1. QL (Qualitative)
2. QT (Quantitative)
3. CT (Category)
4. RL (Relationship)
OK! Let’s learn those (4 thinks) relation to Mathematics itself. First is Qualitative (QL). It means that Mathematics is not only formed by numbers and formulas, but also can be stated by sentences (for example story problem in Mathematics examination). Children must read the story before to understand the problem, and then they can formulate or state the story problem into ‘mathematical sentences’ which is a Quantitative (QT) form. From this formula, they can analyze and solve the problem. Not all of that information used. We must select which is important and which is unimportant for us to solve that problem. So, we must categorize them. After that, we can find the relations of them and get the conclusion because as Mr. Marsigit said that what we say or what we think or what we see can’t represent everything.
Sometimes, children feel difficult in solve Mathematics problem. It happens because the abstract character of Mathematics itself. We, as a Mathematics teacher wannabe should motivate our children to love Mathematics and develop their happiness in studying.
According to Hudoyo (1988:3), learn Mathematics is a high mental activity then teacher should have competences to explain Mathematics well so that students understand the abstract Mathematics concepts. Hudoyo (1988:4) said that Mathematics learning process should did continuously. We, as a teacher should give the previous materials before the students learn the next materials because the materials are related each others, so that they can learn Mathematics happily.
According to Katagiri, there are three aspects in Student Mathematical Thinking in the Framework of the Nature of School Mathematics, they are:
1. Mathematics Attitudes.
2. Mathematics Methods.
3. Mathematics Contents.
Ebutt and Straker (1995) also explained about the nature of School Mathematics. Teacher shouldn’t use Mathematics axioms definitions but school Mathematics definitions. There are Mathematics realities:
a. Mathematics as an identify pattern and relation activity.
Teacher should give opportunity for their students to discover and investigate the pattern in Mathematics problem to find its relation of each others. It also can stimulate the student to do their experiments and understand the materials then make the conclusion.
b. Mathematics is a creativity that need of imaginations, intuitions, and discovery.
By applying Mathematics school, we can support students to think different and explore their curiosity. It also can stimulate them to think critically, logically, consistently, systematically and appreciate people’s opinion.
c. Mathematics is a communication way between teacher and student so that they have the same perception abiut Mathematics itself, for example the characteristics, problem stories, concepts, etc (marsigitpsiko.blogspot.com)
Now we’ll talk about Phenomenology and its Epoche. According to Edmund Husserl (1859 – 1938), phenomenology shows everything which is visible to us in our consciousness without put in some our thinking or our presupposition (rumahmakalah.wordpress.com). So, phenomenology is natural and essential. Husserl use 2 steps to get phenomenology essential, they are epoche method and eidetich vision. Epoche is a Greek language that means “postpone” the agreement or “self empty from any particular belief”. Epoche also means “bracketing” to any information without think its justice.
Epoche contains about everything else which is not too important or unused thing to think about something. For example, when we learn about formula of cube volume and its concepts, we just think about the problem and it’s solving. We only need to analyze how to get the volume formula and understand its concepts. It’s not too important for us to know the way to make the cube, from what materials of the cube made, its cost, what is the color, and etc. Automatically we knew about them and they are not really influence to the volume formula of course. So, we can say that in this case, we just had categorized the one of psychology phenomena. We can separate which is better for us, which is more important and useful to think, which is we must save in ‘Epoch Home’, etc.
There are two methods of thinking, they are Top down and bottom up. The top down method is one of the thinking methods which are use pattern from up, from general thing, some theories or references, and then we must classify or analyze it to be more simple and particular/concrete. We can get the general things from books, journal, report, research or etc.
The second method is Bottom up. It’s the opposite one of the first method. We use an inductive approach. We usually submit some facts or valid samples and then we can conclude the problem.
marsigitpsiko.blogspot.com
rumahmakalah.wordpress.com
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