation R called transitive relation if to every a,b element S if (a,b) element R and (b,c) element R. Example Q is relation minus from.
d. Equivalent relation
Relation R called equivalent relation if relations R are reflective relation, symmetry relation, and transitive relation.
Rabu, 01 April 2009
Reflection in Video
On 19th April 2009 Mr.Marsigit show with my class several video. The video very interesting because gives me motivation. I very heart burning with one people in video besides he is a child. But, I get knowledge that I must believe with myself and I don’t saw something from one different away.
In first video, show how the teacher gives motivation to their students. The teacher tells about W. Shakespeare who writes some interesting story. He tells the story very loudly thus his sound reverberates. Several students listen with him but several students busy with themselves activity for example writes something. Several students very admired with that story because the story waken spirit. Suddenly, the teacher jump on the table, he likes orator who give high spirit. He don’t afraid with his act and he advertise with his student don’t afraid to have a dream or have an ambition. Why the teachers speak it? Because, all this time the students just study oriented. They don’t have skill in outside. Consequently, the students must listen with their breast and the teacher gives freedom to them. The students must find themselves. Possible, we think the teacher stand on the table is one of mistake but let’s we don’t saw from it. We don’t have consider and look at something in different way. If we know something, we must look in the other way. The teacher demands their students to stand on the table likes him. Listen it, the students hurry up do it. In last video, two students stand on the table. They are very happy because they have freedom from their teacher.
In second video, I saw that there is a son stand on the stage and many audiences on his round. In there, he speaks very loudly and makes audiences admired with him. His speak like adult, and his every pronunciation have a meaning. The audiences very surprised with all his gesture. A son gives motivation to audiences so they believe with themselves. He said that “You believe me? You must believe that next week, I still stand on this stage.” Environment very noisy and make audiences give applause more and more loudly and their sound more and more jarring. A son runs to surround stage to give a motivation with audiences. The audience come from various reach, child, and adult, old, young. I become heart burning with him, why tendering like him very brave to speak in front of many people. He is very trust and he is very believed with himself. All of the audiences very enjoy with him. From this video, I get one of knowledge that we must believe with our ability so we don’t doubt with our work. A son in video has a high spirit to give motivation with the audiences.
In third video, there are two collage students song “what you know about math?” They have a high spirit to study about mathematics. I think, mathematics are integral, limit, trigonometry, curve, differential, exponent, and numerical. Really, in my opinion about mathematics is very a little. Because I think, mathematics just a lesson in my class but mathematics becomes breathes all of science. In the video, I look everything use mathematics. It means all the time I don’t understand about mathematics. I still have to study about mathematics. It isn’t just lesson but a knowledge which very important to all people in their life. If there are someone say mathematics just arithmetic is blunder. At last video, two collage students said that they know all about mathematics.
In fourth video, show how to solve differential equation. We will solve differential equation and integral equation. How to solve the differential or integral equation? There are some steps to solve it:
First, we must find y = f(x), satisfies the equation for values x and y.
How to solve ∫ (4x²) dx?
Try to get dependent variable, y all by it self. To solve that equation,
First we write = 4x² then we multiply the both segment with dx so acquirement that
dx (dy/dx) = (4x²) dx
We write with:∫ dy = ∫ (4x²) dx
To solve it, we must know formula of integral that ∫ x square n dx = x square (n+1) divide n+1
So ∫ 4x² = 4/3 x cubic
In fifth video, there is a teacher explain how to solve a linear equation so the students can be understand. So, I will try to solve several equations as the teacher.
1. X – 5 = 3
We can solve a linear equation above with add 5 on each segment, so in left segment just acquirement value from X. So, the equation can be writing with:
X – 5 = 3
X– 5+5 = 3+5
X = 8
Therefore, the solution from X min 5=3 is X = 8.
2. 7 = 4a – 1
Such as number one, we can solve a linear equation above with add 1 on both segment, so in right segment only acquirement value from a. So, the equation can be writing with:
7 = 4a min 1
7+1 = 4a min 1+1
8 = 4a
a = 2
Therefore, the solution from 7 = 4a-1 is a = 2.
3. 2/3 y = 8
We can solve this linear equation such as both the equation above but we don’t add numerically but we must multiply both segments with 3/2 and can acquirement value of y. So, the equation can be writing with:
2/3 y = 8
(2/3 y) times (3/2) = 8 times 3/2
y = 24/2
y = 12
Therefore, the solution from 2/3 y = 8 is y = 12.
Three examples above are very simple, so let’s we solve a linear equation more complex than above. There is several equation and we must solve it.
1. 5 min 2X = 3X+1
Because there is coefficient X on the both segment so we must delete one of them. For example we will delete negative 2X and 1 so we must add 2X and negative 1 on the both segment and acquirement value of X. So, the equation can be writing with:
5─2X+2X─1 = 3X+2X+1─1
4 = 5X
So get value of X, we must multiply the both segment with 1/5 and can be writing that:
4 times 1/5 = 5X times 1/5
X = 4/5
Therefore, the solution from 5─2X = 3X+1 is X = 4/5.
2. 3─5(2m─5) = ─2
To solve the equation above, we must multiply 5 with something on bracket so we get that:
3─10m+25 = ─2
─10m+28 = ─2
─10m = ─30 , to get value of m so we must divide the both segment with ─10 and can be writing with:
─10m/─10 = ─30/─10
m = 3
Therefore, the solution from 3─5(2m─5)= ─2 is m = 3.
3. (1/2y+1/4) = (1/3y+5/4)
We can solve the equation with multiply the both segment with KPK from 2, 3, and 4 but KPK of them is 12. We can write the equation with:
(1/2y+1/4) = (1/3y+5/4)
12(1/2y+1/4) = 12(1/3y+5/4)
6y+3 = 4y+15
2y = 12
y = 6
Therefore, the solution from (1/2y+1/4) = (1/3y+5/4) is y = 6.
4. 0,35a─0,2 = 0,15a+0,1
We can solve the equation with multiply the both segment 100 because number in behind of coma is two number. So, we can write the solution with:
0,35a─0,2 = 0,15a+0,1
100(0,35a─0,2) = 100(0,15a+0,1)
35a─20 = 15a+10
20a = 30
a = 3/2
Therefore, the solution of 0,35a─0,2 = 0,15a+0,1 is a = 3/2.
In sixth video, There is a teacher explains about logarithm. We know that there are many formula bases about logarithm and now I will try explaining about it.
I. log base x A equal B this form have same meaning or equivalent with X square B equal A, so we can write the both form with log base x A equal B equivalent X square b equal A.
Let’s we prove the equation above with multiply the both segment with C so can be writing with:
Log base x A equal B equivalent X square b equal A
C (log base x A)equal BC equivalent (X square b) square c equal A square c
C log base x A equal BC equivalent X square b times c equal A square c
Log base x A square c equal BC equivalent log base x A square equal BC
From explanation above, we can saw that log base A = B equivalent with X square b= A.
II. Log base x A + log base x B = log base x AB
To prove the equation above, we can use that:
If log base x A = k so X square k = A and can be writing with:
Log base x A = k so X square k = A
If log base x B = m so X square m = B and can be writing with:
Log base x B = m so X square m = B
If log base x A/B = n so X square n = A/B
= X square k divide X square m
= X square k minus m
We know that n = k-m so the equation is true. So we get equation that
log base x A+ log base x B = log base x AB
Really, many formulas to logarithm, but in the video just explain two formulas. If multiplication be addition so division is diminution, that statement can be writing with:
Log base x A plus log base x B = log base x AB so log base x A min log base x B = log base x A/B
In first video, show how the teacher gives motivation to their students. The teacher tells about W. Shakespeare who writes some interesting story. He tells the story very loudly thus his sound reverberates. Several students listen with him but several students busy with themselves activity for example writes something. Several students very admired with that story because the story waken spirit. Suddenly, the teacher jump on the table, he likes orator who give high spirit. He don’t afraid with his act and he advertise with his student don’t afraid to have a dream or have an ambition. Why the teachers speak it? Because, all this time the students just study oriented. They don’t have skill in outside. Consequently, the students must listen with their breast and the teacher gives freedom to them. The students must find themselves. Possible, we think the teacher stand on the table is one of mistake but let’s we don’t saw from it. We don’t have consider and look at something in different way. If we know something, we must look in the other way. The teacher demands their students to stand on the table likes him. Listen it, the students hurry up do it. In last video, two students stand on the table. They are very happy because they have freedom from their teacher.
In second video, I saw that there is a son stand on the stage and many audiences on his round. In there, he speaks very loudly and makes audiences admired with him. His speak like adult, and his every pronunciation have a meaning. The audiences very surprised with all his gesture. A son gives motivation to audiences so they believe with themselves. He said that “You believe me? You must believe that next week, I still stand on this stage.” Environment very noisy and make audiences give applause more and more loudly and their sound more and more jarring. A son runs to surround stage to give a motivation with audiences. The audience come from various reach, child, and adult, old, young. I become heart burning with him, why tendering like him very brave to speak in front of many people. He is very trust and he is very believed with himself. All of the audiences very enjoy with him. From this video, I get one of knowledge that we must believe with our ability so we don’t doubt with our work. A son in video has a high spirit to give motivation with the audiences.
In third video, there are two collage students song “what you know about math?” They have a high spirit to study about mathematics. I think, mathematics are integral, limit, trigonometry, curve, differential, exponent, and numerical. Really, in my opinion about mathematics is very a little. Because I think, mathematics just a lesson in my class but mathematics becomes breathes all of science. In the video, I look everything use mathematics. It means all the time I don’t understand about mathematics. I still have to study about mathematics. It isn’t just lesson but a knowledge which very important to all people in their life. If there are someone say mathematics just arithmetic is blunder. At last video, two collage students said that they know all about mathematics.
In fourth video, show how to solve differential equation. We will solve differential equation and integral equation. How to solve the differential or integral equation? There are some steps to solve it:
First, we must find y = f(x), satisfies the equation for values x and y.
How to solve ∫ (4x²) dx?
Try to get dependent variable, y all by it self. To solve that equation,
First we write = 4x² then we multiply the both segment with dx so acquirement that
dx (dy/dx) = (4x²) dx
We write with:∫ dy = ∫ (4x²) dx
To solve it, we must know formula of integral that ∫ x square n dx = x square (n+1) divide n+1
So ∫ 4x² = 4/3 x cubic
In fifth video, there is a teacher explain how to solve a linear equation so the students can be understand. So, I will try to solve several equations as the teacher.
1. X – 5 = 3
We can solve a linear equation above with add 5 on each segment, so in left segment just acquirement value from X. So, the equation can be writing with:
X – 5 = 3
X– 5+5 = 3+5
X = 8
Therefore, the solution from X min 5=3 is X = 8.
2. 7 = 4a – 1
Such as number one, we can solve a linear equation above with add 1 on both segment, so in right segment only acquirement value from a. So, the equation can be writing with:
7 = 4a min 1
7+1 = 4a min 1+1
8 = 4a
a = 2
Therefore, the solution from 7 = 4a-1 is a = 2.
3. 2/3 y = 8
We can solve this linear equation such as both the equation above but we don’t add numerically but we must multiply both segments with 3/2 and can acquirement value of y. So, the equation can be writing with:
2/3 y = 8
(2/3 y) times (3/2) = 8 times 3/2
y = 24/2
y = 12
Therefore, the solution from 2/3 y = 8 is y = 12.
Three examples above are very simple, so let’s we solve a linear equation more complex than above. There is several equation and we must solve it.
1. 5 min 2X = 3X+1
Because there is coefficient X on the both segment so we must delete one of them. For example we will delete negative 2X and 1 so we must add 2X and negative 1 on the both segment and acquirement value of X. So, the equation can be writing with:
5─2X+2X─1 = 3X+2X+1─1
4 = 5X
So get value of X, we must multiply the both segment with 1/5 and can be writing that:
4 times 1/5 = 5X times 1/5
X = 4/5
Therefore, the solution from 5─2X = 3X+1 is X = 4/5.
2. 3─5(2m─5) = ─2
To solve the equation above, we must multiply 5 with something on bracket so we get that:
3─10m+25 = ─2
─10m+28 = ─2
─10m = ─30 , to get value of m so we must divide the both segment with ─10 and can be writing with:
─10m/─10 = ─30/─10
m = 3
Therefore, the solution from 3─5(2m─5)= ─2 is m = 3.
3. (1/2y+1/4) = (1/3y+5/4)
We can solve the equation with multiply the both segment with KPK from 2, 3, and 4 but KPK of them is 12. We can write the equation with:
(1/2y+1/4) = (1/3y+5/4)
12(1/2y+1/4) = 12(1/3y+5/4)
6y+3 = 4y+15
2y = 12
y = 6
Therefore, the solution from (1/2y+1/4) = (1/3y+5/4) is y = 6.
4. 0,35a─0,2 = 0,15a+0,1
We can solve the equation with multiply the both segment 100 because number in behind of coma is two number. So, we can write the solution with:
0,35a─0,2 = 0,15a+0,1
100(0,35a─0,2) = 100(0,15a+0,1)
35a─20 = 15a+10
20a = 30
a = 3/2
Therefore, the solution of 0,35a─0,2 = 0,15a+0,1 is a = 3/2.
In sixth video, There is a teacher explains about logarithm. We know that there are many formula bases about logarithm and now I will try explaining about it.
I. log base x A equal B this form have same meaning or equivalent with X square B equal A, so we can write the both form with log base x A equal B equivalent X square b equal A.
Let’s we prove the equation above with multiply the both segment with C so can be writing with:
Log base x A equal B equivalent X square b equal A
C (log base x A)equal BC equivalent (X square b) square c equal A square c
C log base x A equal BC equivalent X square b times c equal A square c
Log base x A square c equal BC equivalent log base x A square equal BC
From explanation above, we can saw that log base A = B equivalent with X square b= A.
II. Log base x A + log base x B = log base x AB
To prove the equation above, we can use that:
If log base x A = k so X square k = A and can be writing with:
Log base x A = k so X square k = A
If log base x B = m so X square m = B and can be writing with:
Log base x B = m so X square m = B
If log base x A/B = n so X square n = A/B
= X square k divide X square m
= X square k minus m
We know that n = k-m so the equation is true. So we get equation that
log base x A+ log base x B = log base x AB
Really, many formulas to logarithm, but in the video just explain two formulas. If multiplication be addition so division is diminution, that statement can be writing with:
Log base x A plus log base x B = log base x AB so log base x A min log base x B = log base x A/B
Minggu, 15 Maret 2009
My Reflection In Learning English
Two days ago, on 12th March 2009 Mr.Marsigit came late to my English class until fifteen minutes. So, I and two my friends went to Himatika for posting our English home work by blog. Suddenly, my friend missed calls me and finally, we came back to our class and Mr.Marsigit gave English test. I didn’t concentration because I came late to my class and last night I didn’t study. I got bad mark; I want to cry because I disappointed my parents. Besides, the question is at the bottom of mathematics such square, straight line, average, rhombus, etc but to get B, I can’t. I was very regret, but not only it so I must do reformation to my self.
Mr.Marsigit gave short story about a student from California. The student will go to Indonesia to do some research. I very admired with her, because she is very intelligent, diligent, high spirit, and keep one’s chin up to get scholarship. I think why I unable as her? If we are cheeper, so I am cheeper which have not feather. Listen that story, I want to revolt, I want to be her, and I must study hard to run down my ambition. Last day is bad experience but it becomes best teacher for me. It becomes reflection to more advance. I must study hard and I must read the books every day. I must remember with my duty, what the purpose of me goes to Yogyakarta? My parents sent me to Yogyakarta to study and doesn’t to just play. I must responsibility with my self. Although I far from my parents, I must study hard. I must change of my study system. I want to be candidate professional teacher. How that? Now, I make plans for times schedule my activity. I will apply that study principle so success in my study among others many people said that the continuing of study more effectively than study a night through. Besides, learning all of the material is better than learning a part of material. The subject matter which has meaning is nine fold easier then the subject matter which haven’t meaning so I will start to apply that principle. Every night I must study although don’t examination and routine minimal 2 hours. I must have a high motivation to study; even less if I look my friends in my class, they are very intelligent. I must throw away my laziness if I want to success. I must realize expectance my parents. They work hard to fund my study but why with me? Allah SWT gave me, very much comfort so I must study hard as worship with Allah SWT because study is long life education.
Mr.Marsigit also said that we must improve our competence in English. How we improve that? We must use many reference from book, we can go to library and there we can read the books. We can use internet, getting data or information from blog, furthermore IT is more modern. We can practice TOEFL from CD or browsing internet. Furthermore we know that, if we want to get foreign scholarship so our TOEFL score must more than 500. It means, I must increase my TOEFL score to get foreign scholarship. Subhanallah, if a student from California can get scholarship. Really I want as her, certainly her parents proud with her. We also practice communicate, speak, listen, translate, and write in English. We must improve our skill because it is very important. Furthermore English is very important to face globalization era. So, we have to can speak English although just a little. Because we are in mathematics education program so we must improve our competence in mathematics. Mathematics doesn’t experiment but mathematics is analysis, just analysis. In mathematics, there are axioms, theorem, and thesis-anti thesis. We must study to prove theorem because we are candidate the teacher. I remember with Mr.Tuharto, he said that “we must practice how to be a teacher? If we get something so we must extend to anyone. We are in mathematics education program so we must study to love mathematics. Furthermore Yogyakarta State University will become World Class University so we must also study English. If we dislike with mathematics and English so we will difficult next time. Wherefore, if we dislike with them because still semester two so go out from mathematics education program”. From Mr.Marsigit and Mr.Tuharto, I get new lesson that I must become agent of change, bad experience at semester one doesn’t repeat again at semester two. My future stills a long so I want to get much experience. To my parents, my family, my friends, I will study hard to get my ambition. Furthermore, in the Al Qur’an was mention need that Allah SWT will not change their condition if they didn’t have any effort.
Mr.Marsigit gave short story about a student from California. The student will go to Indonesia to do some research. I very admired with her, because she is very intelligent, diligent, high spirit, and keep one’s chin up to get scholarship. I think why I unable as her? If we are cheeper, so I am cheeper which have not feather. Listen that story, I want to revolt, I want to be her, and I must study hard to run down my ambition. Last day is bad experience but it becomes best teacher for me. It becomes reflection to more advance. I must study hard and I must read the books every day. I must remember with my duty, what the purpose of me goes to Yogyakarta? My parents sent me to Yogyakarta to study and doesn’t to just play. I must responsibility with my self. Although I far from my parents, I must study hard. I must change of my study system. I want to be candidate professional teacher. How that? Now, I make plans for times schedule my activity. I will apply that study principle so success in my study among others many people said that the continuing of study more effectively than study a night through. Besides, learning all of the material is better than learning a part of material. The subject matter which has meaning is nine fold easier then the subject matter which haven’t meaning so I will start to apply that principle. Every night I must study although don’t examination and routine minimal 2 hours. I must have a high motivation to study; even less if I look my friends in my class, they are very intelligent. I must throw away my laziness if I want to success. I must realize expectance my parents. They work hard to fund my study but why with me? Allah SWT gave me, very much comfort so I must study hard as worship with Allah SWT because study is long life education.
Mr.Marsigit also said that we must improve our competence in English. How we improve that? We must use many reference from book, we can go to library and there we can read the books. We can use internet, getting data or information from blog, furthermore IT is more modern. We can practice TOEFL from CD or browsing internet. Furthermore we know that, if we want to get foreign scholarship so our TOEFL score must more than 500. It means, I must increase my TOEFL score to get foreign scholarship. Subhanallah, if a student from California can get scholarship. Really I want as her, certainly her parents proud with her. We also practice communicate, speak, listen, translate, and write in English. We must improve our skill because it is very important. Furthermore English is very important to face globalization era. So, we have to can speak English although just a little. Because we are in mathematics education program so we must improve our competence in mathematics. Mathematics doesn’t experiment but mathematics is analysis, just analysis. In mathematics, there are axioms, theorem, and thesis-anti thesis. We must study to prove theorem because we are candidate the teacher. I remember with Mr.Tuharto, he said that “we must practice how to be a teacher? If we get something so we must extend to anyone. We are in mathematics education program so we must study to love mathematics. Furthermore Yogyakarta State University will become World Class University so we must also study English. If we dislike with mathematics and English so we will difficult next time. Wherefore, if we dislike with them because still semester two so go out from mathematics education program”. From Mr.Marsigit and Mr.Tuharto, I get new lesson that I must become agent of change, bad experience at semester one doesn’t repeat again at semester two. My future stills a long so I want to get much experience. To my parents, my family, my friends, I will study hard to get my ambition. Furthermore, in the Al Qur’an was mention need that Allah SWT will not change their condition if they didn’t have any effort.
Rabu, 11 Maret 2009
The Meaning of Mathematics
What is mathematics? Do you can explain about mathematics? We know that everyone can describe about mathematics but of all different. Now, we will discus about mathematics from definition of mathematics, characteristic of mathematics, and type of mathematics. There are difference between school mathematics and university mathematics. In university mathematics study pure mathematics and applied mathematics. But in school mathematics, study general mathematics. The object of mathematics is abstract while abstract is our mine. There are two steps to get mathematics concept:
1. We use abstraction
2. We use idealization
What is abstraction? Abstraction is looking for similarity to get form or simple characteristics to be object of mathematics. For example: “What do you think about the number five?” Every students giving various answer but in English class, the lecture and the students have similar characteristics so they discus about the value of number five. Why? Because this very minute, the lecture explain about English for mathematics so it is abstraction. “And what is idealization?” Idealization is straight or don’t taper because straight just for SIROTOL MUSTAQIM. For example, the teacher make question to their student don’t direct so the students must try to solve this problem and then it is called idealization.
The meanings of object mathematics are structure, system, which go up axiom, formula, theorem and pattern. The characteristics of mathematics is logic and consistent. Prof. Kaye Stacey from Melbourne University said that mathematics is:
1. conjecturing
Conjecturing is when we are given problems and we must to predict, to estimate, so giving solution about it.
2. convincing
Convincing is we communicate the result to people by presentation, conference or test.
Prof. Katagiri from Japan when he presentation in Sapporo-Tokyo said that mathematics is mathematical thinking which consist three aspects are:
1. Mathematical attitude.
It is very important in determining student’s behavior in mathematical thinking. A good attitude is always asks to be perfection.
2. Mathematical method.
Why we prove that? We can study from the specifics to general is called inductive thinking, from general to specifics is called deductive thinking, logical mathematics, or syllogism is one choice to it. Foe example syllogism:
Premise 1 : Every student must wear school uniform
Premise 2 : Fany is a student
We also use preposition. What is preposition? Preposition is sentence which consists true or false. We use conjunction, disjunction, implication (if then), or if then if. Beside that, we use direct or indirect prove.
3. Mathematical content.
Mathematical contents include operation, algorithm, or approximation.
The definition of mathematics from real mathematics is:
1. Horizontal mathematics is daily mathematics, the object of mathematics.
2. Vertical of mathematics is abstract mathematics, pure mathematics.
The Work University said that the power of mathematics is critical thinking. It means every thesis there are anti-thesis and every anti-thesis there are synthesis.
Sources: According to pbmmarsigit.blogspot.com on Tuesday, 10th March 2009
.
1. We use abstraction
2. We use idealization
What is abstraction? Abstraction is looking for similarity to get form or simple characteristics to be object of mathematics. For example: “What do you think about the number five?” Every students giving various answer but in English class, the lecture and the students have similar characteristics so they discus about the value of number five. Why? Because this very minute, the lecture explain about English for mathematics so it is abstraction. “And what is idealization?” Idealization is straight or don’t taper because straight just for SIROTOL MUSTAQIM. For example, the teacher make question to their student don’t direct so the students must try to solve this problem and then it is called idealization.
The meanings of object mathematics are structure, system, which go up axiom, formula, theorem and pattern. The characteristics of mathematics is logic and consistent. Prof. Kaye Stacey from Melbourne University said that mathematics is:
1. conjecturing
Conjecturing is when we are given problems and we must to predict, to estimate, so giving solution about it.
2. convincing
Convincing is we communicate the result to people by presentation, conference or test.
Prof. Katagiri from Japan when he presentation in Sapporo-Tokyo said that mathematics is mathematical thinking which consist three aspects are:
1. Mathematical attitude.
It is very important in determining student’s behavior in mathematical thinking. A good attitude is always asks to be perfection.
2. Mathematical method.
Why we prove that? We can study from the specifics to general is called inductive thinking, from general to specifics is called deductive thinking, logical mathematics, or syllogism is one choice to it. Foe example syllogism:
Premise 1 : Every student must wear school uniform
Premise 2 : Fany is a student
We also use preposition. What is preposition? Preposition is sentence which consists true or false. We use conjunction, disjunction, implication (if then), or if then if. Beside that, we use direct or indirect prove.
3. Mathematical content.
Mathematical contents include operation, algorithm, or approximation.
The definition of mathematics from real mathematics is:
1. Horizontal mathematics is daily mathematics, the object of mathematics.
2. Vertical of mathematics is abstract mathematics, pure mathematics.
The Work University said that the power of mathematics is critical thinking. It means every thesis there are anti-thesis and every anti-thesis there are synthesis.
Sources: According to pbmmarsigit.blogspot.com on Tuesday, 10th March 2009
.
Senin, 02 Maret 2009
An Introduction to English II
In our country, many people say that English is very difficult. Why? Even, if we want to study so English is very fun. There for, there are some preconditions to work in English II:
1. Motivation
What is motivation? Motivation is high spirit, enjoyable, pleasurable, or happiness. First step, we have to release as student. Releasing is the first knowledge. Our high motivation is used to pray with Allah SWT. Our duty as student is study hard to shape of religious serves with Allah SWT. There is no limitation of study. The study doesn’t limit by age an even until we close our eyes because the study is long life education.
2. Attitude
What is the meaning of attitude? Attitude is our behavior or our act. As student, we should have act appropriate with our ambition. We must able to adaption with environment which is support our ambition. For example, we are the students of mathematics education, so it will teach us how tube a teacher. In this case, we have to study how to speak wisely, how to act as a teacher. As we know that a teacher is not a famous artist. The teacher is a person who teaches their students so each of their behavior will imitate by their students. If we able to adaptation well, it’s mean that we understand what our necessary is so it can support our effort.
3. Understanding
What is understanding? Understanding is knowledge. We must conscious and understand that as a student, we have characteristic. What is the mean of those characteristic? The characteristic of student are have responsible, commitment, discipline, etc. As a good student, we should not receive everything from the lecture without effort. Because in university, the lecture will deliver the material only 15%, where as the 85% is achieved by the student by study hard. What is the purpose of the lecture to do this? In order to the student more active, stand alone, creative, and want to know so the student will competence to get knowledge, whether from dictionary, book, reference, internet, library, or even work together to improve information from this case (collaboration with their friend), can be seen the responsibility of the student.
4. Skill
What is the meaning of skill? We have to develop our skill by reading, writing, hearing, talking, and speaking. Reading the text is one of an effort to increase our skill in reading. If we often read, it will increase our pronunciation and vocab. Besides, the using of English when we speak is an effort to increase our skill. Nowadays, English is international language, so we have to master in English to face the globalization era. If we do not master in English we will life behind. In other ways, to increase our skill in listening, we could hear the cassette of TOEFEL. The next, to increase our skill in writing can be done by write about our daily activity in diary. From this view, we should not only study hard but we have to pay attention how to improve our skill. As the result, when we graduate from university, we have skills.
5. Experience
As the student, we should have an experience. An ideal student not only study oriented but also have many experience. For example, get participate in Seminar National, participate in the competition of science, participate in organization (example: HIMATIKA), etc. Those efforts could increase our experience. The experience has important role in people’s life because experience is best teacher.
6. Communication
What is communication? Communication is talking, understanding, hearing, speaking, and translating. Many students can’t communicate well. They tend to keep silent than deliver their aspiration. It can be seen, when the lecturer give chance to ask something, the student doesn’t give response. Usually the student afraid about their opinion or even they feel shy. In other word, communication is the process of delivering information or message from one to another. The aspect of the system communication is speaker, hearer, and message. We know that, communication is very important to get successful. A good communication in the teaching and learning program will happen if there is a good response between teacher and student.
Mathematics
What is mathematics? The definition of mathematics from one to another is different. Even, when greengrocer asked by people about the mark of rapport his children, they answer that the rapport very bad because the mark of mathematics is red. Mathematics isn’t only formula (c2= a2+ b2) but we must do a lot of exercise.
Now, we look what is the meaning of English?
English is not only tenses like present continuous tense (S+Tobe+V1ing) but English is ours. So, that English will not be broken even all of our English books burned out. If we read more, listen more, write more, and speak more so it can improve our knowledge in English. There for, students have to be responsible to there assignment.
1. Motivation
What is motivation? Motivation is high spirit, enjoyable, pleasurable, or happiness. First step, we have to release as student. Releasing is the first knowledge. Our high motivation is used to pray with Allah SWT. Our duty as student is study hard to shape of religious serves with Allah SWT. There is no limitation of study. The study doesn’t limit by age an even until we close our eyes because the study is long life education.
2. Attitude
What is the meaning of attitude? Attitude is our behavior or our act. As student, we should have act appropriate with our ambition. We must able to adaption with environment which is support our ambition. For example, we are the students of mathematics education, so it will teach us how tube a teacher. In this case, we have to study how to speak wisely, how to act as a teacher. As we know that a teacher is not a famous artist. The teacher is a person who teaches their students so each of their behavior will imitate by their students. If we able to adaptation well, it’s mean that we understand what our necessary is so it can support our effort.
3. Understanding
What is understanding? Understanding is knowledge. We must conscious and understand that as a student, we have characteristic. What is the mean of those characteristic? The characteristic of student are have responsible, commitment, discipline, etc. As a good student, we should not receive everything from the lecture without effort. Because in university, the lecture will deliver the material only 15%, where as the 85% is achieved by the student by study hard. What is the purpose of the lecture to do this? In order to the student more active, stand alone, creative, and want to know so the student will competence to get knowledge, whether from dictionary, book, reference, internet, library, or even work together to improve information from this case (collaboration with their friend), can be seen the responsibility of the student.
4. Skill
What is the meaning of skill? We have to develop our skill by reading, writing, hearing, talking, and speaking. Reading the text is one of an effort to increase our skill in reading. If we often read, it will increase our pronunciation and vocab. Besides, the using of English when we speak is an effort to increase our skill. Nowadays, English is international language, so we have to master in English to face the globalization era. If we do not master in English we will life behind. In other ways, to increase our skill in listening, we could hear the cassette of TOEFEL. The next, to increase our skill in writing can be done by write about our daily activity in diary. From this view, we should not only study hard but we have to pay attention how to improve our skill. As the result, when we graduate from university, we have skills.
5. Experience
As the student, we should have an experience. An ideal student not only study oriented but also have many experience. For example, get participate in Seminar National, participate in the competition of science, participate in organization (example: HIMATIKA), etc. Those efforts could increase our experience. The experience has important role in people’s life because experience is best teacher.
6. Communication
What is communication? Communication is talking, understanding, hearing, speaking, and translating. Many students can’t communicate well. They tend to keep silent than deliver their aspiration. It can be seen, when the lecturer give chance to ask something, the student doesn’t give response. Usually the student afraid about their opinion or even they feel shy. In other word, communication is the process of delivering information or message from one to another. The aspect of the system communication is speaker, hearer, and message. We know that, communication is very important to get successful. A good communication in the teaching and learning program will happen if there is a good response between teacher and student.
Mathematics
What is mathematics? The definition of mathematics from one to another is different. Even, when greengrocer asked by people about the mark of rapport his children, they answer that the rapport very bad because the mark of mathematics is red. Mathematics isn’t only formula (c2= a2+ b2) but we must do a lot of exercise.
Now, we look what is the meaning of English?
English is not only tenses like present continuous tense (S+Tobe+V1ing) but English is ours. So, that English will not be broken even all of our English books burned out. If we read more, listen more, write more, and speak more so it can improve our knowledge in English. There for, students have to be responsible to there assignment.
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