Chapter I introduction 1.1 background mathematical problems as science with reasoning deduktifmengandalkan logikadalam convince the truth a statement. Factors intuition and pattern berpikirinduktif many play a role in the process of start in formulating a konjektur (conjecture) that is alleged the early in mathematics. Discovery process in mathematics starting with search pattern and structure, case studies and object mathematics lainnya.selanjutnya, all the facts and information collected individually inidibangun a coherence for later compiled a konjektur. After konjekturdapat evidenced truth or ketidakbenaranya then the next he became a theorem. Statement statement mathematics such as the definition, theorem and statement other. in general shaped sentences the logic, can be implications, biimplikasi, negation, or a sentence berkuantor. Operator logic like and, or, not, xor also often contained in a statement of mathematics. So prove a theorem not the other is prove a sentence logic. Material logic already given since the bench high school. But this time, most students or teacher still consider logic as a matter hapalan, especially memorize the truth table. Do not know why and for what logic dipelajari.tanpa control logic it difficult to the formation of the so-called with logicallythinking. What is formed on the students, students, teachers or even a lecturer during this more dominant in algorithm thinking or think algorithm. .pada the early stages, job understand the evidence is not something interesting because we more wrestle with symbols and statement logic ketimbangberhadapan with numbers are usually considered a character matematika.kenyataan this is to make one of the reasons people lazy to understand buktidalam mathematics. Another reason is a job prove more difficult and tidakpenting. Whereas the many benefits can be obtained on experience membuktikanini, one is train logically thinking in learning mathematics. 1.2 problem formulation based on the background, then obtained problems among others: how the problem of the discovery of and proof in mathematics? 1.3 objectives making this paper is to meet one of duty subjects problem solving in mathematics in Elementary school as well as for the insight and science of US about problems discovery of and proof. 1.4. Methods and procedures method of author in the preparation of this paper is to collect information from various sources of books and browsing on the Internet. Chapter II discussion 2.1. Problem solving in math problem solving is part of the curriculum mathematics very important because in the process of learning and settlement, students possible gain experience using the knowledge and skills that have been held to applied to the problem solving is not routine. Through this activity aspects kemam-Lady mathematics important as the application of the rules of the problem not routine, discovery pattern, penggeneralisasian, communication mathematics and others can be developed better. As stated in the curriculum mathematics school that purpose gave mathematics, among others, so that the student is able to face the state change ever growing, through the exercise acting on the basis of thinking logically, rational, critical, carefully, honest and effective. The demands of the impossible achieved when learning only shape memory, exercise workmanship about the routine, as well as the process of learning "teacher centered" that does not require students to optimize the power fikirnya. According to Gagne (1970), skills intellectual high-level can be developed through the problem solving. Hudojo (1988: 119) States to solve a problem, one must master the things that have been studied previous and then use it in a new situation. The next hudojo (1990: 168) also stated that someone in the planning the completion of a problem should be able to choose the theorem or concept that have been studied for combined so it can be used in the resolve the problem, therefore, the problem is presented to the student must be adapted to the student's readiness. Solving mathematical problems such as well as the problem solving generally have a variety of interpretation. According to baroody (1993: a) there are three interpretation troubleshooting: the problem solving as approach (approach) purpose (goal), and process (process) learning. Troubleshooting as approach to the point of learning begins with a problem, the next students given the opportunity to find and reconstruct the concepts of mathematics. Troubleshooting as purpose related to the question why mathematics taught and what is the purpose of teaching mathematics. Troubleshooting as the process is an activity prioritize the importance of the procedure steps, strategy / how do students to resolve the problem so find jawaban.walaupun third interpretation solving the problem is different, but in practice three complement each other (suharta, 2002: 1). According to polya (1957), there are four steps in the problem solving, that is to understand the problem, plan settlement, complete the time-was as planned, and check the back of all Lang-glue that has been done. In the implementation of the fourth step, the main task teacher is help and facilitate the students to be able to optimize the ability to achieve the completion of the problem faced logically, structured, carefully, and the right. In math to facilitate in elections about the necessary distinction between a matter of routine and about not routine. 2.2 problem discovery of and proof reasoning in math is hard separated from the rules of logic. Reasoning-reasoning such in mathematics known as the term reasoning deductive. According to the rules of Indonesian, reasoning deductive means reasoning is deduction, the reasoning on the basis of the things that general then down to the things that special. While the reasoning inductive, the language means reasoning is induction, the reasoning on the basis of the things that are particular, then concluded be the general. Recorded some explanation of deduction in math, including: 1) the process of reasoning of the general principle down to the conclusion of the fact special 2) the process of reasoning conclusion derived absolute of the premise-premisnya 3) an argument is valid deductive if and only if that is not possible conclusion wrong when premisnya true. Proof that use reasoning deductive usually use sentence implikatif in the form if statement ..., then .... Then, developed by using the mindset called syllogism, which is an argument that consists of three parts. In which there are two true statement (premises) the basis of the argument that, and a conclusion (conclusion) of the argument that. In the logic, as a branch (core) math many discusses syllogism there are some rules which States is syllogism it valid (valid) or not. 1) major premise - premise first must have one thing that relate to the premise that both 2) the premise minor - premise second must have one thing that relate to the premise of the first 3) the conclusion - conclusion must have one thing that relate to both the premise that. As mentioned in the previous section that way reasoning with deductive of which can be done by the rules of inference, direct evidence, evidence indirect, and the induction of mathematics. Here are some simple example of a few rules in reasoning deductive. 1. Direct evidence included in the direct evidence is among the rules of withdrawal conclusion modus ponens, inference deduction, and the implications Transitive. 1). Proof of the rules mode ponen (mode ponendo ponens) rules essentially: "when P cause verse, it turns out P true, then the verse true" premise (1): p verse premise (2): P conclusion: verse or written (p verse) q verse example 2.1 prove that siskriminan quadratic equation is greater than zero has roots real different. Evidence discriminant of x2 - 5x + 1 = 0 is 21. x2 - 5x + 1 = 0 have two root of real different. 2). Proof by implication Transitive rules essentially: premise (1): p verse premise (2): verse R conclusion: P R or written (p verse) (verse R) (P R) example 2.2 prove that in the set of numbers count, quadratic an odd number is an odd number evidence in the form of a symbol of logic can be written as follows. am numbers count, (ad) (am an odd number m2 an odd number) premise (1): am NUM. odd there N NUM. count so am = 2n + 1 premise (2): am = 2n + 1 m2 = (2n + 1) 2 = 4n2 + 4n + 1 = 2 (2n2 + 2n) + 1 = 2p + 1 is an odd number conclusion: so, am an odd number m2 an odd number 2. kontrapositif sometimes we are difficult to prove p verse direct. If so keadaanya, we can prove kontrapositifnya, that prove q p. Because, in the science of logic known that statement p verse and q p is equivalent. Said, (p verse) ↔ (q p) constitute tautology example 2.3 prove that all an odd number not divisible by two evidence of use kontrapositifnya, that is to prove p verse enough evidenced q p. Suppose P: an odd number and verse: not divisible by two, then p: an even number and q: divisible by two. Will be proved if a divisible by two, then a even number if a is the number is divisible by two, it is written a = 2n; for N integers. In fact a = 2n nothing but as a statement from an even number. So, proven if a divisible by two, then a even number. In other words, all of an odd number not divisible by two 3. Evidence indirect evidence argument in this way done Jalan form the negation of the conclusion, which then be used as the premise additional. If the result of this step appear contradiction, then the argument evidenced is invalid. Strategy starting with regard negation of proposisinya proven. For example, we want to prove proposition P. We view negasinya, that is p. We prove that p there contradiction, for example verse and q (not possible two well, so definitely one). From kontrapositif conditions that, we have to prove the negation of negation proposition. Thus, we show that (verse q) (p), so (p) = P. Proof of indirect, is also known with proof contradiction or reduction ad absurdum. Proof by indirect is complicated, but this is done when we faced the problem of proof difficult taken penalarannya directly. Example 2.4 prove when Matrix rectilinear have the inverse, then inversnya the single. Proof of (indirectly) P: Matrix rectilinear who have the inverse verse: the inverse matris rectilinear the single so q: the inverse Matrix rectilinear it's not a single suppose the inverse Matrix rectilinear it's not a single for example, there are two, the l1 and l2, with the l1 l2. Suppose Matrix rectilinear it am having the inverse l1 and l2 with l1 l2, then am l1 = l1m = I (ID), similarly am l2 = l2m = I (ID) in fact, l1 = l1i = l1 (ad l2) = (l1m) l2 = I l2 = l2 so, l1 ¬harus the same as the l2 which means contrary (contradiction) with the assumption that the l1 l2. 4. Mathematical induction of proof way mathematical induction is proof deductive, although his name induction. Induction of mathematics or also known induction complete often used to statements concerning the numbers original .. proof way mathematical induction want to prove that the theory or properties that's right for all the numbers original or all numbers in the set of parts. The trick is to show that the nature that's right to N = 1 (or's (1) is a true), then shown that if nature that's right to N = K (when's (K) true) led to the nature that's right to N = K +1 (or's (K + 1) right). Example 2.5 prove that 1 + 2 + 3 + ... + N = evidence to prove's (N) = 1 + 2 + 3 + ... + N =. (1) for N = 1, true that's (1) = (2) suppose the right to N = K, that's (K) = 1 + 2 + 3 + ... + K =, it will be proved true anyway to N = K + 1, that's (K + 1) = 1+ 2 + 3 + ... + K + (K + 1) =. So 1 + 2 + 3 + ... + K + (K +1) = + (K +1) = (K + 1) = (proven true) so,'s (N) true for all the number of the original. 2.3 mengepa we need to prove the article making mathematics entitled proof, it can be accessed at http: /www2.edc.org/makingmath, described in detail of the evidence in mathematics which includes what is proof, why do we prove, what do we prove, and how do we prove. According to the article, at least there are six motivation why people prove, that is to establish a fact with certainty, to gain understanding, to communicate an idea to others, for the challenge, to create something beautiful, to construct a large mathematical theory. To establish a fact with certainty is motivation most basic why people need to prove a statement of mathematics, that is to ensure that what has been considered to be true is it is true. No doubt for this lot of the truth of the facts in mathematics only believed granted without prejudice to the truth, not trying to prove himself, including the facts a very simple. We only use the fact that due to an existing in books (it was in the text), or because it has been submitted by our master. It is not all the facts of mathematics learned must be understood the proof. Factors density material and limitations of the time is still a constraint classic faced by pengampu mathematics. But a few simple fact was often ignored evidence. An illustration when we teach about the set of real numbers we definitely convey that the set of real numbers symbolized by R split into two subsets each other foreign, that is the set of rational numbers verse and the set of numbers irrational R N Q. is very easy to understand for the definition of rational numbers, but not so clear on the definition of numbers irrational. Numbers irrational only is defined as real numbers are not rational. The question, ever we prove that the p2, ¼ and Hey is the number irrational? When the number irrational can be characterized by not a repeat of figures desimalnya then this evidence temporary. Suppose a student may indicate that the 100-digit numbers in the form of decimal numbers ¼ nonrecurring then the student concluded that ¼ irrational. But so there are other students can indicate the presence of the pattern of repetition, for example from digit ke- 150 then claims students first last fall and must be concluded that ¼ 3 rational. Conclusion students first above is based on the intuition is not based on the method of proof valid. Many of proof that not only to prove a fact but also explain about this fact. Here, proof of theorem serves to gain an understanding (to gain understanding). A medal winner "field", Pierre deligne meyatakan that "I would be grateful if anyone who has understood this demonstration would explain it to me." This statement containing the meaning that when a person can explain back what has been described by Pierre deligne then be able to ensure that the person has understand it, is possible explanation has presented by Pierre there parts unclear. Sometimes, some people have the establishment of a very strong that a konjektur is true. This belief may be derived from the explanation informal or some cases are met. For those there is no doubt the belief that, but not necessarily apply to the people of the other groups. This is evidence can be used as a means to assure others will truth an idea. However, to develop evidence formal against the truth a fact it is not easily. Follow the evidence that have been found and compiled other people's just not easy Moreover prepare yourself. Prove a challenge yourself the mathematician, intriguing and so resolved then obtained satisfaction intellectual. Like the Arts, mathematics was beautiful. This least opinion of the mathematics. For the common people the beauty of mathematics look of the pattern and structure of the object of mathematics, such as the number, wake up geometry, simulation mathematics on the computer. But for those who has reached Begawan mathematics, the beauty of the real of math (the real beauty of mathematics) lies in the pattern of reasoning in the form of interconnection arguments logical. This is reflected in the proof of theorem. Successes formulate a konjektur, then can prove it is a problem in mathematics resolved. Chapter III cover 3.1 conclusion solving the problem is part of the curriculum mathematics very important because in the process of learning and settlement, students possible gain experience using the knowledge and skills that have been held to applied to the problem solving is not routine. Through this activity aspects kemam-Lady mathematics important as the application of the rules of the problem not routine, discovery pattern, penggeneralisasian, communication mathematics and others can be developed better. Proof that use reasoning deductive usually use sentence implikatif in the form if statement ..., then .... Then, developed by using the mindset called syllogism, which is an argument that consists of three parts. In which there are two true statement (premises) the basis of the argument that, and a conclusion (conclusion) of the argument that. In the logic, as a branch (core) math many discusses syllogism there are some rules which States is syllogism it valid (valid) or not. As mentioned in the previous section that way reasoning with deductive of which can be done by the rules of inference, direct evidence, evidence indirect, and the induction of mathematics. 3.2 suggestions learn mathematics in a way to understand the evidence is not easily. It takes to understand the mathematics as a language logic. Also, it takes insight mathematics wide to learn to prove the facts more complicated. In the proof contained the values of strategic can train we think logically. The beauty of mathematics also there are a lot on the harmonization of reasoning-reasoning in the evidence. Understanding the proof we can follow flow think experts first found, which have an impact on the admiration of the inventor of mathematics and in the end enjoying mathematics itself. Practice understand the evidence is a major capital to be able to do the research mathematics.