Small Research

This small research has be done to Muhammad Wahyu Setyo Budi, he is student in SMP N 1 Kotamungkid, class VIII. I do small research about space shape, which is a part of geometry. In this small research, I use some methods; they are observation, test and interview.
1. Observation
Observation in this small research is direct observation, which is I must see and observe directly and then make a note about behavior and condition that happen in real situation. Observation has be done along small research is done, from begin until finish.
2. Test
Test the in this small research was done to know the ability of early student so that researcher can plan the action to be taken in improve repairing study process.
3. Interview
Interview at this small research use the interview that haven't a structure, because researcher look into this model is most supple, where student given free rein to elaborate his answer and his view expression freely and according to his opinion. This interview used to get the data of student's opinion about concerning applying of original object as study media, in space shape material.
Teaching and learning activity about space shape can be presented by using strategy or approach and can be presented by using interesting media and can overcome the problems, that is method of study based on some problems. Finally teaching and learning activity can done well, motivation to learn of the student can increase, and in the end study achievement of student will increase too.
Pursuant to existing condition, so researcher plan the space shape lesson by utilizing study media space shape, so that student has motivation in learning, so that learn achievement will increase too.
Erudite attitude owned by the student will enable the student condition in face to some sciences, especially in learning mathematics because forming student’s view in learning mathematics have to can be learned and exploited for the daily life. For example in mathematics lesson, this erudite attitude can be seen with look at curiosity of student to know how come the formula can be exist, and how formula the applicable. Student in learning something, also represent part of erudite attitude of student. Student in this case will try to evaluate his work.
Erudite attitude of student, which are coming from curiosity of student, student sincerity
and also critical attitude of student in learning a lesson, specially mathematics Lesson, make the student in learning mathematics will serious without there are constraint from others. These erudite attitudes of student will make a student think much of the lesson, so that result of learning obtained student will be good.
Abstract of mathematics which learned by student during the time is abstraction mathematics, so that in the process of its understanding, student often face to constraints too long. So that student requires the map of conception in learning something, especially mathematics. In arrangement of this map compilation conception expected that a student have the path think real correct and systematically in finishing mathematics problem.
In the geometry mathematics, efficiency reached with the following aspect,
1. Identification plane and space shape according to nature of, element, or similarity.
2. Do accounting operation about the perimeter, area, volume and set of measurement.
3. Make approach about size measure (for example: long, wide, volume) from object
4. Make application geometry concept which interconnected in daily life

Acquire important mathematical knowledge (including mathematical facts, mathematical activity experiences), basic mathematical thinking methods, and necessary application skills that of are essential for adapting to future social life and further development.
Begin to know how to deploy various ways of mathematical thinking to observe, analyze realistic world, solve problems encountered in daily living and studies in other disciplinary areas.
When researcher give some question to student about space shape for example about block, cube, cylinder, sphere, and cone, student tend to mention about the form, element, and its size or measure. Not about color, price, and its substance.
- Student does the abstraction to block, cube, cylinder, sphere, and cone.
Model of the block---Abstraction---part of block: pallet, high, blanket, volume block,
Model of the sphere ---Abstraction---- part of sphere: sphere radius, diameter, sphere’s blanket, volume of the sphere,
Model of the cube--- Abstraction--- -- part of cube: pallet, high, blanket, volume block,
Model of cone---Abstraction--- part of cone: cone pallet, top, high, blanket, volume cone
Model of cylinder –Abstraction— part of cylinder: pallet, high, blanket, and volume tube.
Student will be more is clear catch the items space shape that is given, if its clarification also accompanied by the physic appliance, so that student can do the perception manifestly, and can compare the forms space shape with the object [of] exist in around them.
o Define the space shape with the sentences of daily life. Cylinder is object for save water, like “drum". Student cannot define the sphere meaning. So when researcher gives some questions about sphere, student reply that sphere is often used to play at the ball. Or can also like planet form. Cone is object looking like form "contong" ice-cream. Cone is triangle having circle pallet.
In explain the part of space shape, the student will feel easier by showing it with physic appliance. Even when comprehending about volume and area of surface very felt its difference. Student far easier comprehend it if using physic appliance.
When researcher gives some question to student about area of surface space shape, student has initiative to cut the space shape so that become the net of space shape. So that student will itemize the some types of plane which arrange space shape.
a. student explain that plane which arrange a tube are two circle and one rectangle. Student have mentioned that high of cylinder is wide of rectangle and perimeter of the circle is the length rectangle
b. Student found difficulties when asked about net of cone. Student can lay open that cone pallet is circle, but he still Confucius about the form of cone blanket. Initially student assumes that the form of cone blanket is triangle, but in the reality when he tries by physic appliance, its result does not that way.
c. Student not yet can lay open about area of sphere surface, if not related to by an existing formula. Because student can not mention about the net of sphere.
When researcher give some question to student about concept space shape. Reply of the student:
a. Student expresses the cube concept with the concept square. So the cube is square which has contents
b. Student expresses the block concept by rectangle. So, the block is rectangle which has contents.
c. Student express the concept cylinder is circles that having high.
d. Student express the cone concept is triangle that having radian pallet, so that this triangle has contents
When researcher give some question to student about concerning unsure, volume, and area of surface, student have laid open by symbols is mathematics. Student also have comprehended that elementary formula from volume space shape is area of pallet times height.
a. student express that area with “L”, volume with “V”, radius with “r”, length with “p”, wide with ”l”, and high with “t”.
b. student express that area of cube surface is six times the area of square. Student express the volume cube is area of square times the length of square (representing high of cube)
c. student express that area of block surface is amount of the area of rectangle which arrange it, where rectangle which look out on to have same area. Student express that volume block is area of rectangle (representing pallet of block) times the wide of rectangle which straighten.
d. student express that area of cylinder surface is addition the area of two circles and the area of rectangle. Student express that volume of cylinder is the area of circle times the wide of rectangle (representing high of cylinder)
e. student not yet can lay open about the surface area and the volume of cone and the surface area of the sphere, if only seeing physic appliance ( do not see the formula which there have), because student not yet can lay open the form net which both of them.

The Power of Category and Networking

According Kant’s theory, in our mind there are some category. With the categories which are in our mind, we can get some knowledge. In Immanuel Kant’s theory, category involves four things. They are Quantity, Quality, Relation, and Modality.
Every category consists of three aspects:
1. Quantity
• Universal
 Universal is only one
 It can load all of everything
• Particular
 Form a parts or groups
 Easy to be in groups
• Singular
 Form a parts or groups
 Be autonomous
2. Quality
• Affirmative
 All of things which has positive character
 Explanation of some statements
• Negative
 All of things which has negative or abjuration character
 Explanation of some statements
• Infinite
 All of things which has infinite character
 Restrictive
3. Relation
• Category
 Has function to difference thing with another
• Hypothetic
 Explanation about cause and effect relation
• Community
 Interaction between active and passive
4. Modalities
• Probabilities
 Has problematic character
 In between possible and impossible
• Asetorik
 In between exist and not exist
• Apodictic
 Work based on consistency
With those categories, we can build knowledge that we get it before. With use those category, contains of experiences are managed and then will be product.
We study to understand about category, it means we study to aware that there are things that should be in phenomena, there are things that should be in mind, and there are things that should be in “epoke”.
We study about category, will make us easy to face some knowledge. And we can get knowledge from school or from daily life. The example of category is mathematics education phenomena.
In the teaching and learning of Mathematics, there are idealization and abstraction. What are they?
1. Idealization
Idealization is only in our mind. We assume that the characteristic of Mathematics is absolutely true. So we consider that something is perfect. It is just to consider because there is no anything in this world can be perfect.
2. Abstraction
Abstraction is not same with abstract. Abstraction is only to learn some characteristics from object, not at all. There are differences between abstract and abstraction. We know that abstract is not concrete. We can’t see, touch, and observe, but we can imagine about it. On the other side abstraction is the value which is contained in mathematics.
Mathematics consists of three aspect:
1. Math-attitude
As mathematicians which have good attitude, we must always positive thinking, consistent, diligent, and always have questions about problem.
2. Math-method
How to learn mathematics? We can use one of some methods of mathematics. They are deductive, inductive, syllogism.
o Deductive is based of each lesson about formal logic
o Inductive
o Syllogism can be used to make new conclusion from some premise
3. Content
Mathematics consists of two kinds:
o Horizontal mathematics
Example: daily mathematics. The object of this mathematics is real object.
o Vertical mathematics
It is pure mathematics, which is developing in college.