Learning mathematics means decipher truth about what mathematics was, whether the science of mathematics is deductive, inductive science, symbols, abstract science, and so forth.
As a basis, I explain as follows: Mathematics is a science that arises because of mind-the mind of man associated with the idea, process and reasoning, matemtika consists of 4 broad perspective including: arithmetic, algebra, geometry, and analysis.
1.Mathematics is the science of structure of organized
Relationships between the elements that do not terdefinisikan, the elements that are defined, axiom and theorem. That can be described as follows: Evidence that many once formulated, so that mathematics of organized of the elements that are not defined, the elements that are defined, axiom-axiom, and theorem-proof-proof where the proof was proved correct after the general effect, therefore, often referred to as the mathematical sciences deductive.
2.Abstraction and generalization
Very important in mathematics and the abstraksi generalization. Abstraksi understanding is through observation of nature and with the attributes that are not owned in mathematics.Generalization is to make estimates based on knowledge developed through specific examples.
3.Hierarchy Mathematics
In learning mathematics, the material that will be taught should be introduced first as a concept essentially prerequisite to be able to follow the next material that is still associated with these materials.
4.Verification theorem in Mathematics
In proving the theorem in mathematics we can use ponens mode, the mode tolens, the theory of deduction, contra-positive, contra example, mathematics induction, and not direct evidence.
Next, an explanation of mathematical truth in detail is Heart of mathematics divided by mathematics as a structured systematic knowledge and deductive. This is described that mathematics as the paradigm, mathematics as a science support, mathematics as a language of symbols,and mathematics as a product and process.
1.Mathematics as the paradigm
In mathematics, the basic object of the abstract is learned, such as facts, concepts,
operations (relations) and principles. Then this is the basis of the object can be a pattern or structure of mathematics. Fact means that conventions are expressed with the symbols or a certain set of symbols, for example, the symbol "2", 2 x 4 = 8. The concept is an abstract idea that can be used to characterize a set of objects, eg "square". Processing operation is arithmetic operation or algebraic (Answer, multiplication, combined, sliced, etc.). The principle is objects in mathematics that is complex. Including the principles can be axiom,
theorems, nature etc.
2.Mathematics as a science support
Mathematics as a tool to support science and servant is not just for Mathematics itself but also for other sciences, both for theoretical and practical importance as the application of Mathematics.
3.Mathematics as a language of symbols
Mathematics is a universal language that is compared with a structured language with the letters and words into sentences and expressions. Advanced mathematics is used as a tool for studying various physical phenomena do complex, especially the various natural phenomena observed, so that the pattern structure, change, space and nature phenomena can didekati or expressed in the form of a systematic formulation I and full of various conventions, symbols and notation. Results formulation that describes the behavior or the physical phenomenon is usually referred to as mathematical models of phenomena.Return to previous descriptions that mathematics as a means to think scientifically using deductive reasoning pattern. This means to think scientifically in our education process, is a distinctive field of study.
4.Mathematics as a product and process
Mathematics is a series of a long process to go to a product. In mathematics so that there will be no product without a process.
Likewise explanation above, but not necessarily the substance of mathematics, because the truth is something that must continue to be extracted to approach the truth.
Reference:
www.geocities.com/agoes66_gt/Pemanfaatan_Komputer_sebagai_Media.pdf
silabus.upi.edu/upload/G696-PMT%20671-SILABI%20MK-S2-S3PMAT-4.doc –
http://one.indoskripsi.com/judul-skripsi/pendidikan-matematika/alat-peraga-dan-matematika
etd.eprints.ums.ac.id/723/1/A410040149.pdf
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