(Small research of soul symptom a student Junior High School in Study mathematics problem)
In this article, I will try to observe the soul symptom of studying mathematics with listening to the music. Here I have respondent, her name is Siti Fatimah and she is third grade in SMP N (Junior High School) 1 Jetis Yogyakarta. She lives in Ngentak Timbulharjo Sewon Bantul.
Based on, her habitual activity if studying something. I will let Siti to turn on her radio and she can do the question while listening to the music. This observation does at Monday, 5 January 2008 in correspondence’s home at 13.00 pm. The mechanism of this observation is: the respondent will be given one mathematics problem. The observer let her to open the note. I will observe the soul symptom from the respondent when she solve the question.
The mathematics question that given to the respondent:
Eko buy 3 books and 2 pencils. He must pay Rp6.300,00. While Andy buy 1 book and 3 pencils, he must pay Rp4.200,00. How much money does mother pay, if she buys 1 book and 1 pencil?
The answer:
For example : the price of the book is x
The price of the pencil is y
The first equation : 3x + 2y = 6300
The second equation : x + 3y = 4200
Use the elimination and substitution method :
3x + 2y = 6300
x + 3y = 4200 second equation we multiply with 3
3x + 2y = 6300
3x + 9y = 12600
---------------- -
-7y = - 6300
y = 900
substitute y = 900 to the first equation :
3x + 2y = 6300
3x + 1800 = 6300
3x = 4500
x = 1500
Mother buy 1 book and 1 pencil, she must pay : 1500 + 900 = 2400 rupiah.
Here is the result of the observation :
• She could finish the question for 15 minutes 30 second
• She played the pencil during read the question
• She said that her teacher ever taught about the matter but she forgot it, so she must read the note before answer it.
• She sang when her favorites song played on the radio
• She changed the frequency of the radio when she doesn’t like the song.
The analyze of the result in observation :
She can do the question but her concentration is disturbed with the radio, it was proven with she did the question in 15 minutes 30 second. It is a long time to answer 1 easy question. She is more concentrate listening to the radio because the radio played her favorite band. So it’s mean that studying with listening to the music is not a good way because our concentration will divided to the question and the music.
Actually, correspondent doesn’t like mathematics lesson. But she understand if do linear equation problem because she ask her friend to teach her. She said that when his teacher while teaching in front of class, she and her friend often listening music with hand phone. She was bored because her teacher just always talked in front of class and seldom teaches with an innovative method. So it is one of our educational system problems especially in mathematics teaching learning method, we must change for the teacher centered to the student centered system. It’s for build creativity aspect from the student and the teacher.
BY : NURUL NOVIANI
07301244093
Pendidikan Matematika NR D “07
CP : 085729232345
Sabtu, 10 Januari 2009
Deepening and developing terminologies that appears in “PSIKOLOGI PEMBELAJARAN MATEMATIKA” lecturing by Dr. Marsigit
BY : NURUL NOVIANI
In “PSIKOLOGI PEMBELAJARAN MATEMATIKA” lecturing by Mr. Marsigit at Monday 1 December 2008. He is said some words with correlate with psychology. Several words that I write and still recall in my idea are “value psychology” and “problem communication”. In this opportunity I want to explain meaning from words above as according to my idea.
In life, we are found values that develop in it. Values has definition that is something that measurable and be good parameter or bad not it a certain. Of course, in science psychology found values that can we knew as value psychology. When somebody will learn psychology so indirectly he will find value in it. Psychology value explainable as something that be seen by somebody about the psychology and or matters that itself psychology science. So it can be said psychology value every body differs between one with another. This matter, depend on how far a person can detect value meaning in itself and can develop it eminently.
Human is social creature that he can not alive without another person. There factor dependence between one person with other. With communication everyone at world can mutual connected. But, in communicating not forever well, certain happened several problems that can disturb our communication. Problem communication can happen by some factor, caused by difference perception, differences competence, and differences motivation. Problem communication can happen in anywhere, anytime; for example when do we acres in class. On learning process, problem communication can happen between teacher and students. This matter will cause misunderstanding student to the material that taught by teacher. Finally student will not focus in matter and choose to talk with the friend and or play hp etc. Therefore, to avoid problem communication in the class the teacher must can creative in give the matter information so that student felt not bored, hear, and paid attention seriously. So, problem communication can happen in activity learn at class and can be overcome when teacher in teach has creativity to invite the student focus in lesson matter.
In “PSIKOLOGI PEMBELAJARAN MATEMATIKA” lecturing by Mr. Marsigit at Monday 1 December 2008. He is said some words with correlate with psychology. Several words that I write and still recall in my idea are “value psychology” and “problem communication”. In this opportunity I want to explain meaning from words above as according to my idea.
In life, we are found values that develop in it. Values has definition that is something that measurable and be good parameter or bad not it a certain. Of course, in science psychology found values that can we knew as value psychology. When somebody will learn psychology so indirectly he will find value in it. Psychology value explainable as something that be seen by somebody about the psychology and or matters that itself psychology science. So it can be said psychology value every body differs between one with another. This matter, depend on how far a person can detect value meaning in itself and can develop it eminently.
Human is social creature that he can not alive without another person. There factor dependence between one person with other. With communication everyone at world can mutual connected. But, in communicating not forever well, certain happened several problems that can disturb our communication. Problem communication can happen by some factor, caused by difference perception, differences competence, and differences motivation. Problem communication can happen in anywhere, anytime; for example when do we acres in class. On learning process, problem communication can happen between teacher and students. This matter will cause misunderstanding student to the material that taught by teacher. Finally student will not focus in matter and choose to talk with the friend and or play hp etc. Therefore, to avoid problem communication in the class the teacher must can creative in give the matter information so that student felt not bored, hear, and paid attention seriously. So, problem communication can happen in activity learn at class and can be overcome when teacher in teach has creativity to invite the student focus in lesson matter.
How to Uncover Psychological phenomena of mathematics Education by Applying Quantitative Method
BY : NURUL NOVIANI
07301244093
Pendidikan Matematika NR D “07
CP : 085729232345
Mathematics science not only about count, estimates, and uses formulas but also invites us to think creative and has mathematical thinking. In learn mathematics not only ability counts that need but also how do we solve problem by using manner think mathematics. Student that learn mathematics at class shows assorted psychological phenomena which them show when want to do a test. Student will want when do exercise in front of class, when has he do it, hotly he soon will progress and do it as soon as possible, but when can he felt not, he nervous and felt difficulty in do it. Psychological phenomena like this are evaluation aspect for student. Every teacher must give evaluation for every student that dare to progress to do exercise in front of class. This matter is make student motivation to learn mathematics. How to evaluate student development about cognitive aspect, affective, and psychometric is by using quantitative method.
Quantitative method is a research technique that is acres used to gather quantitative data-information dealing with numbers and anything that is measurable. It is a method assessment of liveliness of student contains cognitive aspect, affective and psychometric axis size measure intelligence of student.
(http://www.paranormality.com/quantitative_method)
So, with quantitative method teacher can evaluate development every student. At one particular chance, teacher can give evaluation to the student to evaluate his competence. A result from this evaluation can be in the form of data statistic, tables, and graph. The conclusion passes quantitative method, we are can uncover psychological phenomena of mathematics education.
07301244093
Pendidikan Matematika NR D “07
CP : 085729232345
Mathematics science not only about count, estimates, and uses formulas but also invites us to think creative and has mathematical thinking. In learn mathematics not only ability counts that need but also how do we solve problem by using manner think mathematics. Student that learn mathematics at class shows assorted psychological phenomena which them show when want to do a test. Student will want when do exercise in front of class, when has he do it, hotly he soon will progress and do it as soon as possible, but when can he felt not, he nervous and felt difficulty in do it. Psychological phenomena like this are evaluation aspect for student. Every teacher must give evaluation for every student that dare to progress to do exercise in front of class. This matter is make student motivation to learn mathematics. How to evaluate student development about cognitive aspect, affective, and psychometric is by using quantitative method.
Quantitative method is a research technique that is acres used to gather quantitative data-information dealing with numbers and anything that is measurable. It is a method assessment of liveliness of student contains cognitive aspect, affective and psychometric axis size measure intelligence of student.
(http://www.paranormality.com/quantitative_method)
So, with quantitative method teacher can evaluate development every student. At one particular chance, teacher can give evaluation to the student to evaluate his competence. A result from this evaluation can be in the form of data statistic, tables, and graph. The conclusion passes quantitative method, we are can uncover psychological phenomena of mathematics education.
The anxiety of mathematics teacher and the effect of their mathematic teaching learning method
by Nurul
At this opportunity, I will try to give a comment to an article that posted by Dr. Marsigit on Thursday, November 27, 2008 and the title is “The anxiety of mathematics teacher ant their problem”. My comment is based on my experience during become a student in school not in university. As long as is a student in Junior and High school, all of my mathematic teacher always use traditional teaching method. In each mathematic learning activity in class, my teacher just focuses on their ability student to answer mathematic question especially the material on national examination. Actually the purpose of studying are to make the student can do the problem, understand the material, and can applicant the material in daily activity. But if the teachers use traditional method, just a few of studying purpose can be reached by every student. Maybe, an anxiety of mathematics teacher know about the innovative teaching learning method, like problem solving, CTL, lesson study, etc. but they don’t pretend that innovative mathematics teaching learning method is the answer of student problem in mathematics learning. So they keep on their method with teacher centered not student centered.
As far I know, in the globalization era, every teacher must have an ability to produce the students that have a competence in international level. So the anxiety of mathematics teacher must change their thinking to make a teaching learning process that for the student comfort in class and the material can be understand. The final purpose is produce a student that not just know how to solve the mathematic problem but be a student that can applying their mathematical thinking in daily activity.
At this opportunity, I will try to give a comment to an article that posted by Dr. Marsigit on Thursday, November 27, 2008 and the title is “The anxiety of mathematics teacher ant their problem”. My comment is based on my experience during become a student in school not in university. As long as is a student in Junior and High school, all of my mathematic teacher always use traditional teaching method. In each mathematic learning activity in class, my teacher just focuses on their ability student to answer mathematic question especially the material on national examination. Actually the purpose of studying are to make the student can do the problem, understand the material, and can applicant the material in daily activity. But if the teachers use traditional method, just a few of studying purpose can be reached by every student. Maybe, an anxiety of mathematics teacher know about the innovative teaching learning method, like problem solving, CTL, lesson study, etc. but they don’t pretend that innovative mathematics teaching learning method is the answer of student problem in mathematics learning. So they keep on their method with teacher centered not student centered.
As far I know, in the globalization era, every teacher must have an ability to produce the students that have a competence in international level. So the anxiety of mathematics teacher must change their thinking to make a teaching learning process that for the student comfort in class and the material can be understand. The final purpose is produce a student that not just know how to solve the mathematic problem but be a student that can applying their mathematical thinking in daily activity.
Comment on Marsigit’s paper : presented at one day seminar “about the national Value, the value of mathematics, and the international standard” at Nov
by : Nurul
Globalization era bring assorted challenge that must be faced by everyone. Every country free to mutual cooperates and free to in concurrence to compete in the field of science and technology. For cogent country so it is the winner, if we want to survive for alive so matters that must we do overbearingly information technology and ability speaks, communication in English-speaking good. Indonesia as developing country must prepared itself face globalization challenge. All preparation must be done, from repair government performance and repair education in Indonesia. But is country Indonesia ready for repaired the education system? May be this be our homework all because see education development in Indonesia more concerned.
Based on the paper of Dr. Marsigit with the title “Gerakan Reformasi untuk Menggali dan Mengembangkan Nilai-Nilai Matematika untuk Menggapai Nilai-Nili Luhur Bangsa Menuju Standar Internasional Pendidikan”, there are many things in education system of Indonesia that must be reform. Begin from the moral values and the system because as far I know, the educational system in Indonesia popular with not transparence system, there is a lot of KKN (corruption, collusion, and nepotism). This matter cause’s country is looked at ugly at world eye. matter that can happen Indonesia original ones will be removed from rivalry, many unemployment, work vacancy is taken by foreign labors caused by global market that opens for who opportunity to work at country other.
By the way, I am really agreed with Mr. Marsigit’s paper to reform the educational system in Indonesia and bring it to denunciated international standardization. I am thought, with the standardization, society accustomed to world international that has criteria-criteria particularly. But both merely system education that must be changed but also the teacher must have competence that supports. Therefore must there how be teacher creative, especially in mathematics lesson that intimidated by a part student. Government and Indonesia citizen must mutual cooperate to repair education system in Indonesia. education reformation very need to repair Indonesia the rising generation moral and cause the loss of corruption, collusion, and nepotism (KKN) with increase teacher competence so that proper aim international standardization.
Reference:
Dr. Marsigit’s paper at one day seminar about the national value, the value of mathematics and International standard at November 30th 2008
Globalization era bring assorted challenge that must be faced by everyone. Every country free to mutual cooperates and free to in concurrence to compete in the field of science and technology. For cogent country so it is the winner, if we want to survive for alive so matters that must we do overbearingly information technology and ability speaks, communication in English-speaking good. Indonesia as developing country must prepared itself face globalization challenge. All preparation must be done, from repair government performance and repair education in Indonesia. But is country Indonesia ready for repaired the education system? May be this be our homework all because see education development in Indonesia more concerned.
Based on the paper of Dr. Marsigit with the title “Gerakan Reformasi untuk Menggali dan Mengembangkan Nilai-Nilai Matematika untuk Menggapai Nilai-Nili Luhur Bangsa Menuju Standar Internasional Pendidikan”, there are many things in education system of Indonesia that must be reform. Begin from the moral values and the system because as far I know, the educational system in Indonesia popular with not transparence system, there is a lot of KKN (corruption, collusion, and nepotism). This matter cause’s country is looked at ugly at world eye. matter that can happen Indonesia original ones will be removed from rivalry, many unemployment, work vacancy is taken by foreign labors caused by global market that opens for who opportunity to work at country other.
By the way, I am really agreed with Mr. Marsigit’s paper to reform the educational system in Indonesia and bring it to denunciated international standardization. I am thought, with the standardization, society accustomed to world international that has criteria-criteria particularly. But both merely system education that must be changed but also the teacher must have competence that supports. Therefore must there how be teacher creative, especially in mathematics lesson that intimidated by a part student. Government and Indonesia citizen must mutual cooperate to repair education system in Indonesia. education reformation very need to repair Indonesia the rising generation moral and cause the loss of corruption, collusion, and nepotism (KKN) with increase teacher competence so that proper aim international standardization.
Reference:
Dr. Marsigit’s paper at one day seminar about the national value, the value of mathematics and International standard at November 30th 2008
kamus matematika
Akar: bilangan yang menyelesaikan suatu persamaan; yaitu saat disubstitusikan ke dalam persamaan sebagai bilangan tidak diketahui, di kanan maupun di kiri tanda sama dengan mempunyai nilai sama.
Aksioma: logika atau matematika yang tidak dapat dibuktikan namun sahih.
Bilangan aljabarik: bilangan yang menjadi solusi bagi polinomial dimana koefisien-koefisiennya semuanya adalah bilangan-bilangan rasional.
Bilangan hiperkompleks: suatu bilangan yang terbentuk dari perluasan konsep bilangan untuk dimensi-dimensi dalam lingkup bilangan kompleks dua-dimensi.
Bilangan imajiner: suatu bilangan yang berada pada absis vertikal dalam bidang bilangan kompleks; bilangan dalam bentuk ai dimana a adalah bilangan riel dan i adalah v-1.
Bilangan irrasional: suatu bilangan riel yang tidak dapat diekspresikan dalam bentuk perbandingan (rasio/nisbah) dari kedua bilangan.
Bilangan kardinal: bilangan tertentu yang menyatakan berapa banyak elemen-elemen yang terdapat dalam suatu himpunan.
Bilangan ordinal: bilangan tertentu yang menyatakan posisi relatif dari suatu elemen yang terdapat dalam suatu himpunan.
Bilangan prima: bilangan natural yang hanya dapat dibagi oleh bilangan itu sendiri dan bilangan satu.
Bilangan riel: bilangan yang diasosiasikan dengan semua titik-titik pada garis bilangan; gabungan antara bilangan-bilangan aljabarik dan bilangan-bilangan transendental.
Bilangan sempurna: suatu bilangan natural yang merupakan hasil perjumlahan dari bilangan-bilangan pembaginya. Contoh: 6 = 1 + 2 + 3
Binomial: sebuah pernyataan aljabar yang terdiri dari dua suku.
Contoh: 3x + 5y; 2x4 – 4xyz3
Digit: salah satu dari sepuluh bilangan numeral 0, 1, 2, 3, 4, 5, 6, 7, 8, dan 9 dari sistem bilangan Hindu-Arabik.
Divergen: pernyataan urutan bilangan-bilangan atau deret bilangan-bilangan yang tidak mempunyai batas atau limit.
Elips: Tempat kedudukan atau himpunan titik-titik pada bidang datar yang jumlah jaraknya terhadap dua titik adalah tetap dan merupakan bilangan tertentu, kedua titik tetap disebut fokus.
Empat operasi: dalam aljabar sebagaimana dalam ilmu-hitung (aritmatika), adalah penjumlahan, pengurangan, perkalian dan pembagian.
Faktorial: hasil dari semua bilangan natural lebih kecil atau sama dengan bilangan naturan yang dinyatakan secara spesifik. Contoh, 5! = 1.2.3.4.5 = 120.
Geometri Euclidian: geometri yang dikembangkan oleh Euclid yang berisikan dengan postulat kesejajaran yaitu: pada garis tertentu dan titik di luar garis, ada satu dan hanya ada satu garis lain yang dapat dibuat melewati titik itu dan sejajar dengan garis pertama.
Geometri Non-Euclidian: geometri yang tidak lagi mendasarkan diri pada postulat kesejajaran.
Geometri proyektif: cabang matematika yang terkait dengan bentuk-bentuk geometrikal yang tidak aklan berubah ketika bentuk-bentuk itu diproyeksikan ke bidang yang berbeda.
Harga mutlak: nilai hitung sebuah bilangan berarti bilangan dengan tidak memperhatikan tandanya. Harga mutlak ditunjukkan dengan 2 garis vertikal yang mengelilinginya.
Hiperbola: Tempat kedudukan atau himpunan titik-titik pada bidang datar yang selisih jaraknya terhadap 2 titik tetap merupakan bilangan-bilangan tertentu.
Integer: himpunan bilangan yang terdiri dari bilangan positif dan bilangan negatif termasuk bilangan nol.
Konvergen: pernyataan urutan bilangan-bilangan atau deret bilangan-bilangan yang mendekati limit.
Lingkaran: tempat kedudukan titik-titik (himpunan titik-titik) yang berjarak sama terhadap sebuah titik tertentu.
Origin: suatu titik pada garis bilangan yang diasosiakan dengan angka nol, atau titik pada bidang bilangan kompleks dimana kedua aksis berpotongan.
Parabola:
- Tempat kedudukan titik-titik yang berjarak sama terhadap sebuah titik (disebut fokus) dan sebuah garis (disebut direktriks) tertentu.
- Setiap ruas garis penghubung-penghubung tertentu pada parabola disebut titik busur. Tali busur fokal (melewati fokus) yang sejajar dengan direktriks atau tegak lurus sumbu disebut latus rectum.
Paradoks: suatu alasan yang konklusi-konklusinya sendiri saling bertentangan lewat deduksi sahih yang berasal dari premis-premis yang disepakati secara intuitif.
Persamaan polinomial: persamaan dengan satu atau lebih peubah tidak diketahui dalam bentuk pangkat dan dikalikan dengan bilangan-bilangan yang disebut koefisien-koefisien. Persamaan polinomial dengan satu peubah, x, mempunyai bentuk umum
a0xn + a1xn-1 + … + an-1x + an = 0
Polinomial: sebuah monomial atau multinomial yang setiap suku adalah integral dan rasional dari huruf-huruf.
Contoh: 5x2y3 – 7x4y + 3x + 2
Quaternions: bilangan kompleks dalam bentuk a + bi + cj + dk dimana a, b, c dan d adalah bilangan riel dan i, j, k adalah bilangan hiperkompleks yang dapat ditulis bentuk
i² = j² = k² = ijk = -1.
Radikal: pernyataan berbentuk nva yang berati akar pangkat n bilangan a. Bilangan positif n adalah indeks dari radikal dan bilangan a adalah radikan. Apabila n = 2, maka indeks dihilangkan.
Theorema: pernyataan atau formula yang dideduksi dari seperangkat aksioma dan/atau theorema-theorema lain.
Berasal dari bahasa Yunani yang artinya pernyataan matematikal yang dilengkapi dengan bukti. Pembuktian theorema mempunyai kebenaran dasar yang akurat dan tidak dapat disangkal dan disanggah oleh siapapun yang mengikuti ketentuan-ketentuan logika, juga bagi siapapun yang menerima aksioma-aksioma mendasar sistem logika.
Trigonometri: ilmu tentang keterhubungan antara sisi-sisi dari suatu segitiga dan pengukuran-pengukuran terhadap sudut-sudut didalamnya
Semoga dapat membantu…^_^
Dikutip dari berbagai sumber……….
Aksioma: logika atau matematika yang tidak dapat dibuktikan namun sahih.
Bilangan aljabarik: bilangan yang menjadi solusi bagi polinomial dimana koefisien-koefisiennya semuanya adalah bilangan-bilangan rasional.
Bilangan hiperkompleks: suatu bilangan yang terbentuk dari perluasan konsep bilangan untuk dimensi-dimensi dalam lingkup bilangan kompleks dua-dimensi.
Bilangan imajiner: suatu bilangan yang berada pada absis vertikal dalam bidang bilangan kompleks; bilangan dalam bentuk ai dimana a adalah bilangan riel dan i adalah v-1.
Bilangan irrasional: suatu bilangan riel yang tidak dapat diekspresikan dalam bentuk perbandingan (rasio/nisbah) dari kedua bilangan.
Bilangan kardinal: bilangan tertentu yang menyatakan berapa banyak elemen-elemen yang terdapat dalam suatu himpunan.
Bilangan ordinal: bilangan tertentu yang menyatakan posisi relatif dari suatu elemen yang terdapat dalam suatu himpunan.
Bilangan prima: bilangan natural yang hanya dapat dibagi oleh bilangan itu sendiri dan bilangan satu.
Bilangan riel: bilangan yang diasosiasikan dengan semua titik-titik pada garis bilangan; gabungan antara bilangan-bilangan aljabarik dan bilangan-bilangan transendental.
Bilangan sempurna: suatu bilangan natural yang merupakan hasil perjumlahan dari bilangan-bilangan pembaginya. Contoh: 6 = 1 + 2 + 3
Binomial: sebuah pernyataan aljabar yang terdiri dari dua suku.
Contoh: 3x + 5y; 2x4 – 4xyz3
Digit: salah satu dari sepuluh bilangan numeral 0, 1, 2, 3, 4, 5, 6, 7, 8, dan 9 dari sistem bilangan Hindu-Arabik.
Divergen: pernyataan urutan bilangan-bilangan atau deret bilangan-bilangan yang tidak mempunyai batas atau limit.
Elips: Tempat kedudukan atau himpunan titik-titik pada bidang datar yang jumlah jaraknya terhadap dua titik adalah tetap dan merupakan bilangan tertentu, kedua titik tetap disebut fokus.
Empat operasi: dalam aljabar sebagaimana dalam ilmu-hitung (aritmatika), adalah penjumlahan, pengurangan, perkalian dan pembagian.
Faktorial: hasil dari semua bilangan natural lebih kecil atau sama dengan bilangan naturan yang dinyatakan secara spesifik. Contoh, 5! = 1.2.3.4.5 = 120.
Geometri Euclidian: geometri yang dikembangkan oleh Euclid yang berisikan dengan postulat kesejajaran yaitu: pada garis tertentu dan titik di luar garis, ada satu dan hanya ada satu garis lain yang dapat dibuat melewati titik itu dan sejajar dengan garis pertama.
Geometri Non-Euclidian: geometri yang tidak lagi mendasarkan diri pada postulat kesejajaran.
Geometri proyektif: cabang matematika yang terkait dengan bentuk-bentuk geometrikal yang tidak aklan berubah ketika bentuk-bentuk itu diproyeksikan ke bidang yang berbeda.
Harga mutlak: nilai hitung sebuah bilangan berarti bilangan dengan tidak memperhatikan tandanya. Harga mutlak ditunjukkan dengan 2 garis vertikal yang mengelilinginya.
Hiperbola: Tempat kedudukan atau himpunan titik-titik pada bidang datar yang selisih jaraknya terhadap 2 titik tetap merupakan bilangan-bilangan tertentu.
Integer: himpunan bilangan yang terdiri dari bilangan positif dan bilangan negatif termasuk bilangan nol.
Konvergen: pernyataan urutan bilangan-bilangan atau deret bilangan-bilangan yang mendekati limit.
Lingkaran: tempat kedudukan titik-titik (himpunan titik-titik) yang berjarak sama terhadap sebuah titik tertentu.
Origin: suatu titik pada garis bilangan yang diasosiakan dengan angka nol, atau titik pada bidang bilangan kompleks dimana kedua aksis berpotongan.
Parabola:
- Tempat kedudukan titik-titik yang berjarak sama terhadap sebuah titik (disebut fokus) dan sebuah garis (disebut direktriks) tertentu.
- Setiap ruas garis penghubung-penghubung tertentu pada parabola disebut titik busur. Tali busur fokal (melewati fokus) yang sejajar dengan direktriks atau tegak lurus sumbu disebut latus rectum.
Paradoks: suatu alasan yang konklusi-konklusinya sendiri saling bertentangan lewat deduksi sahih yang berasal dari premis-premis yang disepakati secara intuitif.
Persamaan polinomial: persamaan dengan satu atau lebih peubah tidak diketahui dalam bentuk pangkat dan dikalikan dengan bilangan-bilangan yang disebut koefisien-koefisien. Persamaan polinomial dengan satu peubah, x, mempunyai bentuk umum
a0xn + a1xn-1 + … + an-1x + an = 0
Polinomial: sebuah monomial atau multinomial yang setiap suku adalah integral dan rasional dari huruf-huruf.
Contoh: 5x2y3 – 7x4y + 3x + 2
Quaternions: bilangan kompleks dalam bentuk a + bi + cj + dk dimana a, b, c dan d adalah bilangan riel dan i, j, k adalah bilangan hiperkompleks yang dapat ditulis bentuk
i² = j² = k² = ijk = -1.
Radikal: pernyataan berbentuk nva yang berati akar pangkat n bilangan a. Bilangan positif n adalah indeks dari radikal dan bilangan a adalah radikan. Apabila n = 2, maka indeks dihilangkan.
Theorema: pernyataan atau formula yang dideduksi dari seperangkat aksioma dan/atau theorema-theorema lain.
Berasal dari bahasa Yunani yang artinya pernyataan matematikal yang dilengkapi dengan bukti. Pembuktian theorema mempunyai kebenaran dasar yang akurat dan tidak dapat disangkal dan disanggah oleh siapapun yang mengikuti ketentuan-ketentuan logika, juga bagi siapapun yang menerima aksioma-aksioma mendasar sistem logika.
Trigonometri: ilmu tentang keterhubungan antara sisi-sisi dari suatu segitiga dan pengukuran-pengukuran terhadap sudut-sudut didalamnya
Semoga dapat membantu…^_^
Dikutip dari berbagai sumber……….
The connections between mathematics study with anyone’s contemplative faculties (thinking ability)
When we was born, God has give on 3 matters very valuable for us as human, that is time, contemplative faculties, and ability learns. God gives us all times same that is 24 clocks a day, 1.440 minute, or 86.400 second. God very fair in distribute every thing to the creation result. Belong at the present time problem. God never give different time total to us.
God also give same to all humans, which are contemplative faculties. Biologically may be this contemplative faculties is defined as brain volume same at every human. God also valid have an intention create human ably limited contemplative faculties, alias low IQ. It doesn’t because of God not pity to it, but God gives all that upon which contemplation and study. But basically all humans are given same thing, which are contemplative faculties.
Ability to learn also one of the big gifts that is given by God to us. unconsciously, we are final can to speak, can to walk, can to read, write, and can to do everything, caused by ability learns. We can study certain, and final can do certain that.
Between third gift a while ago, ability learns that given god to every human really same. But god gives freedom to us, give to chance to us to be able to then develop ability learns. Differ from time and contemplative faculties that appointed limit by god.
Article on top is quotation from a blog. Follow me individual, somebody contemplative faculties amendable with increase ability learn it. So, ability learns can be analogized as vehicle to achieve a place, place here that is contemplative faculties that developed. Really contemplative faculties’ capacity there [are] the limit. But, clever human even if, new use several percents from power capacity think it. So permanent, follow me somebody contemplative faculties amendable not capacity (the volume), but the ability.
Does the connection with mathematics? As we know, one of the aims learns mathematics form reasonable patterned thinking, systematic, critical, analytical, and creative.
mathematics comprehension construction form in this time developed even inclined be a “movement” mathematics study model study among others: constructivism, problem solving, problem posing, realistic mathematics education, open-ended approach, communication in mathematics, methacognitif model, cooperative learning, and reinvention in mathematic.
in this time, mathematics study innovation as keyword to overcome problematical mathematics study at high school is realized in the form of “distribution movement” technique/model/ strategy/approach mathematics study (he said) take root in need and habit realistic student at the alive environment everyday. “New object” this given contextual mathematics study name (CTL- contextual teaching and learning - is adopted from the original contextual mathematics).
In daily activity, it is sure that very vast utilization from this mathematics. Why be said very vast? Because in event or an incidents everyday, there are some unconsciously actually found mathematics element in it. Even formerly Pythagoras say that everything exists in world comes from number. So, really that mathematics is there and useful in our life. Why is there one who not yet feel benefit big from mathematics? because may be they are not yet study truly or not yet realize aim learns itself mathematics, also not yet take the benefit. Example, about predict nature phenomenon. That wears also mathematics science. But some people may be saying, that phenomenon only by accident.
How can manner can get patterned thinking that can be taken the benefit from learn mathematics so that ability think one can bloom? In article “developing mathematical thinking” in book thinking mathematically work Kaye Stacey et al., mentioned several the alternative, that is first attitude that must has self confidence. If find a life internal issue everyday, assure own self that I can.
Questioning:
I am can identify questions for investigation, query mine is assumptions, negotiate meanings of ms.
Challenging:
I am can make conjectures, seek justifying or falsifying arguments, check, modify, and alter.
Reflecting:
I am can be self-critical, expect and assess deferent approaches, shift, re-negotiate, change direction.
From article above, can be taken a conclusion, when not yet detect to how manner finish a problem big, begin to try with little problem that resembles with big problem a while ago. Thereby, can be seen problem pattern to then be looked for the completion manner. When never try manner break problem like that, likely difficult. Proved that is by using mathematics way of thinking, we can finish problem or life internal issue everyday. Again, I agree with opinion several mathematicians that benefit learns that mathematics very vast and can be used in life, everyday.
God also give same to all humans, which are contemplative faculties. Biologically may be this contemplative faculties is defined as brain volume same at every human. God also valid have an intention create human ably limited contemplative faculties, alias low IQ. It doesn’t because of God not pity to it, but God gives all that upon which contemplation and study. But basically all humans are given same thing, which are contemplative faculties.
Ability to learn also one of the big gifts that is given by God to us. unconsciously, we are final can to speak, can to walk, can to read, write, and can to do everything, caused by ability learns. We can study certain, and final can do certain that.
Between third gift a while ago, ability learns that given god to every human really same. But god gives freedom to us, give to chance to us to be able to then develop ability learns. Differ from time and contemplative faculties that appointed limit by god.
Article on top is quotation from a blog. Follow me individual, somebody contemplative faculties amendable with increase ability learn it. So, ability learns can be analogized as vehicle to achieve a place, place here that is contemplative faculties that developed. Really contemplative faculties’ capacity there [are] the limit. But, clever human even if, new use several percents from power capacity think it. So permanent, follow me somebody contemplative faculties amendable not capacity (the volume), but the ability.
Does the connection with mathematics? As we know, one of the aims learns mathematics form reasonable patterned thinking, systematic, critical, analytical, and creative.
mathematics comprehension construction form in this time developed even inclined be a “movement” mathematics study model study among others: constructivism, problem solving, problem posing, realistic mathematics education, open-ended approach, communication in mathematics, methacognitif model, cooperative learning, and reinvention in mathematic.
in this time, mathematics study innovation as keyword to overcome problematical mathematics study at high school is realized in the form of “distribution movement” technique/model/ strategy/approach mathematics study (he said) take root in need and habit realistic student at the alive environment everyday. “New object” this given contextual mathematics study name (CTL- contextual teaching and learning - is adopted from the original contextual mathematics).
In daily activity, it is sure that very vast utilization from this mathematics. Why be said very vast? Because in event or an incidents everyday, there are some unconsciously actually found mathematics element in it. Even formerly Pythagoras say that everything exists in world comes from number. So, really that mathematics is there and useful in our life. Why is there one who not yet feel benefit big from mathematics? because may be they are not yet study truly or not yet realize aim learns itself mathematics, also not yet take the benefit. Example, about predict nature phenomenon. That wears also mathematics science. But some people may be saying, that phenomenon only by accident.
How can manner can get patterned thinking that can be taken the benefit from learn mathematics so that ability think one can bloom? In article “developing mathematical thinking” in book thinking mathematically work Kaye Stacey et al., mentioned several the alternative, that is first attitude that must has self confidence. If find a life internal issue everyday, assure own self that I can.
Questioning:
I am can identify questions for investigation, query mine is assumptions, negotiate meanings of ms.
Challenging:
I am can make conjectures, seek justifying or falsifying arguments, check, modify, and alter.
Reflecting:
I am can be self-critical, expect and assess deferent approaches, shift, re-negotiate, change direction.
From article above, can be taken a conclusion, when not yet detect to how manner finish a problem big, begin to try with little problem that resembles with big problem a while ago. Thereby, can be seen problem pattern to then be looked for the completion manner. When never try manner break problem like that, likely difficult. Proved that is by using mathematics way of thinking, we can finish problem or life internal issue everyday. Again, I agree with opinion several mathematicians that benefit learns that mathematics very vast and can be used in life, everyday.
Istilah dalam Psikologi
Beberapa istilah yang mungkin akan anda temui dalam ilmu psikologi :
• Anima : kata latin untuk “jiwa”, yang digunakan Jung untuk menunjukkan lapisan “bawah-sadar” yang lebih daripada “bayang-bayang”nya.
• Asosiasi bebas (free-association) : metode “psikoanalisis” yang didalamnya seseorang secara terbuka melaporkan kepada terapis segala sesuatu yang memasuki pikiran sadarnya sewaktu hal itu muncul. Prosesnya sering berawal dengan pengajuan kata atau sejumlah kata secara acak oleh terapis. Bagi terapis, tujuannya adalah mendeteksi pengaruh “bawah sadar” yang mengendalikan asosiasi itu.
• Bawah-sadar (unconscious): Aspek psiki yang mengandung segala sesuatu yang tidak mudah diakses ke bidang kesadaran terdekat.
• Behaviorisme (behaviorism) : ilmu yang didirikan oleh John B. Watson dan dipopulerkan B.F Skinner, yang mendefinisikan psikologi sebagai studi tentang aktivitas-aktivitas yang bisa diamati (yaitu perilaku).
• Delusi (delusion) : keyakinan sesat yang tidak akan dilepas walaupun bukti kesesatannya dihadirkan.
• Jiwa (soul) : salah satu dari tiga aspek kodrat manusia, yang keabadiannya dihadirkan oleh Plato dan lain-lain.
• Neurosis : kondisi psikologis yang didalamnya pola perilaku abnormal timbul sebagai akibat dari ketidakmampuan dalam menghadapi kecemasan dengan cara-cara yang bisa diterima secara sosial.
Dikutip dari :
http://trescent.wordpress.com/2007/04/04/istilah-dalam-psikologi/
• Anima : kata latin untuk “jiwa”, yang digunakan Jung untuk menunjukkan lapisan “bawah-sadar” yang lebih daripada “bayang-bayang”nya.
• Asosiasi bebas (free-association) : metode “psikoanalisis” yang didalamnya seseorang secara terbuka melaporkan kepada terapis segala sesuatu yang memasuki pikiran sadarnya sewaktu hal itu muncul. Prosesnya sering berawal dengan pengajuan kata atau sejumlah kata secara acak oleh terapis. Bagi terapis, tujuannya adalah mendeteksi pengaruh “bawah sadar” yang mengendalikan asosiasi itu.
• Bawah-sadar (unconscious): Aspek psiki yang mengandung segala sesuatu yang tidak mudah diakses ke bidang kesadaran terdekat.
• Behaviorisme (behaviorism) : ilmu yang didirikan oleh John B. Watson dan dipopulerkan B.F Skinner, yang mendefinisikan psikologi sebagai studi tentang aktivitas-aktivitas yang bisa diamati (yaitu perilaku).
• Delusi (delusion) : keyakinan sesat yang tidak akan dilepas walaupun bukti kesesatannya dihadirkan.
• Jiwa (soul) : salah satu dari tiga aspek kodrat manusia, yang keabadiannya dihadirkan oleh Plato dan lain-lain.
• Neurosis : kondisi psikologis yang didalamnya pola perilaku abnormal timbul sebagai akibat dari ketidakmampuan dalam menghadapi kecemasan dengan cara-cara yang bisa diterima secara sosial.
Dikutip dari :
http://trescent.wordpress.com/2007/04/04/istilah-dalam-psikologi/
Kamis, 01 Januari 2009
Gejala-Gejala Kejiwaan Seorang Pembelajar Matematika
(Suatu Studi Kasus Siswa SD, SMP, dan SMA dalam Belajar Matematika)
A. Landasan Teori
Teori Belajar Kognitif oleh Jean Piaget, mengatakan : Pendekatan psikologi kognitif menekankan arti pentingnya proses internal mental manusia. Menurut teori ini, proses belajar akan berjalan dengan baik bila materi yang baru, beradaptasi secara tepat dan serasi dengan struktur kognitif yang telah dimiliki siswa. Jadi, belajar merupakan proses aktif dari pembelajar untuk membangun struktur pengetahuannya sendiri.
B. Hipotesa
Ada pengaruh factor internal (strukutr kognisi) terhadap cara belajar seorang pembelajar matematika.
C. Data
Biodata nara sumber :
1.Nama lengkap : Salsa Indriyati
TTL : Jakarta, 26 Februari 2002
Alamat rumah : Ngentak, Timbulharjo Sewon Bantul
Nama sekolah : SD N Pacar
Kelas : 1 (satu)
2. Nama lengkap : Novita Febri Kinayungan
TTL : Kalimantan Barat, 1 Februari 2001
Alamat rumah : Ngentak, Timbulharjo Sewon Bantul
Nama sekolah : SD N Pacar
Kelas : 2 (dua)
3. Nama lengkap : Siti Fatimah
TTL : Bantul, 11 Maret 1993
Alamat rumah : Ngentak, Timbulharjo Sewon Bantul
Nama sekolah : SMP N 1 Jetis
Kelas : 3 (IX)
4. Nama lengkap : Lina Latifah
TTL : Bantul, 4 Juni 1992
Alamat rumah : Ngentak, Timbulharjo Sewon Bantul
Nama sekolah : SMA Muhammadiyah I Bantul
Kelas : 1 (X)
D.Hasil wawancara
Keterangan :
--> Salsa dan Febri menyenangi matematika karena di rumah ataupun di sekolah, semua orang memberikan motivasi untuk mereka rajin belajar seperti memberikan permen ataupun makanan apabila bisa menjawab pertanyaan yang diberikan.
--> Siti dan lina lebih memilih ilmu social ataupun kesenian daripada harus menghafal rumus dan mengerjakan soal matematika.
E. Pembahasan
Pelaksana studi kasus ini adalah saya sendiri dengan nara sumber 4 siswa yang merupakan tetangga saya, yang bernama Febri, Salsa, Siti, dan Lina. Pada studi kasus ini, saya menggunakan metode wawancara (Tanya jawab). Sebagian besar responden menunjukkan rasa antusias dalam kegiatan wawancara ini.
Berdasarkan hasil wawancara, dapat diperoleh bahwa untuk siswa SD, rasa senangnya mempelajari matematika lebih besar daripada siswa SMP maupun SMA. Hal ini dikarenakan bagi siswa SD pelajaran matematika merupakan pelajaran hitung-menghitung yang mudah dan penerapannya dapat mudah dijumpai dalam kehidupan sehari-hari, sedangkan untuk siswa SMP dan SMA mengaanggap pelajaran matematika itu sulit karena banyak rumus-rumus yang perlu dipahami dan hitungan angkanya yang semakin rumit serta simbol-simbol/ lambang matematika yang semakin banyak muncul.
Rasa kesukaannya terhadap matematika mempengaruhi mereka dalam frekuensi belajar matematika. Untuk anak SD, 1 atau 2 jam adalah waktu yang diperlukan untuk belajart matematika bahkan dalam aktivitas bermainnya mereka secara tidak sadar melakukan operasi-operasi bilangan seperti permainan petak umpet, yang jaga harus menghitung dari 1-20. sedangkan untuk anak SMP dan SMA sudah beranggapan “matematika tiada hari tanpa ada PR” sehingga mereka hanya terpaksa belajar matematika dan tidak memahami secara benar-benar pelajaran matematika itu sendiri dan pada tugas-tugas selanjutnya mereka mengalami kesulitan.
Hal-hal yang mempengaruhi mereka untuk belajar matematika adalah :
- rasa kesenangan akan pelajaran matematika itu sendiri
- perhatian orang tua, teman, dan guru dalam memotivasi mereka untuk belajar
- hadiah yang akan diberikan sebagai tanda keberhasilan dalam belajar
Bagi anak-anak SD faktor yang berperan untuk memotivasinya belajar matematika adalah pada dirinya sendiri, orang tua, dan guru. Pada masa ini, anak-anak akan senang belajar sesuatu apabila dia menyukainya dan ada perintah dari orang tua ataupun guru karena pada tahap ini anak-anak dengan patuhnya mengerjakan apapun yang dikatakan orang tua dan gurunya. Sedangkan bagi anak-anak SMP dan SMA, motivasi untuk belajar matematika harus berlandaskan kesadaran diri bahwa matematika itu penting dan rasa kesukaannya juga ikut mempengaruhi mereka untuk belajar. Apabila ada anggapan bahwa matematika itu sulit, hal itu tergantung individu masing-masing untuk mengubah persepsi itu, karena apabila dipahami bahwa matematika itu bukan hanya hafalan rumus maka secara berangsur-angsur kiata akan bisa menganggap matematika itu mudah.
Jadi dapat disimpulkan bahwa faktor internal (struktur kognisi) pengetahuan awal yang dimiliki seorang siswa akan mempengaruhinya dalam belajar matematika. Apabila dia merasa senang, menganggap matematika mudah (hanya berupa hitung-menghitung menggunakan angka dari 0-9) maka dengan sendirinya dia akan senang belajar matematika. Begitupun sebaliknya, apabila di dalam pikirannya menganggap matematika itu sulit, maka secara tidak sadar, dia tidak akan termotivasi untuk belajar dan akhirnya mengalami kesulitan belajar.
BY : NURUL NOVIANI
07301244093
Pendidikan Matematika NR D “07
CP : 085729232345
A. Landasan Teori
Teori Belajar Kognitif oleh Jean Piaget, mengatakan : Pendekatan psikologi kognitif menekankan arti pentingnya proses internal mental manusia. Menurut teori ini, proses belajar akan berjalan dengan baik bila materi yang baru, beradaptasi secara tepat dan serasi dengan struktur kognitif yang telah dimiliki siswa. Jadi, belajar merupakan proses aktif dari pembelajar untuk membangun struktur pengetahuannya sendiri.
B. Hipotesa
Ada pengaruh factor internal (strukutr kognisi) terhadap cara belajar seorang pembelajar matematika.
C. Data
Biodata nara sumber :
1.Nama lengkap : Salsa Indriyati
TTL : Jakarta, 26 Februari 2002
Alamat rumah : Ngentak, Timbulharjo Sewon Bantul
Nama sekolah : SD N Pacar
Kelas : 1 (satu)
2. Nama lengkap : Novita Febri Kinayungan
TTL : Kalimantan Barat, 1 Februari 2001
Alamat rumah : Ngentak, Timbulharjo Sewon Bantul
Nama sekolah : SD N Pacar
Kelas : 2 (dua)
3. Nama lengkap : Siti Fatimah
TTL : Bantul, 11 Maret 1993
Alamat rumah : Ngentak, Timbulharjo Sewon Bantul
Nama sekolah : SMP N 1 Jetis
Kelas : 3 (IX)
4. Nama lengkap : Lina Latifah
TTL : Bantul, 4 Juni 1992
Alamat rumah : Ngentak, Timbulharjo Sewon Bantul
Nama sekolah : SMA Muhammadiyah I Bantul
Kelas : 1 (X)
D.Hasil wawancara
Keterangan :
--> Salsa dan Febri menyenangi matematika karena di rumah ataupun di sekolah, semua orang memberikan motivasi untuk mereka rajin belajar seperti memberikan permen ataupun makanan apabila bisa menjawab pertanyaan yang diberikan.
--> Siti dan lina lebih memilih ilmu social ataupun kesenian daripada harus menghafal rumus dan mengerjakan soal matematika.
E. Pembahasan
Pelaksana studi kasus ini adalah saya sendiri dengan nara sumber 4 siswa yang merupakan tetangga saya, yang bernama Febri, Salsa, Siti, dan Lina. Pada studi kasus ini, saya menggunakan metode wawancara (Tanya jawab). Sebagian besar responden menunjukkan rasa antusias dalam kegiatan wawancara ini.
Berdasarkan hasil wawancara, dapat diperoleh bahwa untuk siswa SD, rasa senangnya mempelajari matematika lebih besar daripada siswa SMP maupun SMA. Hal ini dikarenakan bagi siswa SD pelajaran matematika merupakan pelajaran hitung-menghitung yang mudah dan penerapannya dapat mudah dijumpai dalam kehidupan sehari-hari, sedangkan untuk siswa SMP dan SMA mengaanggap pelajaran matematika itu sulit karena banyak rumus-rumus yang perlu dipahami dan hitungan angkanya yang semakin rumit serta simbol-simbol/ lambang matematika yang semakin banyak muncul.
Rasa kesukaannya terhadap matematika mempengaruhi mereka dalam frekuensi belajar matematika. Untuk anak SD, 1 atau 2 jam adalah waktu yang diperlukan untuk belajart matematika bahkan dalam aktivitas bermainnya mereka secara tidak sadar melakukan operasi-operasi bilangan seperti permainan petak umpet, yang jaga harus menghitung dari 1-20. sedangkan untuk anak SMP dan SMA sudah beranggapan “matematika tiada hari tanpa ada PR” sehingga mereka hanya terpaksa belajar matematika dan tidak memahami secara benar-benar pelajaran matematika itu sendiri dan pada tugas-tugas selanjutnya mereka mengalami kesulitan.
Hal-hal yang mempengaruhi mereka untuk belajar matematika adalah :
- rasa kesenangan akan pelajaran matematika itu sendiri
- perhatian orang tua, teman, dan guru dalam memotivasi mereka untuk belajar
- hadiah yang akan diberikan sebagai tanda keberhasilan dalam belajar
Bagi anak-anak SD faktor yang berperan untuk memotivasinya belajar matematika adalah pada dirinya sendiri, orang tua, dan guru. Pada masa ini, anak-anak akan senang belajar sesuatu apabila dia menyukainya dan ada perintah dari orang tua ataupun guru karena pada tahap ini anak-anak dengan patuhnya mengerjakan apapun yang dikatakan orang tua dan gurunya. Sedangkan bagi anak-anak SMP dan SMA, motivasi untuk belajar matematika harus berlandaskan kesadaran diri bahwa matematika itu penting dan rasa kesukaannya juga ikut mempengaruhi mereka untuk belajar. Apabila ada anggapan bahwa matematika itu sulit, hal itu tergantung individu masing-masing untuk mengubah persepsi itu, karena apabila dipahami bahwa matematika itu bukan hanya hafalan rumus maka secara berangsur-angsur kiata akan bisa menganggap matematika itu mudah.
Jadi dapat disimpulkan bahwa faktor internal (struktur kognisi) pengetahuan awal yang dimiliki seorang siswa akan mempengaruhinya dalam belajar matematika. Apabila dia merasa senang, menganggap matematika mudah (hanya berupa hitung-menghitung menggunakan angka dari 0-9) maka dengan sendirinya dia akan senang belajar matematika. Begitupun sebaliknya, apabila di dalam pikirannya menganggap matematika itu sulit, maka secara tidak sadar, dia tidak akan termotivasi untuk belajar dan akhirnya mengalami kesulitan belajar.
BY : NURUL NOVIANI
07301244093
Pendidikan Matematika NR D “07
CP : 085729232345
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