Which I can find for example:
Early from mathematics history is when people have to note and calculate big in number. Initially ancient Nomad tribes calculate by gravel or seed and pack into sack; bag, if small in number. But for big amounts, they use finger to symbolize number 10 and 20. And they develop number concept as separated from device calculated object.
At one time happened more complex calculation and record-keeping, last there is people finding appliance to assist record-keeping process and that calculation. That appliance is Abacus, is one of earliest appliance of invention and its use. Source of from unclear Abacus itself, definitive but this Appliance has been recognized by since Greek era and of Romani Ancient. Initially Abacus in the form of surface of sand, wax; candle sabak, or batu lebar with sign showing number situation and used as gravel numerator.
But in the early of middle ages, middle eastward emerge appliance which in the form of box framework with seeds at a number of bars, later; then this appliance is referred as with swipoa. Hitherto both, ad for Abacus and or Swipe still used widely in Asia East and Mid-East.
Logarithm
A mathematician from English capable to change Logarithm of Napier become public logarithm or Briggs an, He is so called Henry Briggs. In history education of him, Briggs goes to school get title of MA. Briggs publish the masterpiece of in Arithmetic Logarithmical in the year 1624, where in that book was presented by original number logarithm from 1 until 20.000 and 90.000 until 100.000 by 14 number behind comma. There are also function of sin by 15 number behind comma, function of tag and of sec by 10 number behind comma. Briggs suggests that number - number of do not there are can be calculated with table - complete table which published with Trig title of Britannica. Briggs also fined binomial theorem without there is verification. Logarithm studied was this time referred [as] with Brigg a system. Invention of logarithm will not like now without role of Henry of Briggs.
Integral Device and Differential
Leibniz, this Germany mathematics about year 1684 defining integral device and differential which until this time still used. He defines equation of Differential is an equation covering function generation one or more tied to one or more free. Leibniz also explain technique finish equation of ordinary differential, for example
Theorem of Pythagoras express that wide amount of square right angled triangle same elbow broadly square [in] hypotenuse. Pythagoras express that this theorem in geometric style as statement concerning wide square. This theorem proved by Pythagoras though the fact of is not him finding this theorem.
India Sulbasutra express that flung out string as long as diagonal length a square length will yield wide which yielded [by] side - vertical side and horizontal. If right angled triangle have feet with length of a draught of b, hypotenuse with length of c, hence: a + b = c².
Besides nation of Romani and Greek, Moslem man of science coming from Busman, Nishapur also follow colored knowledge of past. The Elman so called Abu Wafer Muhammad Bin Muhammad Bin Yahiya Bin Ismail al-Busman. He personally develops some important theories mathematics area, the core important trig and geometry. In geometry science area, Abu Wafer give contribution isn't it geometry problem for resolving by using compass; construction of equivalent for all areas, public polyhedral; construction of hexagon semi side from isosceles trilateral; parabola construction of geometry solution and dots for equation.
Building version trig construction of Abu Wafer is up to now confessed very big is his him. He is first show the existence of trilateral theory relative parabola. Do not only that, he also develop new method concerning parallelogram construction and also repair of sine value 30 wearied eight denary. Abu Wafer even also develop sine relation and of formula
as well as
Beside it, Abu Wafer makes special study concerning tangent theory and table’s enumeration of tangent. He introduce secant can of cosecant for the first time him, succeeding to know relationship between which trig lines good for the mapping of and also put down base for continuing theory study of conic.
Many erudite masterpiece and books have been yielded [by] him and include; cover many science areas. But do not many the masterpieces of which drop behind till in this time. A number of the masterpieces of losing, which is there is still, have modified. Contribution of in the form of erudite masterpiece for example in the form of book of Elm al-Hsia ( Practical Book Arithmetical), Al-Kitbag Al-Kamala ( Complete Book), and Book of al-Hands ( Geometry of Terrapins). Abu Wafer even also pouring many masterpieces he wrote erudite journal of Euclid, Diaphanous and of al-Khwarizmi, but unhappily many which have loosed.
Even that way, contribution of for trig theory very lash isn't it especially development [at] tangent formula, invention early to formula of secant and of cosecant. Hence from that, a large amount of formulas of trigonometry cannot be discharged from name of Abu Wafer. And hitherto the trig formula still used by most people which learn mathematics.
The Theory Of Probability and Trilateral Pascal
The life of Pascal walk during two years before awaked by Gilberto. Then Pascal collaborated with Fermat to triggering the theory of probability. Like Cardano, Pascal interest with the theory of probability from gambler. He studied the hurl of two dice with his father’s friend, Fermat. Both in the reality can give the base growth of areas like : counting, insurance risk, interpreting statistic, studying clan (Mendel). The Coins which hurl have probability out number 1 from 2 (number and picture) or ½. If downhill probability, small above ratio more and more. If there is no possibility, so the probability is zero. Trilateral Pascal founded for the purpose of this.
This used to determine simple probability problem like in throwing coin. And then it called by Pascal Triangle. Pascal triangle didn’t found by Pascal. It have founded and published on China at 1303 or 320 years before Pascal born. Composition book of Chu Shih-Chieh, Ssu Yuan Yii Chien mention that tables only until 9 story level. Adoption of Pascal Triangle there are in book of Murai Chusen’S of Shampoo of Doshi-Mon the year risingness 1781.
Logic
Logic come from ancient Greek word λόγος (logos) meaning result of consideration of phrased mind pass word and expressed in language. As science, logic referred as logike episteme (logica scientia) or logic science (science) which studying efficiency to think diametrically, precise, and regularly. Science here related at rational ability to know and efficiency relate at kindness mind readiness to realize knowledge into action. Logical word which utilized the can is also interpreted sensiblely.
The History of Logic
Logic started with Thales (624 BC – 548 BC), first Greek Philosopher who leave any fable, takhayul, and non sense stories and looking away to kindness mind to solve universe secret. Thales said that water is arkhe (Greek) which meaning principle or common ground of universe. On that time Thales has defined inductive logic.
Then Aristoteles defining logic as a science, which then called logica scientica. Aritoteles said that Thales concluding that water is arkhe of universe with the reason that water is the soul of anything. On Aristoteles era, logic still called analitica, which specially research the argumentation which started from true proposition, and dialektika which specially research the argumentation which started from proposition which still been hesitated the truth.
Kinds of logic
1. Natural logic
Ability of natural logic [of] human being exist from the day borned
2. Erudite logic
Erudite Logic refine, sharpening mind and also kindness mind.
Paradox of Russell
1901, Russell lay open what is later then known as paradox of Russell (Russell Paradox), which emerge at his masterpiece of Principle of Mathematics (1903). This Paradox arise in the bearing of between a gathering becoming the part of various gathering but itself nonmember. This Paradox Significant follow, according to classic logic view, all statement will is always followed by contradiction. According to other mathematics view (including Hilbert and Brouwer) there is no competent proved to answer logic all statement of mathematics which is contradictive. At the beginning of this century masterpiece which concerning logic, gathering theory, mathematics base and philosophy thrive him.
This Paradox really the side product of undefined axioms (unrestricted) or abstraction which have been the part of gathering theory. Axioms which peeped out by Cantor on a statement P(x), where x is free peubah, where will determined the gathering which the members fulfilling criterion.
• Normal Gathering is the gathering which is unfilled itself as a member of the gathering.
Example : The gathering of all cats, the gathering of students as a normal gathering, because the gathering is not cats or students.
• Not Normal Gathering is a gathering which filled itself as a member.
Example : The gathering of all which is no cats, the gathering of all which is no student.
S = {x x €/ x}
Is S the member of S ?
If S €/ S, so S fulfilled criteria (x €/ x) become the member of the gathering S and paradoxial happened S € S.
If S €/ S, not fulfilled criteria (x €/ x) become the member of the gathering S and paradoxial happened S € S.
€/ ( Gathering nonmemberA); € ( gathering member)
Contradiction: If S €/ S so S € S; if S € S, so S €/ S referred as with paradox of Russell
Idea of Russell
Russell trigger types theory in the year 1908. theory divided become two version, " simple theory" and " generation theory ( ramified)." Both of this theory version get keen criticism. Please mention that this theory is too shallow because cannot finish paradox knew. For the theory other party of too circumstantial because difficult practiced into mathematics definitions-because too consistent, and impinge radian principle don’t tip of ( circle vicious).
Comments of Russell for which is second criticism is, in generation theory scope ( ramified), axiom turned into more simple ( reducibility). Though this axiom can ' loosen' radian principle don’t tip of in his application, but many people expressing that this is way too utilize to be harmonized with philosophy.
At the (time) of at the same time Russell also elaborate logic, theory that mathematics can be altered systematically ( reducible) become logic. First expostulation there are in Principles, and expostulation more there is in Principia Mathematica, logic of Russell consist of two argument or proposisi ( thesis). First, all truthses of matematikal can be specified as part of logic. [Both/ second], all verifications of matematikal earn isn't it as verification of logikal or equally mathematics theorema-theorema become indivisible shares of logic.
Contribution
Give mathematics colour and equipment. Using mathematics, specially gathering theory, to finish mathematics problem-problem, philosophy and try with problem-problem qualitative. Philosophy views and various masterpiece which concerning many topics is ommission of Russell.
Number zero
Number concept zero have expanded since epoch of Babilonia and Ancient Greek, which is at that moment interpreted as no from something. Number concept zero and nature of - in character continue to expand from time to time. Till [at] century to - 7, Brahmagupta a India mathematics introduce some nature of numbers zero. Nature of - in character is an number when summed with zero is remain to, that way also a number if/when multiplied with zero will become zero. This matter continue to become the this topic of research at that moment, even until 200tahun later;then. For example year 830, Mahavira ( India) assure result - result of Brahmagupta and even express that " a number divided by zero is remain to". Of course this fatal mistake.
Idea - idea of India mathematics is hereinafter studied by Moslem mathematics and Arab. This Matter happened [at] phase - early stage when mathematics of Al - Accurate Khawarizmi of system is calculation Hindu ( India) depicting system assess place of number entangling number 0,1,2,3,4,5,6,7,8,9. Al - Khawarizmi is which first time introduce usage of number zero as value space in bases ten. and this system is referred is number system denary.
Mathematics concept, problem of mathematics and solution of mathematics at ancient time which have unused in this time.
Which I can find for example:
Mathematics history re-finding appliance able to assist people away back in calculating, and calculator of sabak. A Both of this is appliance very differ. Firstly, this calculator is ancient Abacus of island of Salamis in Greek is oldest calculator. This calculator in the form of block of harmer as long as 1,5 meter and estimated have been used in a temple by moneychangers. Article which there are this calculator enlist value - number value and currency name like and drachma, talent and oboe.
Second, sabak of Romani. This Sabak is used by using gravel residing in above and below/under winnow line marked with number of Romani according to his column. Order or way use him, each; every gravel below/under ranked among extreme right column line set of, and each; every gravel residing in above valuable line five. If in the calculation of valuable 10, hence there is a gravel brought to left side.
Phi (π)
At former epoch, ancient Egypt people have found and determine the level of π is 3,16 to count area of circle. While for the things in this time the level of π the used is 3,14.
mathematics concept, problem of matematika,or solving of mathematics at the moment which [there] no the relation of with ancient time mathematics at all.
Which I can find for example:
Open-closed Problem
[Is] the same as like social sciences, problems or problems in mathematics even also marginally earn classification become to become two shares. First is the problem oves mathematics of tetutup ( problems closed). And secondly is the problem oves open mathematics ( problems open).
Which during the time emerge on the surface of and taught many schools is the problem oves closed mathematics ( problems closed). Where is true in finishing the problem oves mathematics closed this, prosedure which the was using of have almost can be told standard alias standard. As a result arising rather perception wrong to mathematics. Mathematics considered to be [by] definitive knowledge, prosedural, and saklek.
Meanwhile, problem oves open mathematics ( problems open) alone only just touch, seldom emerge and presented in course of study of mathematics school. As a result if there are any problems of mathematics kinds of this, that problems or problem is assumed ' ad for problem' or incomplete problem.
Simply, problems open alone can be grouped become two shares. Namely problems open-ended and of pure problems open. For the open-ended of problems alone can be grouped become two shares. Namely: ( 1) problems by satu answer many solution ways; and ( 2) problems with many solution ways also many answers.
What is the difference problems closed and of open problems?.
According to Sawada ( 1997), if problems open-ended a kind of mentioned problem passed to students in school, at least there is five advantage which earn to be expected
1. Students involve more active in course of them and study can lay open their idea by lebih sering. students do not only passive imitate examplizeed way is his teacher
2. Students have deeper opportunity use knowledge and skill of their mathematics by totally. Yes, they involve more active in using knowledge potency and skill which have owned before all.
3. Each;Every student can answer problems its own way. This mean, every student creativity can be laid open
4. Study by using problems open-ended a kind of this give experience of reality for student in course of have natural existence
5. There is many experienceses to be got student in the form of satisfaction in course of invention of answer as well as getting confession of other student.
Sumber:
http://www.republika.co.id
http://www.rumahislam.com
http://atrasku.wordpress.com
www.geocities.com
http://www.mate-mati-kaku.com
http://id.wikipedia.org/wiki
http://muhar5yah.wordpress.com
http://mathematicse.wordpress.com
www.my.opera.com
Early from mathematics history is when people have to note and calculate big in number. Initially ancient Nomad tribes calculate by gravel or seed and pack into sack; bag, if small in number. But for big amounts, they use finger to symbolize number 10 and 20. And they develop number concept as separated from device calculated object.
At one time happened more complex calculation and record-keeping, last there is people finding appliance to assist record-keeping process and that calculation. That appliance is Abacus, is one of earliest appliance of invention and its use. Source of from unclear Abacus itself, definitive but this Appliance has been recognized by since Greek era and of Romani Ancient. Initially Abacus in the form of surface of sand, wax; candle sabak, or batu lebar with sign showing number situation and used as gravel numerator.
But in the early of middle ages, middle eastward emerge appliance which in the form of box framework with seeds at a number of bars, later; then this appliance is referred as with swipoa. Hitherto both, ad for Abacus and or Swipe still used widely in Asia East and Mid-East.
Logarithm
A mathematician from English capable to change Logarithm of Napier become public logarithm or Briggs an, He is so called Henry Briggs. In history education of him, Briggs goes to school get title of MA. Briggs publish the masterpiece of in Arithmetic Logarithmical in the year 1624, where in that book was presented by original number logarithm from 1 until 20.000 and 90.000 until 100.000 by 14 number behind comma. There are also function of sin by 15 number behind comma, function of tag and of sec by 10 number behind comma. Briggs suggests that number - number of do not there are can be calculated with table - complete table which published with Trig title of Britannica. Briggs also fined binomial theorem without there is verification. Logarithm studied was this time referred [as] with Brigg a system. Invention of logarithm will not like now without role of Henry of Briggs.
Integral Device and Differential
Leibniz, this Germany mathematics about year 1684 defining integral device and differential which until this time still used. He defines equation of Differential is an equation covering function generation one or more tied to one or more free. Leibniz also explain technique finish equation of ordinary differential, for example
- Direct integration
- Technique dissociation of variable
- Integration factor.
Theorem of Pythagoras express that wide amount of square right angled triangle same elbow broadly square [in] hypotenuse. Pythagoras express that this theorem in geometric style as statement concerning wide square. This theorem proved by Pythagoras though the fact of is not him finding this theorem.
India Sulbasutra express that flung out string as long as diagonal length a square length will yield wide which yielded [by] side - vertical side and horizontal. If right angled triangle have feet with length of a draught of b, hypotenuse with length of c, hence: a + b = c².
Besides nation of Romani and Greek, Moslem man of science coming from Busman, Nishapur also follow colored knowledge of past. The Elman so called Abu Wafer Muhammad Bin Muhammad Bin Yahiya Bin Ismail al-Busman. He personally develops some important theories mathematics area, the core important trig and geometry. In geometry science area, Abu Wafer give contribution isn't it geometry problem for resolving by using compass; construction of equivalent for all areas, public polyhedral; construction of hexagon semi side from isosceles trilateral; parabola construction of geometry solution and dots for equation.
Building version trig construction of Abu Wafer is up to now confessed very big is his him. He is first show the existence of trilateral theory relative parabola. Do not only that, he also develop new method concerning parallelogram construction and also repair of sine value 30 wearied eight denary. Abu Wafer even also develop sine relation and of formula
as well as
Beside it, Abu Wafer makes special study concerning tangent theory and table’s enumeration of tangent. He introduce secant can of cosecant for the first time him, succeeding to know relationship between which trig lines good for the mapping of and also put down base for continuing theory study of conic.
Many erudite masterpiece and books have been yielded [by] him and include; cover many science areas. But do not many the masterpieces of which drop behind till in this time. A number of the masterpieces of losing, which is there is still, have modified. Contribution of in the form of erudite masterpiece for example in the form of book of Elm al-Hsia ( Practical Book Arithmetical), Al-Kitbag Al-Kamala ( Complete Book), and Book of al-Hands ( Geometry of Terrapins). Abu Wafer even also pouring many masterpieces he wrote erudite journal of Euclid, Diaphanous and of al-Khwarizmi, but unhappily many which have loosed.
Even that way, contribution of for trig theory very lash isn't it especially development [at] tangent formula, invention early to formula of secant and of cosecant. Hence from that, a large amount of formulas of trigonometry cannot be discharged from name of Abu Wafer. And hitherto the trig formula still used by most people which learn mathematics.
The Theory Of Probability and Trilateral Pascal
The life of Pascal walk during two years before awaked by Gilberto. Then Pascal collaborated with Fermat to triggering the theory of probability. Like Cardano, Pascal interest with the theory of probability from gambler. He studied the hurl of two dice with his father’s friend, Fermat. Both in the reality can give the base growth of areas like : counting, insurance risk, interpreting statistic, studying clan (Mendel). The Coins which hurl have probability out number 1 from 2 (number and picture) or ½. If downhill probability, small above ratio more and more. If there is no possibility, so the probability is zero. Trilateral Pascal founded for the purpose of this.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
This used to determine simple probability problem like in throwing coin. And then it called by Pascal Triangle. Pascal triangle didn’t found by Pascal. It have founded and published on China at 1303 or 320 years before Pascal born. Composition book of Chu Shih-Chieh, Ssu Yuan Yii Chien mention that tables only until 9 story level. Adoption of Pascal Triangle there are in book of Murai Chusen’S of Shampoo of Doshi-Mon the year risingness 1781.
Logic
Logic come from ancient Greek word λόγος (logos) meaning result of consideration of phrased mind pass word and expressed in language. As science, logic referred as logike episteme (logica scientia) or logic science (science) which studying efficiency to think diametrically, precise, and regularly. Science here related at rational ability to know and efficiency relate at kindness mind readiness to realize knowledge into action. Logical word which utilized the can is also interpreted sensiblely.
The History of Logic
Logic started with Thales (624 BC – 548 BC), first Greek Philosopher who leave any fable, takhayul, and non sense stories and looking away to kindness mind to solve universe secret. Thales said that water is arkhe (Greek) which meaning principle or common ground of universe. On that time Thales has defined inductive logic.
Then Aristoteles defining logic as a science, which then called logica scientica. Aritoteles said that Thales concluding that water is arkhe of universe with the reason that water is the soul of anything. On Aristoteles era, logic still called analitica, which specially research the argumentation which started from true proposition, and dialektika which specially research the argumentation which started from proposition which still been hesitated the truth.
Kinds of logic
1. Natural logic
Ability of natural logic [of] human being exist from the day borned
2. Erudite logic
Erudite Logic refine, sharpening mind and also kindness mind.
Paradox of Russell
1901, Russell lay open what is later then known as paradox of Russell (Russell Paradox), which emerge at his masterpiece of Principle of Mathematics (1903). This Paradox arise in the bearing of between a gathering becoming the part of various gathering but itself nonmember. This Paradox Significant follow, according to classic logic view, all statement will is always followed by contradiction. According to other mathematics view (including Hilbert and Brouwer) there is no competent proved to answer logic all statement of mathematics which is contradictive. At the beginning of this century masterpiece which concerning logic, gathering theory, mathematics base and philosophy thrive him.
This Paradox really the side product of undefined axioms (unrestricted) or abstraction which have been the part of gathering theory. Axioms which peeped out by Cantor on a statement P(x), where x is free peubah, where will determined the gathering which the members fulfilling criterion.
• Normal Gathering is the gathering which is unfilled itself as a member of the gathering.
Example : The gathering of all cats, the gathering of students as a normal gathering, because the gathering is not cats or students.
• Not Normal Gathering is a gathering which filled itself as a member.
Example : The gathering of all which is no cats, the gathering of all which is no student.
S = {x x €/ x}
Is S the member of S ?
If S €/ S, so S fulfilled criteria (x €/ x) become the member of the gathering S and paradoxial happened S € S.
If S €/ S, not fulfilled criteria (x €/ x) become the member of the gathering S and paradoxial happened S € S.
€/ ( Gathering nonmemberA); € ( gathering member)
Contradiction: If S €/ S so S € S; if S € S, so S €/ S referred as with paradox of Russell
Idea of Russell
Russell trigger types theory in the year 1908. theory divided become two version, " simple theory" and " generation theory ( ramified)." Both of this theory version get keen criticism. Please mention that this theory is too shallow because cannot finish paradox knew. For the theory other party of too circumstantial because difficult practiced into mathematics definitions-because too consistent, and impinge radian principle don’t tip of ( circle vicious).
Comments of Russell for which is second criticism is, in generation theory scope ( ramified), axiom turned into more simple ( reducibility). Though this axiom can ' loosen' radian principle don’t tip of in his application, but many people expressing that this is way too utilize to be harmonized with philosophy.
At the (time) of at the same time Russell also elaborate logic, theory that mathematics can be altered systematically ( reducible) become logic. First expostulation there are in Principles, and expostulation more there is in Principia Mathematica, logic of Russell consist of two argument or proposisi ( thesis). First, all truthses of matematikal can be specified as part of logic. [Both/ second], all verifications of matematikal earn isn't it as verification of logikal or equally mathematics theorema-theorema become indivisible shares of logic.
Contribution
Give mathematics colour and equipment. Using mathematics, specially gathering theory, to finish mathematics problem-problem, philosophy and try with problem-problem qualitative. Philosophy views and various masterpiece which concerning many topics is ommission of Russell.
Number zero
Number concept zero have expanded since epoch of Babilonia and Ancient Greek, which is at that moment interpreted as no from something. Number concept zero and nature of - in character continue to expand from time to time. Till [at] century to - 7, Brahmagupta a India mathematics introduce some nature of numbers zero. Nature of - in character is an number when summed with zero is remain to, that way also a number if/when multiplied with zero will become zero. This matter continue to become the this topic of research at that moment, even until 200tahun later;then. For example year 830, Mahavira ( India) assure result - result of Brahmagupta and even express that " a number divided by zero is remain to". Of course this fatal mistake.
Idea - idea of India mathematics is hereinafter studied by Moslem mathematics and Arab. This Matter happened [at] phase - early stage when mathematics of Al - Accurate Khawarizmi of system is calculation Hindu ( India) depicting system assess place of number entangling number 0,1,2,3,4,5,6,7,8,9. Al - Khawarizmi is which first time introduce usage of number zero as value space in bases ten. and this system is referred is number system denary.
Mathematics concept, problem of mathematics and solution of mathematics at ancient time which have unused in this time.
Which I can find for example:
Mathematics history re-finding appliance able to assist people away back in calculating, and calculator of sabak. A Both of this is appliance very differ. Firstly, this calculator is ancient Abacus of island of Salamis in Greek is oldest calculator. This calculator in the form of block of harmer as long as 1,5 meter and estimated have been used in a temple by moneychangers. Article which there are this calculator enlist value - number value and currency name like and drachma, talent and oboe.
Second, sabak of Romani. This Sabak is used by using gravel residing in above and below/under winnow line marked with number of Romani according to his column. Order or way use him, each; every gravel below/under ranked among extreme right column line set of, and each; every gravel residing in above valuable line five. If in the calculation of valuable 10, hence there is a gravel brought to left side.
Phi (π)
At former epoch, ancient Egypt people have found and determine the level of π is 3,16 to count area of circle. While for the things in this time the level of π the used is 3,14.
mathematics concept, problem of matematika,or solving of mathematics at the moment which [there] no the relation of with ancient time mathematics at all.
Which I can find for example:
Open-closed Problem
[Is] the same as like social sciences, problems or problems in mathematics even also marginally earn classification become to become two shares. First is the problem oves mathematics of tetutup ( problems closed). And secondly is the problem oves open mathematics ( problems open).
Which during the time emerge on the surface of and taught many schools is the problem oves closed mathematics ( problems closed). Where is true in finishing the problem oves mathematics closed this, prosedure which the was using of have almost can be told standard alias standard. As a result arising rather perception wrong to mathematics. Mathematics considered to be [by] definitive knowledge, prosedural, and saklek.
Meanwhile, problem oves open mathematics ( problems open) alone only just touch, seldom emerge and presented in course of study of mathematics school. As a result if there are any problems of mathematics kinds of this, that problems or problem is assumed ' ad for problem' or incomplete problem.
Simply, problems open alone can be grouped become two shares. Namely problems open-ended and of pure problems open. For the open-ended of problems alone can be grouped become two shares. Namely: ( 1) problems by satu answer many solution ways; and ( 2) problems with many solution ways also many answers.
What is the difference problems closed and of open problems?.
According to Sawada ( 1997), if problems open-ended a kind of mentioned problem passed to students in school, at least there is five advantage which earn to be expected
1. Students involve more active in course of them and study can lay open their idea by lebih sering. students do not only passive imitate examplizeed way is his teacher
2. Students have deeper opportunity use knowledge and skill of their mathematics by totally. Yes, they involve more active in using knowledge potency and skill which have owned before all.
3. Each;Every student can answer problems its own way. This mean, every student creativity can be laid open
4. Study by using problems open-ended a kind of this give experience of reality for student in course of have natural existence
5. There is many experienceses to be got student in the form of satisfaction in course of invention of answer as well as getting confession of other student.
Sumber:
http://www.republika.co.id
http://www.rumahislam.com
http://atrasku.wordpress.com
www.geocities.com
http://www.mate-mati-kaku.com
http://id.wikipedia.org/wiki
http://muhar5yah.wordpress.com
http://mathematicse.wordpress.com
www.my.opera.com
