PERAN INTUISI DALAM MATEMATIKA MENURUT IMMANUEL KANT

by Masigit
reviewed by Naafi Awwalunita (09301241024)
According to Kant, mathematics as a science is possible if the concept of mathematical intuition constructed based on spatial and time. Construction of mathematical concepts by intuition of space and time will come in result that mathematics as a science is "synthetic a priori". By Kant’s view, synthetic methods opposed to analytic methods and the concept of "a priori" opposed to "a posteriori". If the mathematics is developed only by the method of "analytic" it will not be generated (constructed) a new concept, and because of that, math is just as science fiction.
According to Kant, mathematics was not developed just by the concept of "a posteriori" because if so, math would be empirical. But the empirical data obtained from sensory experiences are needed to explore mathematical concepts that are "a priori". This is where the unique role of Kant's theory, which attempts to give a solution (middle) of extreme conflict between the rationalist and the empiricist in building the foundation of mathematics. According to Kant, intuition becomes the core and key to the understanding and construction of mathematics.
Kant's view of mathematics can contribute significantly in terms of the philosophy of mathematics, especially regarding the role of intuition and the construction of mathematical concepts. Michael Friedman (Shabel, L., 1998) mentioned that what Kant accomplished has given the depth and accuracy of the mathematical basis, and therefore its achievement cannot be ignored. In the ontology and epistemology, after the era of Kant, mathematics has been developed with these approaches are somewhat influenced by Kant's view.
Some authors argue that Kant's philosophy of geometry to depart from the bridge to the philosophy of arithmetic and algebra philosophy. But if you listened further, the views of Kant's prefer to basic on the role of intuition for the concepts of mathematics and only rely on the concept of construction as in Euclidean geometry. There was the view that the construction of spatial concepts of Euclidean geometry is actually based on "pure intuition" but Kant gave a new trend on the view of mathematics a more constructive (Palmquist, SP, 2004).
According to Kant (Wilder, RL, 1952), mathematics must understood 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 to explain and predict natural phenomena. According to him, mathematics can be understood through "sensing intuition", as long as the results can be customized with 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 we will also get an overview of the development of mathematical foundation of the philosophy of Plato to contemporary mathematics, through the common thread of philosophy and constructivism intuitionism.
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.) concluded that mathematical truths are synthetic a priori truths. Truths of logic and truth are revealed only through the definition of the truth of which is analytic.
Truth can be intuitive analytic a priori. But, the truth of mathematics as 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 result in a decision. 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 arithmetic concepts 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
sensing intuition, but human reason can not reveal the nature of mathematics as "noumena" but only revealed as a "phenomenon".
Kant has an important contribution because his theory 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 by 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.

Memanfaatkan Microsoft Word 2007 Sebagai Media Pembelajaran Geometri di SMP

by: Dr. Marsigit M.A.
Jurusan Pendidikan Matematika, FMIPA Universitas Negeri Yogyakarta
reviewed by Naafi Awwalunita (09301241024)

Geometry in middle school instructional media developed as the business implications of achieving the Standard of Competence and competency as its written in Kurikulum Tingkat Satuan Pendidikan (KTSP). Development of instructional media geometry is determined also by the method and type of learning approach that teachers do. On the other hand, computers today are widely used in schools. Use of computers, particularly Microsoft Word 2007 is one of the efforts that teachers could do toward existing learning resources. Microsoft Word 2007 is easy to use and easy to access because the software is almost available in all the latest computer. Utilization of Microsoft Word as a medium of learning geometry in junior high will make a positive contribution to both the teachers and their students.

With Microsoft Office 2007, we can develop learning teaching geometry at school. Microsoft Office 2007 provide Smart Art Graphic so that users can create different kinds of graphs. With Smart Art graphics tools, we can create different kinds of geometry dimensions 2 or 3 dimensions. With Smart Art graphics devices we also create animation in our shapes as well as add text for explanation in any kinds of images.

By utilizing the various facilities within the Microsoft Office 2007, we can develop a medium of learning geometry in junior high. Media learning geometry at school is an implication of the elaboration of the Standard of Competence (SK) and Basic Competence (KD) as follows. In particular, the Standard of Competence junior high school students related to the geometric capability can be mentioned as follows:

1. Understanding the relationship line to line, line with an angle, corner angle, and determine its size

2. Understand the concept of a rectangle and a triangle and determine its size

3. Use the Pythagoras Theorem in problem solving

4. Determine element, the circle and its size

5. Understanding the properties of the cube, beam, prism, pyramid, and their parts, and determine its size

6. Understand basic shapes and its use in problem solving

7. Understand the properties of tubes, cones and spheres, and could determine its size

The use of Microsoft Word 2007 software can be easily done because the software is available on all new computers. The tools will help a lot in building geometry using Microsoft Word 2007. The tools can help us to make more complex of 2-dimensional geometry such as 3-dimensional geometry. Student skills can be improved by studying the aspects of geometry with a higher standard of competence, for example to determine the value of pi.
From the above description can be concluded that:

a. The use of Microsoft Word 2007 easily done by the teacher because the software is available in almost every new computer generation.

b. The use of Microsoft Word 2007 will increase the motivation and pleasure in studying geometry.

c. Students can use Microsoft Word 2007 to study the geometry either independently or through collaboration.

d. By using Microsoft Word 2007, students can investigate concepts of geometry.

e. By using Microsoft Word 2007, students can perform activities of problem solving or solving mathematical problems.

f. By using Microsoft Word 2007, students can communicate its results to both the teacher and to other friends.

Karakteristik Matematika, Subyek Didik dan Belajar Matematika Sebagai Dasar Pengembangan Kurikulum Matematika Berbasis Kompetensi di SMP

By : Marsigit

Reviewed by Naafi Awwalunita

Curriculum developing and planning are not an easy task because it need strive and comprehensive analyze to fulfill the standard requirements. Nowadays in Indonesia, the curriculum development need to notice about: the newest education issues, problems in fields, school variations, education workers, skill and students interest, school need, science and technologies. There are also six basic principal which should be noticed when we’re about to develop mathematics subjects based on basic competence such as:

1.       Study chance for all people without any exception.

2.       Curriculum is not only about material composition but also it could reflect mathematics activities coherently.

3.       Mathematics teaching learning process need an understanding point about students need, ready, and teaching learning facility services.

4.       Students have a chance to study about mathematics actively to build a concept structure through science and their experience.

5.       It needs assessment activities to increase the quality of learning process as the time goes by.

6.       Using various strategies and method of mathematics teaching learning difficulties and flexibilities based on learning context.

Teaching mathematics is not an easy job because facts had shown to us that students feel difficulty in learning mathematics (Jaworski, 1994). It seems like we should differentiate between mathematics and mathematics in school. In order to fulfill the innovation of education demand in common, Ebutt and Straker (1995: 10-63) defined that mathematics in school which later on it called mathematics as:

1.       Mathematics is experiencing pattern and relation activities

2.       Mathematics as creativity which needs imaginations, intuition and research

3.       Mathematics as a problem solving activities

4.       Mathematics as a communication tool

Now we will talk about student characteristic. Ebutt and Staker (1995: 60-75) gave us their view that in order to maximize student potential character, we should give an assumption and implication to mathematics teaching learning process like:

a.       Student will comfortably learning mathematics if they have motivation.

b.      Student learn mathematics with their own style

c.       Student learn mathematics by their self or cooperate with their friends

d.      Student need different context and  situation when it comes to learn mathematics

Experience and learning activities are a must for students to get through in order to achieve the goals of basic competence and learning subjects. If we looked at the goals, learning experience could be gained from remembering, using and finding. In the other hand, if we looked at material side, then we can conclude that learning experience could be related by gaining facts, concept, principal, etc. learning experience could be gained either from inside or outside of the class.

Student experience should be supported by sources including direct objects or indirect objects which have contextual meaning. With that condition, developing learning strategies could have meaning such as: 1. Strive in solving problems, 2. Learn in every daily context of life, 3. Push the student as an active learner, 4. Respect the unique of each student and notice the differences between students, 5. Learn by cooperative learning and 6. Develop assessment in the middle of test system.

Pemanfaatan Video Tape Recorder (VTR) Untuk Pengembangan Matematika Realistik di SMP

By Dr. Marsigit, MA

Reviewed by Naafi Awwalunita

As we know, realistic mathematics concern about construction and concrete content as the first step for students to again mathematics concept. Real things and another objects among us in our environmental could actually used as learning-teaching mathematics when the students are about constructing the relation between concepts of mathematics trough social interaction.

According to Hans Freudental in Sugiman (2007), mathematics is a human activities and it is indeed need to be related with reality. Hence, when students are learning mathematics, the mathematical thinking is actually going on student’s mind. In this article, Dr. Marsigit would later describe and analyze about mathematics teaching learning which recorded in the video tape recorder is one of million ways that teachers could choose from. Using video tape recorder, the writer hope that later on, the teacher could learn more on how:

1.       Prepare mathematics teaching learning in Junior High School based on PMRI principal.

2.       Develop learning sources for mathematics teaching learning process in Junior High School based on PMRI principal.

3.       Develop assessments activities for mathematics teaching learning in Junior High School based on PMRI principal.

4.       Do the mathematics teaching learning in Junior High School based on PMRI principal.

Implementation of PMRI could barely describe as realistic type that has a bottom-up type of approaching method where the student develop their own model and later, that model become basic understanding to develop formal mathematics. There are two models which happen in that process such as model of situation and model for formal mathematics. In the realistic model which emerges from informal strategy as student respond over real problems for that later they will form it as a formal mathematics. This process is actually as the same as the history of mathematics development itself (Sugiman, 2007).

By observing and analyzing the use of video tape recorder for mathematical study, the teacher use realistic approach so that other teacher could test it and look for another option to develop any concepts or ideas about concrete things and objects among us which can be used as mathematics teaching learning context in building mathematical relation through social interaction.

There are some pictures in this article which describe about what kind of action did the writer record for his research. It showed that the writer use video tape recorder for geometry teaching learning. It showed that there are two or more students tried to find a formula for ball vast by covered up the surface. There were also sequence caption that show on how two or more students using a can and cone model also sand to find the formula for cone’s volume.

Using video tape recorder for mathematics teaching learning with realistic approaching gives us a lot of advantages:

1.       Teachers could have a chance to test concrete things and objects among our environment which can be used as mathematics teaching learning context in building mathematics relation through social interaction.

2.       Teachers could have a chance to gain and reflect realistic mathematics teaching learning concepts.

3.       Teachers could have a chance to exchange experiences with another teachers about developing realistic mathematics teaching learning.

4.       Teachers could have a chance to reflect their preparation in realistic mathematics teaching learning process in Junior High School based on PMRI’s principal.

5.       Teachers could have a chance to reflect the development of learning sources for mathematics teaching learning based on PMRI’s principal.

6.       Teachers could have a chance to reflect the development of assessment activities for mathematics teaching learning based on PMRI’s principal.

The Effort to Increase The Student’s motivation in Mathematics Learning with Some Teaching Aids in Junior High School 5 Wates, Kulon Progo, Yogyakarta, Indonesia

By Marsigit & Ida Supadmi

Reviewed by Naafi Awwalunita

Salah satu cara yang dilakukan seorang guru untuk meningkatkan motivasi seorang murid pada pembelajaran matematika di sekolah menengah pertama adalah dengan membuat belajar dan mengajar matemtika menjadi proses belajar mengajar yang menyenangkan, menarik karena dihubungkan langsung dengan kebutuhan sehari-hari. Memaksimalkan peran guru dan alat-alat untuk pendemonstrasian yang diharapkan dapat membantu proses belajar siswa yang kesulitan.

Riset yang bertujuan untuk menyelesaikan masalah yang ditemukan dalam kelas dua sekolah menengah pertama 5 Wates, Kulon Progo, Yogyakarta pada tahun ajaran 2001/2002. Pendekatan yang digunakan adalah untuk memilih dan menggunakan bantuan pengajar yang digunakan sebagai model belajar pada proses belajar mengajar matematika melalui riset tersebut. Diharapkan nantinya dengan metode seperti yang telah disebutkan, minat belajar siswa akan bertambah.

Sukses tidaknya suatu proses belajar mengajar tidak luput dari peran guru sebagai informatory, komunikator, dan fasilitator. Metode pengajaran yang digunakan guru akan sangat berpengaruh pada interaksi diantara guru dan murid. Sampai sekarang kita masih mendengar banyak komplain yang diutarakan para murid bahwa matematika adalah sesuatu yang menyeramkan, tidak menarik, sangat susah dipahami, dan tidak berkaitan dengan kehidupan sehari-hari. Hal ini dibuktikan melalui hasil tes ujian nasional yang masih dibawah rata-rata. Walaupun begitu, tentu saja masih banyak anak-anak yang menyukai matematika.

Sikap/kelakuan murid dipengaruhi oleh dua factor yaitu internal dan eksternal (Winoto Putro, 1993:33). Sama seperti sikap/kelakuan murid, proses belajar mengajar juga dipengaruhi oleh dua factor di bawah ini. Factor internal pada murid, guru harus memotivasi murid-murid seperti apa yang telah diajarkan oleh Ki Hajar Dewantara “Ing Madyo Mangun Karsa” yang berarti bahwa guru harus mendukung motivasi belajar peserta didiknya (Mugiharso, 1933).

Murid-murid sekolah menengah pertama yang berada pada umur 12 – 15 tahun menurut perkembangan kognitif Piaget, termasuk ke dalamoperasi formal. Pada level ini, pemahaman muncul dari ide-ide untuk membandingkan, berdiskusi, dan membuat kesimpulan. Ada perubahan dari fungsi intelektual dari berpikir konkrit ke abstrak (Suardiman, 1986,36). Bantuan guru akan sangat berguna bagi proses berpikir abstrak para siswa.

Setelah dilakukan beberapa percobaan/riset yang dilakukan langsung di kelas matematika menggunakan metode yang telah disebutkan sebelumnya, hasilnya menunjukkan bahwa menggunakan bantuan guru seperti papan tulis paku, karet, kartu, kertas kerja siswa, kertas transparan, dan masih banyak lagi ternyata menaikkan motivasi dalam proses belajar mengajar siswa. Merujuk pada hasil riset, penulis menganjurkan para guru sekolah menengah pertama untuk menggunakan variasi dalam proses belajar mengajar siswa yang bertujuan untuk meningkatkan motivasi para siswa dan menghindari kebosanan, juga selalu menggunakan demonstrasi alat bantuan secara optimal untuk menjelaskan konsep, ide, definisi, atau beberapa prosedur.