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As one of the lesson subjects in school, mathematics has an important role to build students’ thinking. It’s not a lie. Mathematics school gives an impact for students although they don’t realize clearly. When we talk about mathematics, we should discuss about mathematical thinking too. I am curious with senior high school students’ mathematical thinking. I would like to know how far they understand about the content of mathematics that they’ve learned, how they build their competence in mathematics, and how they love mathematics. That’s the reason why i made a small research related to mathematics psycology.
Based on Katagiri (2004), mathematical thinking has many characteristics. First, Focus on Sets
Mathematical thinking is like an attitude, as in it can be expressed as a state of “attempting to do” or “working to do” something. It is not limited to results represented by actions. Second, Thinking Depends on Three Variables. it means the way of thinking depends on three variables: the problem (situation), the person involved, and the strategy. Third, Denotative Understanding. Even the concept of mathematical thinking is expressed with words, but it should be shown with concrete examples. Fourth, Mathematical Thinking is the Driving Force.
Mathematical thinking is like an attitude, as in it can be expressed as a state of “attempting to do” or “working to do” something. It is not limited to results represented by actions. Second, Thinking Depends on Three Variables. it means the way of thinking depends on three variables: the problem (situation), the person involved, and the strategy. Third, Denotative Understanding. Even the concept of mathematical thinking is expressed with words, but it should be shown with concrete examples. Fourth, Mathematical Thinking is the Driving Force.
Still from Katagiri (2004), mathematical thinking has three types. First, Mathematical Attitude. It is related with students attitude in learning mathematics. It can be their curiousity with mathematics, their motivation to learn mathematics, etc. The second type is mathematical method. This type is related to how the students solve mathematics problem, what kinds of method that they use, etc, and the last is mathematical content. It shows the students understanding in materials and how far they can develop their ability in real life.
In this research, I had three respondents. They have good and closer relationship with me. First, I would like to describe them.
1. Akhmad Akbar (1st grade of Muntilan Senior High School). He is my little brother. He has good competence in mathematics but he’s lazy. He studies mathematics rarely. He thinks if he understands, he shouldn’t learn more. He just studies when there will be a test or when he has assignments. It makes him don’t get maximal results.
2. Ayu Wulandari (2nd grade of SMKN 1 Salam). She is my neighbor. She is average students. Truly she doesn’t have good ability in mathematics. But she is interested to solve mathematics problem when she get a task. She always tries to do it. Even, she would ask me when she couldn’t do it.
3. Akhmad Wildan Listyanto (2nd grade of Kota Mungkid Senior High School). He is my cousin. He is in natural science major. He has average ability but he is diligent. So he can understand the material well. He has a regular time to study.
I have seen their development in mathematical thinking for a month. With the different characteristics that they show when they learn mathematics, they got different results in their 1st semester report. Akbar didn’t get maximal results because he didn’t study hard. He just got 75. It isn’t like what he should get. Ayu got 60. She studied hard, but she had low understanding. It made she couldn’t get good result. Then Wildan got 79. Those comparation shows that every person has different ability, different way, and different result when he/she learn mathematics.
I also gave some questions to them related to their learning in mathematics.
1. Do you like mathematics?
2. What can make you motivated to learn mathematics?
3. What is your favourite material?
4. What is the difficulty that you find when you learn mathematics?
5. Do you have special time to learn mathematics?
6. What is the method that you use to understand the content of the material?
Their answers are:
Akbar
1 He likes mathematics very much
2 The teacher and the materials
3 Exponential
He can’t read the mathematics language well
5 No
6 Listen the teacher’s explanation then understand it at the same
Ayu
She likes mathematics
Because mathematics is one of school lesson
She doesn’t have favourite material
She can’t find the concept of materials quickly
Sometimes
Need others help to explain the material.
Wildan
He likes mathematics
Because mathematics is difficult
Statistics
He gets difficulties when he learns about trigonometry
Yes
Read the material seriously. Then do some exercises to time understand in depth.
Based on the research that i’ve done, i got information that SMK students have different view with senior high school students. Ayu likes mathematics because it is one of the school lesson. On the other side, Akbar and Wildan like mathematics because they are interested with mathematics unique. The difficulty that always happen in senior high school students is when they have to change the problems into mathematics language. They are difficult to visualize the abstract concepts that it make them don’t get full concepts in their mind. I also can compare the students thinking from different grade. I find that the higher grade student has more awareness to learn mathematics although they don’t understand well. On the other side, some students which is in lower grade learn mathematics when they get tasks or tests.
I think the phenomena above show that students in senior high school still need motivation and awareness to learn mathematics. They also need more realistic example when understanding the
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