sifaf dan unsur bangun ruang lengkung

Bangun ruang

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Materi GT untuk UK 3

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Persaingan Tak Sehat

Sore itu,, aku pulang kuliah pukul 18.00. Sampai di kos,, langsung kutatap jajanan yang biasa tertata rapi di dekat TV.
tuing...saat itu pula aku terkejut karena jajanan kripik singkong pedas yang tebal dan biasa kami serbu tak terlihat olehku. Dan anehnya...bakul jajanan yang satunya (bukan penjual kripik) menaruh jajanannya di dekat TV dan menyembunyikan kripik di suatu tempat yang susah kami raih dan ditutupi penutup TV. Astagfirullah...

Memang kami menyadari, kalau kosan kami diprop kripik, kripik itu biasanya 2 hari sudah lenyap alias kami borong. Tapi ketika didrop jajanan yang lain (bukan dari penjual kripik) satu minggu aja masih banyak yang sisa. Tapi persaingan yang tidak sehat itu apakah halal????hehehe

Menurutku, bersaing iu sah-sah saja tapi bukan gini caranya... Tunjukkan bahwa dagangan anda patut untuk bersaing. Kita perbaiki tampilan dagangan kita, bukan dengan menyembunyikan dagangan orang lain dengan alasan yang tidak jelas.

Begitu pula dengan studi kita, Yuk kita bersaing sehat!!! Kalo menang karena mencontek apakah itu sehat???
Semangat,,kita ciptakan generasi penerus yang berkarakter dan jujur...

Materi Lomba MTK se karisidenan Surakarta

Happy Ramadhan

Happy Ramadhan for all mooslem
I hope wi will be better than before.
Forgive me with everithing my weak,, my ego.


I hope our fasting is afdhol and barokah..

Daftar Nilai Maple UK 1&2

Daftar Nilai Maple UK 3&4

Indefined Integral

Realistic Mathematics Education

RME in brief

Realistic Mathematics Education, or RME, is the Dutch answer to the world-wide felt need to reform the teaching and learning of mathematics. The roots of the Dutch reform movement go back to the early seventies when the first ideas for RME were conceptualized. It was a reaction to both the American "New Math" movement that was likely to flood our country in those days, and to the then prevailing Dutch approach to mathematics education, which often is labeled as "mechanistic mathematics education."

Since the early days of RME much development work connected to developmental research has been carried out. If anything is to be learned from the Dutch history of the reform of mathematics education, it is that such a reform takes time. This sounds like a superfluous statement, but it is not. Again and again, too optimistic thoughts are heard about educational innovations. The following statement indicates how we think about this: The development of RME is thirty years old now, and we still consider it as "work under construction."

That we see it in this way, however, has not only to do with the fact that until now the struggle against the mechanistic approach to mathematics education has not been completely conquered— especially in classroom practice much work still has to be done in this respect. More determining for the continuing development of RME is its own character. It is inherent to RME, with its founding idea of mathematics as a human activity, that it can never be considered a fixed and finished theory of mathematics education.

"Progress" issues to be dealt with

This self-renewing feature of RME explains why it is work in progress. But, there are at least two more aspects. One significant characteristic of RME, is the focus on the growth of the students’ knowledge and understanding of mathematics. RME continually works toward the progress of students. In this process, models which originate from context situations and which function as bridges to higher levels of understanding play a key role. Finally, considering the TIMSS results, it seems that RME really can elicit progress in achievements.

RME, History and founding principles

The development of what is now known as RME started almost thirty years ago. The foundations for it were laid by Freudenthal and his colleagues at the former IOWO, which is the oldest predecessor of the Freudenthal Institute. The actual impulse for the reform movement was the inception, in 1968, of the Wiskobas project, initiated by Wijdeveld and Goffree. The present form of RME is mostly determined by Freudenthal’s (1977) view about mathematics. According to him, mathematics must be connected to reality, stay close to children and be relevant to society, in order to be of human value. Instead of seeing mathematics as subject matter that has to be transmitted, Freudenthal stressed the idea of mathematics as a human activity. Education should give students the "guided" opportunity to "re-invent" mathematics by doing it. This means that in mathematics education, the focal point should not be on mathematics as a closed system but on the activity, on the process of mathematization (Freudenthal, 1968).

Later on, Treffers (1978, 1987) formulated the idea of two types of mathematization explicitly in an educational context and distinguished "horizontal" and "vertical" mathematization. In broad terms, these two types can be understood as follows.

In horizontal mathematization, the students come up with mathematical tools which can help to organize and solve a problem located in a real-life situation.

Vertical mathematization is the process of reorganization within the mathematical system itself, like, for instance, finding shortcuts and discovering connections between concepts and strategies and then applying these discoveries.

In short, one could say — quoting Freudenthal (1991) — "horizontal mathematization involves going from the world of life into the world of symbols, while vertical mathematization means moving within the world of symbols." Although this distinction seems to be free from ambiguity, it does not mean, as Freudenthal said, that the difference between these two worlds is clear cut. Freudenthal also stressed that these two forms of mathematization are of equal value. Furthermore one must keep in mind that mathematization can occur on different levels of understanding.

Misunderstanding of "realistic"

Despite of this overt statement about horizontal and vertical mathematization, RME became known as "real-world mathematics education." This was especially the case outside The Netherlands, but the same interpretation can also be found in our own country. It must be admitted, the name "Realistic Mathematics Education" is somewhat confusing in this respect. The reason, however, why the Dutch reform of mathematics education was called "realistic" is not just the connection with the real-world, but is related to the emphasis that RME puts on offering the students problem situations which they can imagine. The Dutch translation of the verb "to imagine" is "zich REALISEren." It is this emphasis on making something real in your mind, that gave RME its name. For the problems to be presented to the students this means that the context can be a real-world context but this is not always necessary. The fantasy world of fairy tales and even the formal world of mathematics can be very suitable contexts for a problem, as long as they are real in the student's mind.

The realistic approach versus the mechanistic approach

The use of context problems is very significant in RME. This is in contrast with the traditional, mechanistic approach to mathematics education, which contains mostly bare, "naked" problems. If context problems are used in the mechanistic approach, they are mostly used to conclude the learning process. The context problems function only as a field of application. By solving context problems the students can apply what was learned earlier in the bare situation.

In RME this is different; Context problems function also as a source for the learning process. In other words, in RME, contexts problems and real-life situations are used both to constitute and to apply mathematical concepts.

While working on context problems the students can develop mathematical tools and understanding. First, they develop strategies closely connected to the context. Later on, certain aspects of the context situation can become more general which means that the context can get more or less the character of a model and as such can give support for solving other but related problems. Eventually, the models give the students access to more formal mathematical knowledge.

In order to fulfil the bridging function between the informal and the formal level, models have to shift from a "model of" to a "model for." Talking about this shift is not possible without thinking about our colleague Leen Streefland, who died in April 1998. It was he who in 1985* detected this crucial mechanism in the growth of understanding. His death means a great loss for the world of mathematics education.

Another notable difference between RME and the traditional approach to mathematics education is the rejection of the mechanistic, procedure-focused way of teaching in which the learning content is split up in meaningless small parts and where the students are offered fixed solving procedures to be trained by exercises, often to be done individually. RME, on the contrary, has a more complex and meaningful conceptualization of learning. The students, instead of being the receivers of ready-made mathematics, are considered as active participants in the teaching-learning process, in which they develop mathematical tools and insights. In this respect RME has a lot in common with socio-constructivist based mathematics education. Another similarity between the two approaches to mathematics education is that crucial for the RME teaching methods is that students are also offered opportunities to share their experiences with others.

In summary, RME can be described by means of the following five characteristics (Treffers, 1987):

* The use of contexts.
* The use of models.
* The use of students’ own productions and constructions.
* The interactive character of the teaching process.
* The intertwinement of various learning strands.

Perjalanan kurikulum di Indonesia

Inequalities of Trigonometry

Differential Equation

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics, and other disciplines.
Differential equations arise in many areas of science and technology, specifically whenever a deterministic relation involving some continuously varying quantities (modeled by functions) and their rates of change in space and/or time (expressed as derivatives) is known or postulated. This is illustrated in classical mechanics, where the motion of a body is described by its position and velocity as the time varies. Newton's laws allow one to relate the position, velocity, acceleration and various forces acting on the body and state this relation as a differential equation for the unknown position of the body as a function of time. In some cases, this differential equation (called an equation of motion) may be solved explicitly.
An example of modelling a real world problem using differential equations is determination of the velocity of a ball falling through the air, considering only gravity and air resistance. The ball's acceleration towards the ground is the acceleration due to gravity minus the deceleration due to air resistance. Gravity is constant but air resistance may be modelled as proportional to the ball's velocity. This means the ball's acceleration, which is the derivative of its velocity, depends on the velocity. Finding the velocity as a function of time involves solving a differential equation.
Differential equations are mathematically studied from several different perspectives, mostly concerned with their solutions—the set of functions that satisfy the equation. Only the simplest differential equations admit solutions given by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form. If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.
In the first group of examples, let u be an unknown function of x, and c and ω are known constants.

• Inhomogeneous first-order linear constant coefficient ordinary differential equation:

• Homogeneous second-order linear ordinary differential equation:

• Homogeneous second-order linear constant coefficient ordinary differential equation describing the harmonic oscillator:

• First-order nonlinear ordinary differential equation:

• Second-order nonlinear ordinary differential equation describing the motion of a pendulum of length L:

In the next group of examples, the unknown function u depends on two variables x and t or x and y.

• Homogeneous first-order linear partial differential equation:

• Homogeneous second-order linear constant coefficient partial differential equation of elliptic type, the Laplace equation:

• Third-order nonlinear partial differential equation, the Korteweg–de Vries equation:

Linear Programming

Dalam matematika, pemrograman linear ialah teknik optimisasi yang melibatkan variabel-variabel linear. Dalam model pemrograman linear dikenal dua macam fungsi, yaitu fungsi objektif (objective function) dan fungsi kendala (constraint function) yang linear.
Pemrograman linear dapat direpresentasikan dalam notasi matematis sebagai berikut:

Maksimalkan

dengan syarat

dan

Dalam hal ini, x ialah vektor variabel, sedangkan c dan b ialah vektor koefisien dan A ialah matriks koefisien. Fungsi objektifnya ialah ekspresi yang hendak dimaksimalkan atau diminimalkan (yaitu c^Tx). Persamaan Ax ≤ b ialah fungsi kendala yang menunjukkan polihedron konveks tempat fungsi objektifnya dioptimisasi.
Pemrograman linear dapat diterapkan pada berbagai bidang studi. Metode ini paling banyak digunakan dalam bisnis dan ekonomi, namun juga dapat dimanfaatkan dalam sejumlah perhitungan ilmu teknik. Misalnya, dalam ekonomi, fungsi tujuan dapat berkaitan dengan pengaturan secara optimal sumber-sumber daya untuk memperoleh keuntungan maksimal atau biaya minimal, sedangkan fungsi batasan menggambarkan batasan-batasan kapasitas yang tersedia yang dialokasikan secara optimal ke berbagai kegiatan. Industri yang memanfaatkan pemrograman linear di antaranya ialah industri transportasi, energi, telekomunikasi, dan manufaktur. Pemrograman linear juga terbukti berguna dalam membuat model berbagai jenis masalah dalam perencanaan, perancangan rute, penjadwalan, pemberian tugas, dan desain.