Matematika, suatu bidang studi yang sering menantang. Materinya yang berhubungan dengan angka-angka menjadikan bidang studi ini menarik bagi saya. Sejak di Sekolah Dasar, saya sudah menyukai bidang studi ini. Alhamdulillah saya tidak mengalami kesulitan dalam mempelajarinya sampai saya duduk di SMP. Pada waktu SMP, saya juga sempat menjadi peserta lomba Matematika yang mewakili sekolah saya di tingkat Kabupaten Klaten. Guru Matematika semasa SMP dulu baik-baik, oleh karena itu saya menjadi makin cinta dengan matematika.
Pada awal-awal SMA, saya tidak mengalami kesulitan yang berarti dalam mempelajari Matematika. Lagi-lagi karena saya menyukai metode yang diajarkan guru Matematika saya, santai tetapi tegas. Saya sempat mewakili SMA saya dalam beberapa Lomba Matematika di Kabupaten Sleman. Di kelas dua SMA pun saya tidak menghadapi kendala yang berarti karena guru Matematika saya mampu menarik perhatian lewat canda tawanya. Barulah di kelas tiga saya mengalami kendala yang cukup berarti dalam pelajaran Matematika. Waktu itu saya merasa tidak nyaman dan kurang menyukai gaya mengajar guru Matematika saya. Beliau jarang sekali melakukan timbal balik dengan muridnya. Beliau terlalu monoton dan tidak memberikan suatu penghargaan pada setiap tugas-tugas. Hal itulah ynag kemudian membuat saya malas mengerjakan tugas dan latihan yang pada akhirnya merugikan saya sendiri.
Ujian Nasional SMA pun tiba, hasil Ujian Nasional saya yang terendah adalah MATEMATIKA. Itu merupakan pukulan tersendiri dan terburuk bagi saya. Waktu itu, saya sempat tidak percaya diri. Guru Matematika saya sewaktu kelas dua pun mulai komentar dengan hasil ujian yang saya peroleh. Beliau berkata: "Masak anak Olpid Matematika cuma dapat nilai 6". Saya tidak membeci guru saya itu tapi justru itu yang menjadi motivasi saya untuk menunjukkan pada semua oramg bahwa saya mampu dalam Matematika. Akhirnya, saya pun mencoba masuk Pendidikan Matematika UNY melalui jalur SPMB. Dan Alhamdulillah saya diterima.
Untuk pak Herlin, perkataan Bapak mampu menjadi motivasi bagi saya. Untuk semua guru-guru saya, thank's for all.
Sabtu, 27 Desember 2008
Kamis, 11 Desember 2008
What I can reflect about psychological aspects if the student is confronted with the following questions?
On Saturday 6 December 2008 , I have observation to know psychological aspects if the student is confronted with the following questions:
1. Determine function formula g : x ---> x2 – 1 and determine function value for x = - 4 and x = 3 !
2. Determine h(-5) if h : x ---> -3x + 4 and determine value if h (c) = - 8 !
From result of observation, I can get the following data:
1. From three student of class 1 at SMP N 2 Manisrenggo, altogether confess that:
Before doing the questions, they have anxiety.
Moment do the questions, they feel hopeless
After doing the questions, they sneaking with their answers which it is correct or is wrong.
Their reason is they never get the material previously. After confirmation with their mathematics teacher, their teacher say that the material is never taught in class 1 because the material is material in class 2.
2. From two student of class 1 at SMP N 2 Manisrenggo, altogether confess that:
Before doing the questions, they feel happy because the questions is easy
Moment do the questions, they feel spirits because the material have been taught previously After doing the questions, they feel peaceful because they sure that their answers is correct.
3. From one student of class 1 at SMP N 2 Manisrenggo, she confess that:
Before doing the questions, she feel anxiety because she rather forget the material.
Moment do the questions, she feel spirits because she have started to remember the material After doing the problem, they feel peaceful because she sure that their answers is correct.
From data, I can conclude that:
1. Student will feel anxiety if the student is confronted with the questions because they have never accepted material in question and if they forget about the material.
2. Student will feel happy if the student is confronted with the questions because they have accepted material in questions and remember about the material.
3. Student will feel spirits if the student is confronted with the questions because they have accepted items in problem and remember about items
4. Student will be peaceful if the student is confronted with the questions because they sure that their answers is correct.
Rabu, 03 Desember 2008
Descriptive Statistics, One of Quantitative Methods in Research of Psychology Study of Mathematics
There are two methods that we can use in research of Psychology Study of Mathematics.
1. Qualification methods is methods which use subjective value to take conclusion of the problems.
2. Quantitative methods is methods which use objective value in mathematical calculation to take conclusion of the problems
Statistical methods have found extensive application in the psychological and educational testing field and in the study of human ability. Since the time of Binet, who developed the first extensively used and successful test of intelligence. We can use quantitative prediction to research human behavior, human ability, personality characteristics, attitudes, etc.
In this paper, we will concern to quantitative methods, specially descriptive statistics in research of psychology study of mathematics.
A. Definition Of Descriptive Statistics
Descriptive statistics is the part of statistics which process, presenting data without taking conclusion for population. Descriptive Statistics are used to describe the basic features of the data gathered from an experimental study in various ways. A descriptive Statistics is distinguished from inferential statistics. They provide simple summaries about the sample and the measures.
We can use descriptive statistic in psychology research. Example, if we measure the IQ of the complete population of students in a particular university and compute the mean IQ, the mean is a descriptive statistic because it describes a characteristic of sample population. If, on other hand, we measure the IQ of a sample of 100 students and compute the mean IQ for the sample, that mean is also a descriptive statistic because it describes a characteristic of the sample.
B. Steps in Descriptive Statistics
- Collect data
- Summarize data
- Present data
- Proceed to inferential statistics if there are enough data to draw a conclusion
C. Univariate Analysis
Univariate analysis involves the examination across cases of one variable at a time. There are three major characteristics of a single variable that we tend to look at:
- the distribution
- the central tendency
- the dispersion
In most situations, we would describe all three of these characteristics for each of the variables in our study.
The Distribution
The distribution is a summary of the frequency of individual values or ranges of values for a variable. The simplest distribution would list every value of a variable and the number of persons who had each value. For instance, a typical way to describe the distribution of college students is by year in college, listing the number or percent of students at each of the four years. Or, we describe gender by listing the number or percent of males and females. For example, we will measure the student problems in mathematics. We can identification it from mathematics test scores. There are the mathematics test score of 10 students.
Table 1. Frequency distribution of mathematics test score of 10 students
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One of the most common ways to describe a single variable is with a frequency distribution. Variable x is the mathematics test score and variable f is the frequency. Frequency distributions can be depicted in two ways, as a table or as a graph.
Table 2. Frequency distribution histograms.
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Table 3. Frequency distribution polygons.
Central Tendency
The central tendency of a distribution is an estimate of the "center" of a distribution of values. There are three major types of estimates of central tendency:
- Mean
- Median
- Mode
The Mean or average is probably the most commonly used method of describing central tendency. To compute the mean all you do is add up all the values and divide by the number of values. For example, the mean or average quiz score is determined by summing all the scores and dividing by the number of students taking the exam. For example, The sum of 10 values in table 1 is 81, so the mean is 810/10 = 8,1
The Median is the score found at the exact middle of the set of values. One way to compute the median is to list all scores in numerical order, and then locate the score in the center of the sample. If we order the10 scores shown above, we would get:
60,60,70,80,80,80,90,90,100,100
There are 10 scores and score #5 and #6 represent the halfway point. Since both of these scores are 80, the median is 80. If the two middle scores had different values, you would have to interpolate to determine the median.
The mode is the most frequently occurring value in the set of scores. To determine the mode, you might again order the scores as shown above, and then count each one. The most frequently occurring value is the mode. In our example, the value 80 occurs three times and is the model. In some distributions there is more than one modal value. In a bimodal distribution there are two values that occur most frequently.
Dispersion refers to the spread of the values around the central tendency. There are two common measures of dispersion, the range and the standard deviation. The range is simply the highest value minus the lowest value. In our example distribution, the high value is 36 and the low is 15, so the range is 100 - 60 = 40.
The Standard Deviation is a more accurate and detailed estimate of dispersion because an outlier can greatly exaggerate the range. The Standard Deviation shows the relation that set of scores has to the mean of the sample. To compute the standard deviation, we first find the distance between each value and the mean. We know from above that the mean is 81. So, the differences from the mean are:
60 – 81 = -21
60 – 81 = -21
70 – 81 = -11
80 – 81 = -1
80 – 81 = -1
80 – 81 = -1
90 – 81 = 9
90 – 81 = 9
100 - 81 = 19
100 - 81 = 19
Notice that values that are below the mean have negative discrepancies and values above it have positive ones. Next, we square each discrepancy and then we :
-21 X -21 = 441
-21 X -21 = 441
-11 X -11 = 121
-1 X -1 = 1
-1 X -1 = 1
-1 X -1 = 1
9 X 9 = 81
9 X 9 = 81
19 X 19 = 361
19 X 19 = 361
Now, we take these "squares" and sum them to get the Sum of Squares (SS) value. Here, the sum is 1890. Next, we divide this sum by the number of scores minus 1. Here, the result is 1890 /9 = 210. This value is known as the variance. To get the standard deviation, we take the square root of the variance (remember that we squared the deviations earlier). The standard deviation is 14,49. Although this computation may seem convoluted, it's actually quite simple. To see this, consider the formula for the standard deviation:
In the top part of the ratio, the numerator, we see that each score has the the mean subtracted from it, the difference is squared, and the squares are summed. In the bottom part, we take the number of scores minus 1. The ratio is the variance and the square root is the standard deviation.
After we analysis the data by descriptive statistics, we can take a conclusion, for example: student who get score under mean value have problem in study mathematics, etc.
D. References
http ://en.wikipedia.org/wiki/Descriptive_statistics
http://www.socialresearchmethods.net/kb/statdesc.php
Selasa, 02 Desember 2008
Teori Belajar Humanisme
Menurut teori ini, tujuan belajar adalah untuk memanusiakan manusia. Proses belajar dianggap berhasil jika si pelajar telah memahami lingkungannya dan dirinya sendiri. Siswa dalam proses belajarnya harus berusaha agar lambat laun ia mampu mencapai aktualisasi diri dengan sebaik-baiknya. Teori belajar ini berusaha memahami perilaku belajar dari sudut pandang pelakunya, bukan sudut pandang pengamatnya.
Tujuan utama para pendidik ialah membantu siswa untuk mengembangkan dirinya, yaitu membantu masing-masing individu untuk mengenal diri mereka sendiri sebagai manusia yang unik dan membantu dalam mewujudkan potensi-potensi yang ada dalam diri mereka.
1. proses pemerolehan informasi baru,
2. personalisasi informasi ini pada individu
Tokoh penting dalam teori belajar humanistik secara teoritik antara lain, adalah Arthur W.Combs, Abraham Maslow dan Carl Rogers.
1. Arthur W. Combs (1912-1999)
Bersama dengan Donald Snygg (1904-1967) mereka mencurahkan banyak perhatian pada dunia pendidikan. Meaning (makna atau arti) adalah konsep dasar yang sering digunakan. Belajar terjadi bila mempunyai arti bagi individu. Combs memberikan lukisan persepsi diri dan dunia seseorang seperti dua lingkaran (besar dan kecil) yang bertitik pusat pada satu. Lingkaran kecil (1) adalah gambaran dari persepsi diri dan lingkungan besar (2) adalah persepsi dunia. Makin jauh peristiwa-peristiwa itu dari persepsi diri makin berkurang pengaruhnya terhadap perilakunya. Jadi, hal-hal yang mempunyai sedikit hubungan dengan diri, makin mudah hal itu terlupakan.
2. Abraham Maslow
Teori Maslow didasarkan pada asumsi bahwa di dalam diri individu ada dua hal :
(1) suatu usaha yang positif untuk berkembang
(2) kekuatan untuk melawan atau menolak perkembangan itu.
Maslow mengemukakan bahwa individu berperilaku dalam upaya untuk memenuhi kebutuhan yang bersifat hirarkis. Maslow membagi kebutuhan-kebutuhan (needs) manusia menjadi lima hirarki.
| Kebutuhan untuk aktualisasi diri |
| Kebutuhan untuk dihargai |
| Kebutuhan untuk dicintai dan disayangi |
| Kebutuhan akan rasa aman dan tentram |
| Kebutuhan fisiologis / dasar |
Hirarki Kebutuhan Maslow
3. Carl Rogers
Carl Ransom Rogers lahir pada tanggal 8 Januari 1902 di
Ide pokok dari teori - teori
Kelebihan Teori Humanistik
Pembelajaran dengan menggunakan teori ini sangat cocok untuk diterapkan untuk materi-materi pembelajaran yang bersifat pembentukan kepribadian, hati nurani, perubahan sikap, dan analisis terhadap fenomena sosial. Indikator dari keberhasilan aplikasi ini adalah siswa merasa senang bergairah, berinisiatif dalam belajar dan terjadi perubahan pola pikir, perilaku dan sikap atas kemauan sendiri. Siswa diharapkan menjadi manusia yang bebas, berani, tidak terikat oleh pendapat orang lain dan mengatur pribadinya sendiri secara bertanggung jawab tanpa mengurangi hak-hak orang lain atau melanggar aturan, norma, disiplin atau etika yang berlaku.
Kelemahan Teori Humanistik
Karena dalam teori ini guru adalah sebagai fasilitator maka kurang cocok diterapkan yang pola pikirnya kurang aktif atau pasif. Karena bagi siswa yang kurang aktif dia akan takut atau malu untuk bertnyan pada gurunya sehingga dia akan tertinggal oleh teman-temanya yang aktif dalam kegiatan pembelajaran, padahal dalam teori ini guru akan memberikan respons bila murid yang diajar juga aktif dalam menanggapi respons yang diberikan oleh guru.
Karena siswa berperan sebagai pelaku utama (student center) maka keberhasilan proses belajar lebih banyak ditentukan oleh siswa itu sendiri, peran guru dalam proses pembentukan dan pendewasaan kepribadian siswa menjadi berkurang.
References:
http://novinasuprobo.wordpress.com/2008/06/15/teori-belajar-humanistik/
Sugihartono,dkk. 2007. “Psikologi Pendidikan”.
http://blog.kenz.or.id/2005/05/02/carl-rogers-psikolog-aliran-humanisme.html
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