Logika untuk Membangun Filsafat

Logika merupakan sebuah ilmu pengetahuan di mana obyek materialnya adalah berpikir (khususnya penalaran/proses penalaran) dan obyek formal logika adalah berpikir/penalaran yang ditinjau dari segi ketepatannya. Sedangkan filsafat itu sendiri merupakan suatu kegiatan olah piker. Oleh karena itu, tentu terdapat suatu keterkaitan antara logika dan filsafat.
Logika lahir bersama-sama dengan lahirnya filsafat di Yunani. Dalam usaha untuk memasarkan pikiran-pikirannya serta pendapat-pendapatnya, filsuf-filsuf Yunani kuno tidak jarang mencoba membantah pikiran yang lain dengan menunjukkan kesesatan penalarannya.
Logika digunakan untuk melakukan pembuktian. Logika mengatakan yang bentuk inferensi yang berlaku dan yang tidak. Secara tradisional, logika dipelajari sebagai cabang filosofi, tetapi juga bisa dianggap sebagai cabang matematika. Logika tidak bisa dihindarkan dalam proses hidup mencari kebenaran. Demikian halnya dalam pembelajaran matematika. Perlu diketahui bahwa hakekat matematika yang tidak tunggal, maka dalam hal ini logika sangat diperlukan sekali dalam mencari kebenaran dalam matematika.
Dasar penalaran dalam logika ada dua, yakni deduktif dan induktif. Penalaran deduktif, kadang disebut logika deduktif yaitu penalaran yang membangun atau mengevaluasi argumen deduktif. Argumen dinyatakan deduktif jika kebenaran dari kesimpulan ditarik atau merupakan konsekuensi logis dari premis-premisnya. Argumen deduktif dinyatakan valid atau tidak valid, bukan benar atau salah. Sebuah argumen deduktif dinyatakan valid jika dan hanya jika kesimpulannya merupakan konsekuensi logis dari premis-premisnya. Penalaran induktif, kadang disebut logika induktif, yaitu penalaran yang berangkat dari serangkaian fakta-fakta khusus untuk mencapai kesimpulan umum.
Dengan menggunakan logika, ada beberapa manfaat yang dapat kita peroleh antara lain yaitu (1) membantu setiap orang yang mempelajari logika untuk berpikir secara rasional, kritis, lurus, tetap, tertib, metodis dan koheren. (2) Meningkatkan kemampuan berpikir secara abstrak, cermat, dan objektif, (3) menambah kecerdasan dan meningkatkan kemampuan berpikir secara tajam dan mandiri, (4) memaksa dan mendorong orang untuk berpikir sendiri dengan menggunakan asas-asas sistematis, (5)meningkatkan cinta akan kebenaran dan menghindari kesalahan-kesalahan berpikir, kekeliruan, serta kesesatan, (6)mampu melakukan analisis terhadap suatu kejadian, (7) terhindar dari klenik , gugon-tuhon ( bahasa Jawa ), (8) apabila sudah mampu berpikir rasional, kritis ,lurus,metodis dan analitis sebagaimana tersebut pada butir pertama maka akan meningkatkan citra diri seseorang.
Denga demikian, dengan menggunakan logika kita dapat mempelajari dan membangun filsafat secara logis, sistematis, mensintesis tesis dan tesis, analitis, sehingga kita dapat meningkatkan dimensi kita dalam kaidah ruang dan waktu yang sesuai, dengan tetap menyertakan hati sebagai komandan dalam setiap langkah kita.

Sumber:
http://id.wikipedia.org/wiki/Logika

Some Important Things in Life

Ask your Self about:

What do yo want?
what do you need?
What do yo Learn?
What do you have been done?
What do you get?
what do you feel??

All the things that you have done are meaningful.

the esthetic of mathematics

PSYCHOLOGY AND SOCIOCULTURAL TO FIND THE ESTHETIC OF MATHEMATICS

INTRODUCTION
Mathematics, numbers, theorm, axioms, formula, and difficulties. Is it true that several things will be appear when we talk about “mathematics”? some people still suppose that mathematics is one of the difficult science. And it’s as same as my thinking before. But for some people who have found the esthetic of mathematics, exactly they will feel enjoy to studying mathematics.
Surely, the nature of mathematics is a problem solving. But, many students don’t like to find and solve the difficulties in mathematics problems. Whereas, surely they have capability to do it. There so many aspect to be the reasons for it. The main aspects that can describe why some students feel difficult in mathematics are social environment, the education character which maybe has make them do not to open and explore their thinking. And the other aspect is from the side of individual psychology. It is the basic aspect for every student, because psychology is an important part which can define the behavior and also person’s thinking.
Basically psychology is related with sociocultural, because psychology can’t separate with human life. And every person is a biososiocultural creature. So, educational process in the personal activity also has a relation with psychology, socioanthropology , and also sociocultural.

PSYCHOLOGY AND SOCIOCULTURAL TO FIND THE ESTETHIC OF MATHEMATICS.
Such I have said that between psychology and sociocultural have a relation. Psychology is in human life. Because psychology is a science or condition of personality, behavior, feeling, etc. According to Allport that say “personality is a dynamic organization in pshycis and physic which define behavior and thinking characteristic”. Someone also has an attitude, mental character, emotion behind their behavior which can depend or influence by themselves, or by the external. The external factor is related by social and cultural condition in their life. And sociocultural condition means that the condion of role relationship system in the society which has a norm, value, custom, etc.
In case of studying mathematics, psychology and sosiocultural aspect are needed because it define or give influence to the student thinking or behavior in study. Especially in studying mathematics, motivation as a part of someone’s psychology is very needed to support in getting success in studying mathematics. And motivation can be form by themselves and also from the others.
For an example about my experience in studying mathematics, I feel the main thing in mathematics is a problem solving. Problem solving is always exist in mathematics. When I feel difficult and hate, because I can’t find the solution whereas I have tough hard Problem solving doesn’t mean solve the problem so quick. And also feel happy when I can solve mathematics problem, then I feel interest to study more about mathematics. But sometimes, I feel that I want to study mathematics as well as possible because my parents or maybe the other people suppose that I have the ability in studying mathematics then they and I hope that I can get the optimal assessment in mathematics.
From it, I realize that the social condition such as the habit or the social perspectif, both from my family or from the environment has helped me to get the motivation as a part of my psychology to study mathematics well. After I feel the contribution of psychology and sociocultural condition in studying mathematics, the result of it can be used in life especially in the society, such as the logic thinking, regularity, and the other advantages of studying mathematics especially in the process of problem solving in learning mathematics. Because according to Dr. Walter A. Shewhart , problem solving is a ciclic process which consist of four step, those are plan, do,check and act.
I think that to find the esthetics of mathematics such as the logical thinking and others, you must love mathematics, so you can be able to get the motivation to study it. And to get the motivation, I can get it as a part of my psychology from my self and also from my sociocultural condition as a part of my life. I must realize that I can get the logical thinking, and the others from the process of problem solving in mathematics, although I find some difficulties and then I must solve it in mathematics.

Reference
http://rumahbelajarpsikologi.com/index.php/kepribadian.html

My reflection of student psychological aspects

What I Can Reflect about Psychological Aspects if the Student is Confronted with the following Question:
Mono is 7 years older than Edi. Cahyo is 4 years older than Mono. If the total age of Mono and Edi is same with the age of Cahyo, so the age of Mono is … years.
a. 6 b. 5 c. 4 d. 3

The value of y from linear equation 2x + 3y = 11 and x - y = 3 is …
a. 1 b. 2 c.3 d.4

If the students are given some mathematics question in form of multiple choice, there will be some psychological aspect from the student which can be reflect. Some questions those are in form of multiple choice can be said as an instant culture in mathematics education. Because students will solve the problem quickly without hard thinking. So it’s not impossible, if the student just ask the question with luckily not from their thinking or not use the mathematics formula.
To solve the question in form of multiple choice, the student also usually use “ Gambling “ method, that the student just approximate the answer without use mathematics procedure. Because in the question, there are some choice of answer so the student just need to choose one of the answer from the question.

If the question is a story question, there will be a “cruel” feeling from student so that the student will feel difficulties and lazy to thinking hard to find the answer. Finally student only choose the answer unserioussly. By approximating the answer, it will not support the improvement of student thinking, especially in mathematics thinking.

For some students, if they are given some multiple choice question, they will fell easier to finish the question because they must not think too hard. But for several people, multiple choice will make disappointed. The student who have thought to solve the problem with mathematics formula will be disappointed if their answer is not in the choice. And if their choice is wrong, so they will not get score. But if the form of the question is not multiple choice, the can explore their thinking, and if there are a mistake, they still get score for their question, although the score is not perfect.

Sometimes if the student are given multiple choice problems, they suggest that they don’t need to study or maybe prepare some matery for do or solve the exams. But for some student who have prepare the matery will lose their spirit, because basically they have been already to get the challenge but the question that is given is multiple choice so that they fell disappointed and finally their spirit is decrease. It’s according with Law of readiness from Edward L. Thorndike, that said “the student will lose their spirit If something is not in accord with their readiness”. (Sugihartono, 2007:92 )

Almost of student will be lazy to study before they solve multiple choice problems. So that they don’t have motivation to study before they do the exam. Because they suggest that without study they still can answer the question. If the student don’t have motivation to study so they can not improve their ability. Because according to Gleitman and Roger motivation is an internal condition of organism to support their activity, so that motivation is a power for people to do something. If the student lose their motivation to study they will not have power for studying, so they will get the optimum result.

Beside that, in mathematics the important thing in solving the problem is the process, or in the other word it’s important to do problem solving in mathematics. It’s not effective to get the answer of the mathematics problem directly, because it will not improve student’s thinking in mathematics.
But in the other hand, multiple choice can make easier for teacher when they check the result of student’s work. So I can reflect that if student is confronted with multiple choice question, it will hamper the student ability in mathematics thinking because it will decrease the student motivation but it also will make easier for the student to solve the question although they don’t need to think hard, they also can answer the question by approximate and then choose the answer.

References
http://duniapsikologi.dagdigdug.com/category/psikologi-kepribadian/
Sugihartono,dkk.2007.Psikologi Pendidikan.Yogyakarta:UNY Press
UKI RAHMAWATI
07301241003
MATHEMATICS EDUCATION

statistical method

Statistical method to solving the study of using teaching aid in the relation with student’s interest and student’s understanding in teaching and learning of Cartesian Plane

Introduction

In some research or study of case, there is used some method such as quantitative and qualitative method. For the research that needs some mathematical analysis for its data, so it used quantitative method. One of the most uses in quantitative method is statistical method. Such as in research of psychology that also use quantitative method that is statistical methods to :

· To describe in numerical terms defined aspect of the behavior of individuals: by the refinement of measures

· To describe the characteristics of individuals and groups in terms of these measures

· To describe the relationships among these variables

· To generalize the finding within specifics samples of individuals to wider population

· To predict the behavior of individuals under specified conditions, and

· To estimate the consistency or reliability of information ( Philip H. Dubois, 1965: 1 )

In statistical methods there are two kind of statistics, that are Descriptive statistics and inferential statistics. The descriptive statistics refers to procedures for the simplifying quantitative information so that the structure or form of the data becomes easier to perceive. And inferential statistics refers to the procedure to analyze data to get the conclusion.

Before show the data, in descriptive statistics there are some ways to get the data, those are: by sampling such as random sampling, areal sampling, systematical sampling, cluster sampling, quota sampling, purposive sampling, proportional sampling or stratified sampling. To get the data it can be done by some technique such as: questionnaire, test, observation, check list, or interview. After get the data then show the data by making the graphic, curve, diagram, chart, or frequency distribution diagram.

After that, the data that we have is counting for some value such as mean, modus, median, variance, etc. the using of statistical methods in this experiment is purposed to test the hypothesis to make the conclusion.

Statistical method in the know the student’s interest and student’ s understanding in learning Cartesian plane by using teaching add.

if we want to know the influence of using teaching add in teaching mathematics ( Cartesian plane ) for student’s interest and student’s understanding by using statistical methods, there are some step that must be done, such as ( Sumitro Djojohadikusumo,1985:18):

· Plan the experiment

Its include the place that the experiment will be done, the person ( student ) as the object of the experiment, and some requirement that needs for the experiment soon. For the example : this experiment will be done for the elementary student in the 5^th grade in SD N Nusawangkal. For this experiment, teacher uses board (as Cartesian plane) and some ball in teaching Cartesian plane for the student.

· Collect the data

To get the data, it can be done by sampling so we must not take the data from all students. We can use questionnaire, interview, observation, or by doing some test for some students to get the data. In this experiment, for the main information that must be taken from the student, that are some information about their impression when the teacher use the teaching add to teach the matery, and about the assessment of study from the student when they learning by using teaching add, and etc. Besides that, there are some three main system of statistical description by numerical methods:

1. Counting, there is nominal scale which is not a scale in the ordinary sense of the word but simply two or more classes in the same general domain. For examples: sex, and race.

2. Rangking, there is ordinal scale which comprises case or categories placed in order, as from high to low, with regard to a characteristic.

3. Averaging and summing, there are interval and ratio scales.

After we get the data, then we must process the data. In descriptive statistics there some numerical methods, such as :

1. Measures of central tendency : mean, median, modus

2. Measures of variability : variance, standard of deviation

3. Measures of variables : the obtain scores are interpreted by means of norms, which are transformations of the scores, standing of the same individual on several variables may be readily compared.

From the data that we have got, then those data are processed by some statistics method above.

· Show the data

Data that we have processed then shown in a diagram, table of frequency distribution, graphic, chart or in the other form. For example we want to show the sum or compare the proportion of student that is interest, interest enough, very interest with the using teaching add in the study or maybe the proportion of the student that enough understand, understand, and more understand the subject by using Cartesian board and ball in teaching learning. By show the data in form of diagram or tables, it makes easier to perceive and understands.

· Analyze and interpret data

When the data has been shown, then it must be analyze to check the first hypothesis in the beginning of experiment, so that we can get the conclusion about the experiment that we have done. To analyze and interpret data we use inferential statistics such as:

1. Statistic assumption method.

2. Testing of statistic hypothesis

3. Regretion and correlation

In this case I will not discuss inferential statistic more far, because there are much kind of testing to make the conclusion. And inferential statistic, its also use mathematical counting to do some testing.

· Making the conclusion.

After the hypothesis has been tested, so it can be made the conclusion. For the example in this experiment, finally it can be concluded that actually by using teaching aid ( board of Cartesian plane and balls ) can improve student’s interest in studying this submatery and it also can make easier for student to understand the matery.

Quantitative ( statistical method )applied to generalization, and gives the accurate conclusion because statistical method uses objectivity not subjectivity.

References

http://js.unikom.ac.id/kualitatif/beda.html

http://ssantoso.blogspot.com/2008/08/format-penelitian-kuantitatif-materi.html

http://id.wikipedia.org/wiki/Statistik_deskriptif

Dubois, Philip H.1965.An Introduction to Psychological Statistics.United States of America: Harper and Row Publisher

Djojohadikusumo,Sumitro dkk.1985.Pengantar Metode Statistik Jilid 1.Jakarta:LP3ES

Walpole,Ronald E.1995.Pengantar Statistika.Jakarta:PT Gramedia Pustaka Utama

UKI RAHMAWATI

07301241003

PENDIDIKAN MATEMATIKA R'07

CP. 085647663476

uki.rahmawati@gmail.com

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