“How To Implement Design Instructional Into Inovatif Teaching Learning Of Mathematics”

            To explore the philosophical foundations of design development, to extend our visim, if we compare it with the philosophy of education so if that education is it characters stop to educational figure, if that philosophy, then the characters stop to philosophy figure.

            Emmanuel Kant's statement "if you want to see the world, then behold your intellect and mind" that means the world is none other than your own mind. Then we use the analogy to the mathematical world of mathematics is none other than your own mind. If students want to study mathematics then peek at the student's mind about math. So teachers have to look at the student's mind if you want to teach math. It is then a problem of Emmanuel Kant's statement, that is how far the teacher looked at students' thinking about mathematics. If we lower the world of science in education or psychology, it will be the theory of constructivism (Vygoski, Piaget, Paul Ernest). That means Emmanuel Kant has made ​​the development scheme of mathematics in students who are called schemata and use architecture word "to construct". By using the architecture word, we have a scheme of our mathematical knowledge from each other and are subjective or objective.

            Emmanuel Kant also defines mathematics as synthetic a priori. Formal mathematics is defined as the a priori nature of mathematics makes mathematics as a science that is coherent or consistent with one idea to another idea. According to the formalists, we can build a mathematical basis of the definition set out as a basic assumption, then become axioms, and theorems and find another new theorems. But according to Emmanuel Kant, before the formal mathematical founded, Emmanuel Kant (18th century) also have outlined that mathematics is synthetic. Synthetic is the nature properties of concrete objects or the law of cause and effect are attached to  concrete objects of experience. So Emmanuel Kant said that mathematics is a combination of logic and experience. Without the experience, the logic will not run, without the logic, the experience also is not run.

            The concept of constructivism are made ​​more concrete and more operational. The problem is how students construct their own mathematics while mathematics is the students' own self. And then came the problem is how our role as teachers facilitate students so students are able to build the world / character of its own. Character is not something given but something to be built by the students themselves. But teachers also have the prerogative rights in this case the teacher has the schema and the competence to create the conditions for students to build his own world. Because science will be more meaningful if obtained or discovery of herself through the experience and logic respectively.

            It is not easy to facilitate the students to be able construct their own knowledge because all things have dimensional, vertical and horizontal dimensions. In the framework of the implementation of innovative learning, then there is a class, lesson plans, syllabi, curriculum, paradigm, philosophy, etc.

            Viewed in terms of curriculum, so the problem is the curriculum as it is able to support the design facilitates learning in which students can construct their own math. The curriculum is divided into three, namely instrumental curriculum, individualized curriculum, and interactive curriculum. But if  the curriculum is divided into two so there are individual instrumental and curriculum / interactive.

            Instrumental curriculum is the curriculum in which is dominated by the spirit of implementing, achieving goals of the purpose of state both formally and operational  in education and considers the teacher as an instrument to achieve it. We can do the analysis and compare it with examples of which exist as it does in the partial state (usually former colonizer), developing countries that usually prefer to use the curriculum implementation or instrument because it is more easily reviewed or regulated by the government such as Indonesia.

            Paradigm of Instumental curriculum is the behaviorist or changes in behavior such as that implemented in Indonesia in 1975, it is highly behaviorist. In the government Orde Baru also instrumental curriculum is also very closely monitored by the government till everything was arranged by the government. Until Orde Reformasi, which occurred the tug between Orde Baru dan Orde lama, between container and content, between the local value and  global value, etc. that make it to a compromise - a compromise and the result are delamatis and contradictions. So KTSP is actually a contradiction because the label Education Unit Level Curriculum that should the curriculum but it turns out it contains nearly 80% of the content standards and content standards that comes from government or centralized curriculum. This could happen because of two lawsuits as a connector that can not be communicated so that everything can be accommodated. National Examination actually is an external examination which is characteristic of centralized curriculum.

            So if we want to create an instructional design that guarantees can facilitate students to be able to construct their own mathematics knowledge,  teacher should be smart to strengthen the content of the curriculum or the standards process. The more that can fullfill the standards in education then the better.

            So actually to build the country with a national curriculum, it will not work as it did in the Orde Baru dan Orde lama, but unfortunately Orde Reformasi have not been able to handle it. The problem in the implementation of this curriculum is the implementation of  National Examination. Because learning refers to the national exam do not need the theory to practice, but only work on the problems. But it can not build students own knowledge. So that a suitable curriculum to be able to develop an instructional design that facilitates students to be able to construct their own knowledge is individual / interactive curriculum and instrumental curriculum do not match with it. While the curriculum of individual / interactive underdeveloped in Indonesia because of the fear of an uprising that occurred as the effects of application of the individual / interactive. In the instrumental curriculum, the teacher's role is as a giver of knowledge. But if the curriculum of individual / interactive, teacher's role is as a facilitator of students.

            If viewed from the instrumental curriculum, Lesson Plan is uniform starting from the format until the components. If viewed from the curriculum of individual / interactive / innovative the Lesson Plan is belong to the teacher because of the Lesson Plan is the prerogative right of the teacher. Although there are basic components of the same ontology as its identity from the school's name, course name, teacher's name. But for components such as standards of competence, basic competence or outcome is left to the teachers want to use which. Learning stategy, method of learning and assessment are belong to the teacher. Of particular interest is how far the Lesson Plan is to ensure to facilitate the students to be able to construct their own knowledge. Lesson Plan also be kontextual the Lesson Plan should be different at each meeting. The Lesson Plan is used to control the good or not, can be done naturally by looking at graduates of the school or school quality.

            During the student worksheets teachers can buy it for that instead of student worksheet. But just a collection of student worksheet is a matter for each year kontextual which must be different because of differences in time so that differences in implementation. Student worksheet for the curriculum is simply a collection of instrumental but for learning about innovative student worksheet is a medium that is able to facilitate students to construct their own mathematics through innovative worksheet.Innovative learning is not learning the same two because of the time difference so that the implementations is different.

            How to construct mathematical knowledge:

1.      To breakdown the procedur into the component.

2.      The rasional of each components.

3.      The contribution each components.

4.      The relationship among the components.

5.      Herarki stucture of each goal components

6.      The direct logical implecation to the conclution.

            Student worksheet also lists their information  such as the extensive definition. Learning device is the Lesson Plan, student worksheet, and modules.

            Assesesment can be made into a portfolio. Portfolio can be divided into two, namely a portfolio compiled by the teacher and the portfolio is collected by the students. Differences in assessments that are authentic, classroom-based assessments and assessments that are formative, assessments are subjective or objective.