SMALL RESEARCH

MY SMALL RESEARCH OF MATHEMATICAL THINKING
The small research is the research to complete the task of the lecture of psychology. This research also aimed to be the way to show the real mathematical phenomenon in the frame work of school mathematics. The knowledge of real phenomenon of school mathematics is used to helps us study about the best way to make a good conditions of teaching and learning mathematics in the school. So it’s much needed for the teacher and everyone who concern about the education, especially mathematical education.
According to Katagiri as the expert of mathematics from Japan, mathematics consists of three things.
1. Mathematics Attitude
Mathematics Attitude is shown by always has a question. Always keep the positive thinking and always be consistent and critical, and always be careful to learn, see and understand mathematics as the important science.
2. Mathematics Methods
Methods in Mathematics are how to learn Mathematics. There are So many ways to learn it, for example:

Deductions Method
It means explaining something from general to specific items, for example, if we meet someone and know him or her, we a the first sight is just know about the general characteristics, but if we always meet him or her, we can know him until the details characteristics.

Inductions Method
Inductions method means we look something from specific items to general items. For example, we study mathematics in the first time from learn 1+1=2, 2+1=3, 3+1=4, and etc. And after that we learn about something larger from it. That is an example from inductions method.

Syllogism Method
It is the method that taking a conclusion according some
Premises or some statements. To be the example is:
Lyra is student.
Every student has an id card.
The conclusion: Lyra has an id card.
Logical Method
It is about mathematics sentence and mathematics prepositions. Mathematics sentence is the sentence that from that we can take a conclusion it is true or not.
(And the other mathematical methods).
3. Mathematics Content
Mathematics content is the object of mathematics because we can find there are
many roles and the process to understanding and to solve the mathematical problems.
To build the mathematical concept and theorem, we must collect the mathematical evidences first. The mathematical evidences are very close to our life in the world. Everything is can be inferred into mathematics. For example the economical terms is always related from the linear equation system. The mathematical evidences are not always same for everyone. Of course mathematical evidences for the expert are different from mathematical evidences for the student when learning mathematics. The expert see more complicated real evidences than the student because their necessary and aim to learn mathematics maybe different, and then they have the different level of mathematical knowledge too.
Now we will just concern about the student’s sight of mathematical evidences. Student usually thinks that mathematical evidences in our life are not too clear. It’s because their knowledge of mathematics is not deep enough. They see mathematics just like a counting science and it’s very complicated. They don’t have the awareness that mathematics is very close with our life, and factually the mathematical evidences are taken from the real phenomenon of life. The student finds the mathematical evidences are simpler than the expert. They usually find the evidences after they study about mathematical material first. It’s not too good for the mathematical building in their mind because it can make they think that mathematics application is not as many as what they hope before.
The mathematical evidences can be collected by student from the events of some facts. For the student, the mathematical evidence is same with the mathematical object. Mathematical object become a very important thing because we get the data and we do the analyzing from that object and also it usually shows the quantitative data. In other word, mathematical object as the object in common become the center of the mathematical topic. Mathematical object have some mathematical problems, and it’s needed for us to investigate it.
A bit different from the mathematical object, the mathematics educational object is the object that shows the quantitative also qualitative data. The example of mathematics educational object is the mathematical reactions or mathematical attitude by the student. Student’s mathematical thinking become important because we can analyze what is the problem that immediately occurred in the student’s mind when the face the mathematical problems. The aim from this small research is to uncover the difficulties of student learning mathematics, and from that we can make some correction about the mathematics education to create the good quality of mathematics education and to recover mathematical thinking. After this part, we can see the facts that I collected from the junior high school of Bantul 2, located in Yogyakarta.
To collect the data of this small research, I observe the student thinking of mathematics by ask them to fill a kind of blanket and answer some questions there, for example about mathematical difficulties, mathematical motivation, and also the method that used by the teacher in the class, so from this activity I got the qualitative data.
The questions are:
1. Is mathematics difficult?
2. If mathematics is difficult, what is the reason?
a. The complicated material and problems of mathematics
b. Communication problems
3. What is the most difficult subject?
a. Natural science (consists of biology and physics)
b. Social science
c. English
4. What is the method that used by the teacher to do the mathematical teaching?
a. Lecture (teacher explanation)
b. Discussion
c. Both
5. Is the teacher uses the mathematical model?
6. What is the most difficult material in mathematics according to you?
a. Exponent
b. Line analysis
c. Probability
d. Linear equation system
7. What is the simplest material in mathematics according to you?
a. Statistics
b. Algebra
c. Linear equation system
d. Probability
e. The set material
f. Dimensional figure
8. Are you continuing learn mathematics in home?
9. Are you motivated to learn mathematics?
10. If you motivated to learn mathematics, who is your big motivator?
a. Your own self
b. Parent
c. Friend
The respondents consist of seven students who become the student in the junior high school at fifth semester, IX grade in the same class. The data will be shown below.
Result 1
Mathematics is difficult: 1
Mathematics is not difficult: 6
Result 2
The reason why mathematics difficult:
Because of the difficult and complicated material of mathematics: 1
So much material in mathematics: 0
Problem of teacher communication: 0
Result 3
The most difficult subject in the school
Natural science: 6
Social science: 4
English: 2
Result 4
The method that used by the teacher in the mathematics class
Lecturing: 0
Discussion: 1
Both: 6
Result 5
Is the teacher uses mathematical model?
Yes: 6
No: 0
Result 6
The most difficult material in mathematics;
Exponent: 3
Line equation: 4
Probability: 1
Linear equation system: 1
Result 7
The simplest material in mathematics;
Statistics: 4
Algebra: 1
Linear equation system: 1
Probability: 2
The set material: 1
Dimensional figure: 3
Result 8
They continue to learn mathematics in the home:
Yes: 2
No: 4
Result 9
They motivated to learn mathematics;
Yes: 6
No: 0
Result 10
The biggest motivation of learning mathematics;
Their own self: 4
Parent: 2
Friend: 1
The result of the data in the table tells us that the students basically have no problem with the mathematical material, and their understanding is good enough. It shown from the answer of the first question is mostly “no”. From the seven answer, we get 6 “yes” and 1 “no”, so 6 respondents said that mathematics is not difficult, and 1 respondent said that mathematics is difficult. And then the problem of student learning mathematics is because of the material and role is complicated. From the second respondent that stated that mathematics is difficult we get the reason why. Mathematics is quite difficult for her (as her statement) because mathematics has a complicated role and material.
Go to the next analysis from third question, we can see from the result that the most difficult subject in junior high school is natural science (6 arguments), and then second is social science (4arguments) and the last is English language (2 arguments). No one said that mathematics is difficult. Although the second respondent think that mathematics is a difficult science, but she stated that natural science is the most difficult subject for her.
From the fourth question, we can conclude that the teacher use the mixed method from lecturing method and the discussion method to explain the student about the mathematical material. It’s quite effective because the student need a lot of new interesting way to learn mathematics. The creativity is much needed in the mathematical teaching and learning because it can be the power of the teacher to can always find some mathematical model to help them teaching. The teacher in the ninth grade of junior high school of Bantul 2 uses some models to explain the mathematical concept in the school. It’s a good conditions to make the mathematical education involve, and then it’s much helps the student to understand and absorb the knowledge as good as they can.
The respondents as the student who still learn mathematics state that there is some most difficult material in mathematics. The examples most difficult mathematics materials are exponent, line analysis, probability and the linear equation system. From the result, we know that the most difficult material in mathematics is line analysis in the line equation. This material maybe difficult because of it’s a bit hard to explain the material by use model. From the facts, we also know that the simplest material of mathematics according to the respondent is statistic. Statistic is a branch of mathematics that concern about the data processing, in the case analyzing every conclusion that we will find in the data. The student feel enjoy and think that statistics is easy because in the statistics there are a lot of real problem in daily life that can become the mathematics problems, so the understanding and the study process can be more real than if they study about some abstract material like the line and line equation, graph, Cartesian axis, and others.
Students as the respondent not always continue to learn mathematics again in their hum. It’s shown by the answer of the 8th question, almost of them stated not continue than continue. The mathematical understanding can be better if they always keep the spirit and the curiosity to learn mathematics. From the facts, we can conclude that everything that they get in mathematics lesson in the school is not the maximal value. They still can improve and make it better by study and continue the mathematical pattern everywhere. Related to the nature of school mathematics by Ebutt and Straher in 1995, they denoted that school mathematics is the pattern, problem solving, investigation and communication. So to make student can learn mathematics good, they must apply the statement, to understand the mathematics pattern by always make the investigation and finally find the problem solving of mathematics, and communicate it to the others.
The student motivated to learn mathematics mostly because of their own self. It’s better than they motivated by the other because if their self can motivating them to learning mathematics deeply, they will always find the new spirit and they are free from the other influence. It’s very important because the spirit of learning mathematics is much needed to make them have a lot curiosity of mathematics and it’s can make them continue to learn mathematics again and again. And finally they can get a lot of information by learn mathematics and they change their opinion about mathematics, because in reality mathematics is much helps us in our life.
References: http://powermathematics.blogspot.com
Wikipedia.com (philosophy of power)