Pembudayaan Matematika di Sekolah Untuk Mencapai Keunggulan Bangsa
By: Drs. Marsigit MA
By: Drs. Marsigit MA
Reviewed By : Eka Sulistyawati
Materially, mathematics can be concrete objects, pictures or models of cube, colorful symbol of big or small numbers, square-shaped pond, pyramid-shaped roofs, the pyramids in Egypt, the horses roof right triangle-shaped, wheel-shaped circle, and so on. Formally, the math can take the form of pure mathematics, mathematical axiomatic, formal mathematics or mathematics deductively defined. Normatively, then we do not just learn math, both materially and formally, but we concerned with by value in reverse mathematics. As for the metaphysical, mathematical reveal various levels dimension of meaning and value can only be achieved by metacognition.
A. Preface
For example, the object of mathematical material in the form "number 2 which is made of plywood boards are sawn and then given a beautiful color. " So in the realm of mathematics material we can think number two is bigger, the smaller the number 2, number 2 red, 2 blue numbers etc. On formal dimensions then there are mixing mortar between definition numbers and figures. But, once we enter the dimension formal mathematics, then all the properties of the number 2 before we get rid of, and we only think about the nature of "value" its course of 2. So we are not able to think about the value of 2 if we have no other numbers. The value of 2 is greater than the number 1, but smaller than the number 3. Normatively, then the meaning of number 2 had extension and intentions. If intensified, then the number 2 can mean "even", can means "pair", can mean "rather odd", can mean "father and mother", or can mean "not one". Metaphysically, the number 2 can mean "not a single or not the One God or not about God or it is all God's creation ". If extensively, then the meaning of number 2 can be two theories, two theorems, two mathematical systems, 2 variables, two systems of equations,etc.. If it is extensived the same way we can think about it for all the objects of mathematics.
For example, the object of mathematical material in the form "number 2 which is made of plywood boards are sawn and then given a beautiful color. " So in the realm of mathematics material we can think number two is bigger, the smaller the number 2, number 2 red, 2 blue numbers etc. On formal dimensions then there are mixing mortar between definition numbers and figures. But, once we enter the dimension formal mathematics, then all the properties of the number 2 before we get rid of, and we only think about the nature of "value" its course of 2. So we are not able to think about the value of 2 if we have no other numbers. The value of 2 is greater than the number 1, but smaller than the number 3. Normatively, then the meaning of number 2 had extension and intentions. If intensified, then the number 2 can mean "even", can means "pair", can mean "rather odd", can mean "father and mother", or can mean "not one". Metaphysically, the number 2 can mean "not a single or not the One God or not about God or it is all God's creation ". If extensively, then the meaning of number 2 can be two theories, two theorems, two mathematical systems, 2 variables, two systems of equations,etc.. If it is extensived the same way we can think about it for all the objects of mathematics.
B. Various Views About Math and How to Learn it
The unwavering absolutist stance of looking at it objectively neutrality of formal mathematics. But in reality, the values contained in the the things mentioned above, makes the problems can not be solved. This is due was based on things that are only able to reach a formal course on discussion of the outside of mathematics itself. Mathematics promoted itself in fact contain implicit values.
The "social constructivits" view that mathematics is a copyrighted work humans through a certain period of time. All the differences of knowledge generated human creativity is intertwined with nature and history. Consequently, mathematics is seen as a science that is bound to the culture and creators values in its cultural context.
The absolutist believes that an invention was not yet a mathematical and modern mathematics is the inevitable result. However, for the "social constructivist "modern mathematics is not an inevitable outcome, but represents the evolution of human culture.
Accordance with the views of "social constructivist" mathematics can not be developed if no other knowledge associated, and which together has its roots, which in itself is not freed from the values of the field professed knowledge, because each is connected by it. Since the mathematical associated with all the knowledge of the human self (subjective), it is clear that mathematics is not neutral and free value.
The unwavering absolutist stance of looking at it objectively neutrality of formal mathematics. But in reality, the values contained in the the things mentioned above, makes the problems can not be solved. This is due was based on things that are only able to reach a formal course on discussion of the outside of mathematics itself. Mathematics promoted itself in fact contain implicit values.
The "social constructivits" view that mathematics is a copyrighted work humans through a certain period of time. All the differences of knowledge generated human creativity is intertwined with nature and history. Consequently, mathematics is seen as a science that is bound to the culture and creators values in its cultural context.
The absolutist believes that an invention was not yet a mathematical and modern mathematics is the inevitable result. However, for the "social constructivist "modern mathematics is not an inevitable outcome, but represents the evolution of human culture.
Accordance with the views of "social constructivist" mathematics can not be developed if no other knowledge associated, and which together has its roots, which in itself is not freed from the values of the field professed knowledge, because each is connected by it. Since the mathematical associated with all the knowledge of the human self (subjective), it is clear that mathematics is not neutral and free value.
C. Cultivating Learning Mathematics Through Mathematics Communication
In order to an attempt is made to civilize math in school, then we should use dimensional math or math on the dimensions of the material transition to formal mathematics.
In order to an attempt is made to civilize math in school, then we should use dimensional math or math on the dimensions of the material transition to formal mathematics.
1. The nature of the School of Mathematics and learning
Ebbutt, S and Straker, A., (1995) defines school mathematics as: (1) mathematical activity is an activity tracking patterns and relationships, (2) mathematical activities requires creativity, imagination, intuition and invention, (3) activities and results of mathematical needs to be communicated, (4) activities are part of the problem solving mathematical activities, (5) algorithm is a procedure to obtain answers to math problems, and (6) social interaction is needed in mathematical activities. Acculturation of mathematics in schools can emphasize the human relationships in the dimensions and value of both individual differences in ability and their experience. Therefore mathematics is seen as more humane, among others, can be considered as language, human creativity. Personal opinions are highly valued and emphasized. Student have the right of individuals to protect and develop themselves and their experiences according to its potential. The ability to do math problems is the nature individuals. Learning theory based on the assumption that every student is different from one with others in the mastery of mathematics. Students are considered to have the mental preparedness and different abilities in learning mathematics. Therefore each individual need the opportunity, treatment, and the different facilities in the study mathematics.
Mathematics deemed not to be taught by the teacher but to be studied by students. Student placed as the central point of learning mathematics. The teacher in charge of creating an atmosphere, provide other facilities and more teachers and role as manager of the teacher
Ebbutt, S and Straker, A., (1995) defines school mathematics as: (1) mathematical activity is an activity tracking patterns and relationships, (2) mathematical activities requires creativity, imagination, intuition and invention, (3) activities and results of mathematical needs to be communicated, (4) activities are part of the problem solving mathematical activities, (5) algorithm is a procedure to obtain answers to math problems, and (6) social interaction is needed in mathematical activities. Acculturation of mathematics in schools can emphasize the human relationships in the dimensions and value of both individual differences in ability and their experience. Therefore mathematics is seen as more humane, among others, can be considered as language, human creativity. Personal opinions are highly valued and emphasized. Student have the right of individuals to protect and develop themselves and their experiences according to its potential. The ability to do math problems is the nature individuals. Learning theory based on the assumption that every student is different from one with others in the mastery of mathematics. Students are considered to have the mental preparedness and different abilities in learning mathematics. Therefore each individual need the opportunity, treatment, and the different facilities in the study mathematics.
Mathematics deemed not to be taught by the teacher but to be studied by students. Student placed as the central point of learning mathematics. The teacher in charge of creating an atmosphere, provide other facilities and more teachers and role as manager of the teacher
2. Hermenitika acculturation of Mathematics
The basic elements of mathematics is an activity hermenitika civilizing communicate mathematics in various dimensions.
The basic elements of mathematics is an activity hermenitika civilizing communicate mathematics in various dimensions.
a. Material Communication Mathematics
Communications material is dominated by the nature of mathematics from the direction of the horizontal nature of its vitality. Some people can gain awareness that material communication mathematics is the communication with the lowest dimension.
Communications material is dominated by the nature of mathematics from the direction of the horizontal nature of its vitality. Some people can gain awareness that material communication mathematics is the communication with the lowest dimension.
b. Formal communication of mathematics
Formal communication of mathematics is dominated by correlational properties out or into the of the vitality of its potential. Correlation to the outside or into a meaningful difference Among the properties that are out and the properties inside.
Formal communication of mathematics is dominated by correlational properties out or into the of the vitality of its potential. Correlation to the outside or into a meaningful difference Among the properties that are out and the properties inside.
c. Normative communication of mathematics
Normative mathematical communication is characterized by the properties of the appointment corelasion appointment on the subject and the object itself. Disintegrating nature of the appointment correlational horizontal are not due to lack of potency and vitality communication, but solely because of the extensive reach and engagement units of both the potential and vitality of the subject himself and to himself its object. So, normative communication can be described on the properties on the subject and object as subjects who have the potential and vitality of higher mathematics, but have correlational horizontal low.
Normative mathematical communication is characterized by the properties of the appointment corelasion appointment on the subject and the object itself. Disintegrating nature of the appointment correlational horizontal are not due to lack of potency and vitality communication, but solely because of the extensive reach and engagement units of both the potential and vitality of the subject himself and to himself its object. So, normative communication can be described on the properties on the subject and object as subjects who have the potential and vitality of higher mathematics, but have correlational horizontal low.
d. Spiritual communication of mathematics
Korelasionalitas potential and vitality of mathematics to the above will transforming dimensional forms of communication into a more upon the spiritual communication of mathematics, while the correlational potential and vitality to the below will transforming mathematical form of communication into a lower dimensional. Formal communication is the communication of mathematics or mathematical material. Then the communication mathematics spiritual nature of all communications to accommodate existing and possible there.
Korelasionalitas potential and vitality of mathematics to the above will transforming dimensional forms of communication into a more upon the spiritual communication of mathematics, while the correlational potential and vitality to the below will transforming mathematical form of communication into a lower dimensional. Formal communication is the communication of mathematics or mathematical material. Then the communication mathematics spiritual nature of all communications to accommodate existing and possible there.
D. Cultivating Math Advantage To Acquire Nation
Various activities carried out writers on the various activities PLPG Mathematics, seminars and workshops mathematics, gained the perception that the innovation of learning mathematics teacher should be able to answered the challenge as follows:
Various activities carried out writers on the various activities PLPG Mathematics, seminars and workshops mathematics, gained the perception that the innovation of learning mathematics teacher should be able to answered the challenge as follows:
1. How to promote mathematics PBM that emphasize the process
2. How to develop cooperative learning in mathematics PBM
3. How to make group learning in mathematics PBM
4. How to make studying math outside the classroom: an alternative.
5. How to develop learning mathematics through games
Tidak ada komentar:
Posting Komentar