PERAN INTUISI DALAM MATEMATIKA MENURUT IMMANUEL KANT

By : Dr. Marsigit, M. A.
Reviewed by: Resti Safitri (09301241012)

According to Kant (Wilder, RL, 1952), mathematics must dipahamai and constructed using pure intuition, that intuition "space" and "time". Mathematical concepts and decisions that are "synthetic a priori" will cause the natural sciences had become dependent on mathematics in explaining and predicting natural phenomena. According to him, mathematics can be understood through "intuition sensing", as long as the results can be adapted to our pure intuition.

Kant's view about the role of intuition in mathematics has provided a clear picture of the foundation, structure and mathematical truth. Moreover, if we learn more knowledge of Kant's theory, in which dominated the discussion about the role and position of intuition, then we will also get an overview of the development of mathematical foundation from Plato to the contemporary philosophy of mathematics, through the common thread intutionism philosophy and constructivism .

Kant (Randall, A., 1998) concluded that the mathematics of arithmetic and geometry is a discipline that is synthetic and independent from one another. In his work The Critique of Pure Reason and the Prolegomena to Any Future Metaphysics, Kant (ibid.) concludes that mathematical truths are synthetic a priori truths. Logic of truth and the truth is revealed only through the definition of the truth of which is analytic.

Truth is intuitive analytic a priori. But, the truth of mathematics as a synthetic truth is a construction of a concept or several concepts that generate new information. If the concept is derived purely from empirical data obtained then the verdict was the verdict of a posteriori. Synthesis derived from pure intuition a priori decision produces.

Kant (Wegner, P.) concluded that intuition and decisions that are "synthetic a priori" applies to geometry and arithmetic. The concept of geometry is "intuitive spatial" and the concept of arithmetic are "intuitive time" and "numbers", and both are "innate intuitions". With the concept of intuition, Kant (Posy, C., 1992) wanted to show that mathematics also requires empirical data is that the mathematical properties can be found through intuition sensing, but the human mind can not reveal the nature of mathematics as "noumena" but only reveal as a "phenomenon".

Kant (ibid.) to contribute because it gives a middle way that mathematics is synthetic a priori decision, the decision which first obtained a priori from the experience, but the concept is not obtained empirical (Kant, I, 1783), but rather pure. Knowledge of geometry is synthetic a priori be possible if and only if understood in a transcendental concept of spatial and generate a priori intuition.

Pembudayaan Matematika di Sekolah Untuk Mencapai Keunggulan Bangsa

By : Dr. Marsigit, M. A.
Reviewed by: Resti Safitri (09301241012)

Materially, mathematics can be either concrete objects, pictures or models of cubes, colorful emblem or large numbers of small, square-shaped pond, pyramid-shaped roofs, the pyramids in Egypt, easel-shaped roof of a right triangle , wheel-shaped circle, and so on. Formally, the mathematics may take the form of pure mathematics, mathematical axiomatic, formal mathematics or mathematics deductively defined. Normatively, then we not only learn mathematics, both materially and formally, but we related by value or value in reverse mathematics. As for the metaphysical, mathematical dimensions reveal different levels of meaning and value can only be achieved by metacognition. That is one form of awareness of the various dimensions of mathematics. Civilize mathematics in schools is the range between the awareness of the various dimensions of mathematics, learn and develop attitudes that are supported by methods and content knowledge of mathematics, so that acquired skills
doing mathematics, to obtain a variety of experience conducting and researching mathematics and present it in various forms according to its dimensions.

In the effort to obtain objective knowledge or learning of mathematics, students may need to develop procedures for example: follow the steps made by others, creating an informal step, determining a first step, using the steps that have been developed, defining the steps that can be understood other people, comparing different step, and adjusting steps. Through such measures, the student will acquire mathematical concepts that have been actualized in him, so it can be said that mathematical knowledge is subjective. However, in some cases, subjective mathematical knowledge does not necessarily correspond to objective knowledge. To determine whether subjective mathematical knowledge in accordance with objective knowledge, students need to be given the opportunity to conduct publicity activities. Publication activity in practice can be either mathematical tasks given by teachers, homework, make paper, or take exams.

To be able to cultivate the necessary mathematical understanding of the meaning of mathematics in various dimensions. Dimensional mathematical meaning can be seen from the side dimensions of mathematics to objects and concrete objects to dimensions of mathematical objects - objects of mind. Mathematical communication includes communication materials, formal communication, the communication of normative and spiritual communication. In relation to the learning of mathematics then we are more suitable to define mathematics as the mathematics school, but for college-level mathematics as we define a formal mathematical or axiomatic. Acculturation of mathematics can contribute to the nation through innovation excellence pembelajran math is done continuously. In relation to gain superiority nation then we can think about mathematics, teaching mathematics and mathematics education at various levels of hierarchy levels or intrinsic, extrinsic or systemic.

MENGEMBANGKAN NILAI-NILAI FILOSOFIS MATEMATIKA DALAM PEMBELAJARAN MATEMATIKA MENUJU ERA GLOBAL

By : Dr. Marsigit, M. A.
Reviewed by: Resti Safitri (09301241012)

The development of mathematics education can be done at two levels ie at the macro and micro. At the macro level, the development of mathematics education should be able to renew the vision and develop as well educational paradigm of education while maintaining and improving the quality and professionalism and empowerment of communities towards the New Indonesia Indonesia is an open, democratic and united. For a practitioner of education (teachers), educational development on a macro level for a few things are beyond the scope of his thinking and his ability. But considering teacher education is a critical success, then teachers can play a role object and subject of the development of education by increasing the ability to educate and manage the classroom. But reality is not easy because it educates students find that learning is not easy. There are still a considerable gap between educational ideals and practices in the field.

Math scores can be seen from the context of ontological, epistemological and axiological within the limits of intrinsic value, extrinsik and systemic. For a self-learner of mathematics then the lowest value of mathematics is that if only his own use, a higher value if math can be used for public interest. But the highest math scores is if it can be used systemically for wider interest. But the values ​​of mathematics that is developed should be coupled with critical thinking because mathematics is none other than critical thinking itself. The sharpness of the future of mathematics can wander through the concept of teleology that what happens in the future at least be photographed through the present.

Nevertheless there are still other values ​​are related to levels of quality. At first the quality of math scores only appear on the outside, but on the quality of the second and third and so on then nilaimatematika is metaphysical. This is then known people with hermenitika method.
In the field of education, teachers need to continually evaluate deficiency or excess of teaching in order to obtain information for improvement of teaching; kalauperlu learn new techniques are more attractive and effective (Alexander, et al, in Bourne, 1992). For that teachers need to receive encouragement and assistance from relevant parties, especially the principal and school inspector, so that they can realize a good teaching; but it is important to the role and functions of the Principal,

Supervisors and Supervisors redefined return to conditions more conducive to the educational environment teachers and students to develop themselves. A teacher can reflect the style of teaching is good and flexible if the teacher is concerned to master the ways of organizing the classroom, teaching use of resources, achievement of the goal of teaching students according to ability, development of evaluation systems, the handling of individual differences, and the realization of a particular teaching style according to the needs .

LANDASAN PENGEMBANGAN DESAIN PEMBELAJARAN MATEMATIKA DI SEKOLAH LANJUTAN

By : Dr. Marsigit, M. A.
Reviewed by: Resti Safitri (09301241012)

Teach mathematics is not easy because we find that the (infinite) students are also not easy in learning mathematics. It is not there a best way untukmendidik mathematics. Method - appropriate learning methods are as follows:

•  method of exposition by the teacher.
• Method of discussion, between teachers and pupils and between pupils and students.
•  Method of problem solving (problem solving).
•  Method of discovery (investigation)
•  Methods of basic skills training danprinsip principles.
•   Method of application.

Constraints in the application of the above learning methods are:

• understanding of the
• meaning of the theory.
• how to implement it.
• the existing system
• environmental conditions.
•   learning facilities

The nature of learning is to bring together subjective and objective mathematical knowledge through social interaction to obtain, test, represents the new knowledge they have gained. Next will be discussed what is the nature of learning mathematics. The nature of learning mathematics are as follows:

1.      Mathematics is the search activity patterns and relationships.
 The implication of this view of the efforts of teachers are:

• Gives students the opportunity to conduct discovery and investigation of the pattern - the pattern to determine the relationship.
• provide an opportunity for students to experiment with a variety of ways.

2.      Mathematics is the creativity that requires imagination, intuition and invention.
The implication of this view of the efforts of teachers are:

•  Encourage  students to discover mathematical structures and designs.
• Encourage  students to other students who appreciate the discovery.
• Encourage  students to think reflexively.
• Do not recommend the use of a  particular method.

3.       Mathematics is a problem solving activity
The implication of this view of the efforts of teachers are:

•  Provide  an environment that stimulates learning math mathematical problem.
•  Help  students to solve mathematical problem using his own way. 
•    Help  students find the information needed to solve mathematical problems.

4.       Mathematics is a tool to communicate
The implication of this view of the efforts of teachers are:

•   Encourage students to recognize the nature of mathematics.
• Encourage  students to make an example the nature of mathematics.
•   Encourage  students to  explain the nature of mathematics.
•   Encourage  students to give reasons for the necessity of  mathematical activities.
• Encourage  students to discuss mathematical problems.  
• Encourage  students to read and write mathematics.