Monday, August 5, 2019

Underdevelopment: The Democratic Republic Of Congo

Underdevelopment: The Democratic Republic Of Congo Most of African countries are underdeveloped, and according to theories of modernization factors such as population, traditional agrarian structure, and illiteracy, low division of labor, poor infrastructure and communication. For development to take place there has to be change in these factors for example the rate of population growth has to change, infrastructure has to be improved and so on. Countries in the world are ranked in terms of development from the most to the least developed and each country has its position. In that regard, Democratic Republic of Congo ranks among the underdeveloped countries in the world. According to Theodore, (2009) The Democratic Republic of Congo earlier known as Zaire is the biggest nation in Africa. This country is rich in valuable natural resources, which include petroleum, cobalt, diamond, and copper. Since its independence in 1960, the country knows not what true democracy is. It has been faced with prolonged civil and ethnic strife. This has led to political, economic, and social instability all over the country, making this country to remain underdeveloped despite its wealth in natural resources. Mining and exportation of diamond, copper, cobalt and other resources have greatly contributed to internal conflicts. According to Hope (2004) civil war started as early as after the independence; however, the United Nations intervened on a peacekeeping mission. The country experienced thirty-six years of conflict from 1964 to 1997 when Mobutu Sese Sekou was overthrown from presidency by the present President Kabila forces. Though the neighboring countries came, in to support restores peace in the country but this has not been a success as these countries also show interests in getting a share of the wealth got from mining of these resources. The peace deal signed in 1999 by the concerned parties did not stop the civil war (Udombana, 2000). Political situation of the country has been a major contribution to the countries underdevelopment. Countries that are developed or developing normally are good democracies. The rule of the people by the people, political stability is very critical in providing room for change in the factors that cause underdevelopment. Contrary to democratic rule, the country experienced seen a long dictatorial regime during the era of Mobutu Sese Seko. Underdevelopment was fuelled by the fact that power was concentrated to the president. The government institutions were stifled and their role was to rubber stamp orders from above. Compromising the role played by institutions is a major hindrance to the path of development. The dictatorial regime controlled all the corporations and every aspect of the administration. This contributed to the countries underdevelopment in that decisions were centralized and in a top down approach. Since the country was had one party, the dictator took advantage of his power to make sure that only those who were in support and loyal to the party become CEOs, directors and union leaders (Lubeck, 1992). This led to mismanagement of public institutions and much looting at the expense of poor citizens widening the gap between the rich and the poor. When president Kabila was elected many thought that the country was on the road to democracy. However, the regime maintained the status quo in that the president had legislative. Executive and military powers vested in him. This kind of a government structure does not give full support of development because the executive is not accountable for any omission or commission in any act regarding the country. After the assignation of Kabila in 2001, his son Kabila took over with the objective of developing the country. The transition constitution has greatly contributed in determining the structure and organization of the countrys institutions helping put them back on development track. The constitution has also caused devolution of powers between the central and provinces governments. From the economic perspective, the Democratic Republic of Congo is economically underdeveloped compared to other countries in Africa and all over the world. Democratic Republic Congo is very rich in valuable minerals and favorable climate that can spur economic growth to great height however, the country is still underdeveloped mainly due to the political instability of the country. Economic development is what causes an increase in the living standards of a countrys population. In Congo the citizens, live in poor conditions despite the presence of mining firms in the country the citizens earn very little wages, which translates into poor quality of life (Mbaku, 2004). Though there has been several economic development plans set as early as 1982 the expenditure called for in the development of infrastructure, agriculture, forestry, and light industry is never reached due to economic difficulties. One main challenge to economic development in the country is the overdependence on petroleum at the expense of other industries. The country has not succeeded in boosting those economic activities that do not mainly rely on imports. Despite the favorable climate sector such as agriculture have been neglected. Thus, the income earned in exportation of minerals is used to import food supplies. Overreliance on international aid is a major bottleneck to economic development in the country (Porter, Craig 2004). Countries such as China, Soviet Union, and France provided significant aid with France being the leading donor. Although international aid is normally given to spur economic development, countries that relies much on foreign aid face economic challenges when the donors withdraw or fail to give what such countries expected. The political instability in the country has made many donors to withdraw their pledges put strain on the Congos economy, which is a combination of industrial sector relying on petroleum mining, traditional agriculture and services. Congos economy has however, made substantial progress mainly because of the reforms. The country has taken measures to liberalize the economy through investment, hydrocarbons, and tax reforms. However, not all these reforms have succeeded some are yet to be felt by neither the common citizens on the ground nor the investors. Plans to privatize main parastatals the transportation and telecommunication monopolies, was a good one that would have helped improve unreliable and dilapidated infrastructure. Nevertheless, the plans were never implemented and the state of telecommunication and infrastructure is still very poor. To achieve economic development the country needs to make serious moves towards economic stabilization through restructuring external debt and public finances improvement. In the late 1990, the country was back on track in terms of economic development with major economic reforms. However, this later hindered by several external and internal factors that followed. For example, in 1998 the oil prices slumped put much strain on the countrys budget deficit. Armed conflict broke out in the same year straining the economic prospects, which chiefly depend on political stability (Booth, 1985). The country has to make the investment climate remains unfavorable making many investors to shy away from investing in the country. Investors especially foreign investors have in many countries contributed to spur the economic growth of these countries. Slater (1993) argues that development from the social perspective refers to qualitative changes in the society structure and functioning, in a bid to achieve the objectives better. To attain social development there has to be increased awareness that will lead to better organizations. In the Democratic Republic of Congo from the social perspective is poorly developed. The structure and functioning of the society is poor there is need to create awareness among the Congolese to help create better organizations. This will help improve their living standards, health, education and other quality life measures. Education levels and access to facilities such as hospitals in the country is still very poor (Brohman, 1996). Most of the citizens are either illiterate or only have basic education. The political instability has played a significant role in hindering human development this further deters social development. Political instability of the country has caused major social injustices; social development takes place in societies that have democratic rule and freedom. This freedom promotes creativity and invention for the betterment of a society. The social welfare in the country has for a long time been compromised, the economic gains only benefit a few who are in power. Women have over the years fallen victims of social injustices from rape especially during conflicts to discrimination in the job market. The country has failed to provide social services such as security and health care to its population. Social services are not equally distributed in the country (Harrison, 2005). Conclusion It is no doubt that The Democratic Republic of Congo is an underdeveloped country despite its wealth in valuable resources. Political instability has been the main challenge to a successful economic development strategy. The country has poor transportation networks, which is still a major challenge to economic development. The country needs major reforms be on the development track. To achieve overall development the country must not overlook any of the development perspectives (Simon, 2003). The political development is crucial for any development or growth to take place. It is through political stability and democratic rule that lead to the development of other sectors such as economic, social and technological. Fences by August Wilson: Analysis of Troy Fences by August Wilson: Analysis of Troy Unintentional Effect Around the early 1900s, racism was prominent and wasnt sugarcoated at all. African Americans had to deal with several obstacles around this period because of the discrimination in certain things they wanted to partake in. These actions effected many African Americans because it forced some of them to look at the world with hatred and it limited many of their opportunities in life. Racism is sad reality in our nation that affects all types of people and it continues to shake and alter lives. People use racism as a sort of way to detect the differences with their peers and spike bias towards a group of people. Some people go the extra mile in insulting, attacking or mentally attacking others because of racist ideals they believe in. In the play Fences by August Wilson, Troys dreams of becoming a professional baseball player got ripped away because of his racial appearance. This single experience has slowly made him look at life differently. He easily gets fooled by his inner thoughts b ecause of the past racial discrimination he endured and believes his self-created illusions. Racism has played an important role in Troys life which is evident based on the certain decisions he has made in his life. Because of these experiences in his life, Troys rash decisions in the play causes tensions and conflicts with his family. One of the rash decisions Troy does in the play is when he prevents his son from playing football. Based on the college scholarship, Cory had a bright future in playing football but Troy completely neglects that and says that Cory will not get involved in no sports. Not after what they did to me in the sports (Wilson 1053). Because of the past discrimination Troy faced in his life, Troy also assumed that Cory wouldnt get a fair shake either because of his skin color. Troy argued that because of his skin color, he was prevented from playing in the Major Leagues. Later in the story, he tells the coach that Cory isnt allowed to play football and he told the recruiter to leave and to never come back. Troy doesnt see that by pulling Cory away from achieving his dream at being a football player, he is creating tension and he is subconsciously not allowing Cory to have a better life than him. If Cory had got the opportunity and played football in college, he would have been able to get a co llege education while playing the sport he loves. Troy doesnt see that however because Troy is still effected from the denial he got when he was trying to play professional baseball. Although he cares about Cory and he thinks by preventing him from playing football is only for his own good, that decision wasnt wise because he is basically doing what society did to him which is preventing him from achieving his dreams. Troy aspires to be fighter and a survivor in life and from Roses perspective that shows through his son Cory. Troys true intentions are to show his son that nothing comes easy. The ultimate flaw however is that Troy looks at the world in his perspective. Troy is trying to prevent Cory from going through the same harsh experiences as him but he is unintentional recreating the same obstacles which are preventing Cory from becoming the full potential of himself. Throughout the play, Troy is imposing his will on Cory and he is basically preventing him from exploring the world for himself. This causes Cory to have conflicts with his dad because they dont agree completely. In the article Baseball as History and Myth in August Wilsons Fences by Susan Koprince, Susan says that Troys front yard is literally turned into a battleground during his confrontations with his younger son Cory (Koprince 354). With each argument and conflict, Cory slowly characteristics change in the story. In the begi nning of the story, he was a cheerful kid hopeful for his future. However because of the denial of pursing football and the constant back and forth between him and Tory, he becomes very bitter just like his father. This isnt a good thing because once Cory picks up his father characteristics, it forces him to see the world in a single perspective and thats not his full potential but an intentional effect from Troys reactionary decision. Like stated before Troy isnt trying to harm his family at all. Troy went through a lot in his past and he doesnt want his family to go through that same experience he went through. He felt it was his job to be a father and protect his family from his past mistakes. Troy went to jail for fifth teen years for murder. A man he tried to rob pulled a gun on him so in retaliation he stabbed him. Experiences like this Troy doesnt want any of his sons to go down that path. Lyons is Troys son from a previous relationship. While Troy was in prison, Lyons didnt have a dad growing up and he didnt really have guidance in the world. Lyons doesnt seem particularly bitter about any of this. He just seems to accept things as they come. Lyons passion is becoming a musician. Troy however doesnt see that as a serious thing. He instead sees that as a dangerous path. Troy says You living the fast lifeà ¢Ã¢â€š ¬Ã‚ ¦wanna be a musicianà ¢Ã¢â€š ¬Ã‚ ¦running around in them clubs and thingsà ¢Ã¢â€š ¬Ã‚ ¦ (W ilson 1041). Although Troy sounded harsh there, this was probably the most honest and sincere thing he told Lyons. Troy views Lyons dream as a risk because hes not getting any income from this profession. Every time Troy gets paid, Lyon appears asking for a handout. This offends Troy because he never had handouts coming up. From the experiences of growing up in a white society, he believes that African Americans have to work for everything that they want. From the article, Susan writes that Instead of limitless opportunity, [Troy] has come to know racial discrimination and poverty (353). He wants Lyons to take on a safer route which is working somewhere with a structure rather than the freelance world of music. He doesnt want Lyons to get lost in that music world and result into doing the things he used to do that caused him to go to jail. Lyons doesnt see the world like Troy. Lyons isnt bitter at the world like Troy and he expresses himself through music. Lyons has the same mindset as Cory which is that they can do something special for their lives in this society full of opportunities. Troy believes that Lyons isnt aware on the harsh treatment African Americans go through and it shows clearly when his son asks him for ten dollars. This conflict shows how Troy distance himself away from Lyons. Troy doesnt feel comfortable giving out ten dollars because he feels like hes being taken advantage of. This goes back to the self-created illusions Troy creates because of the past experiences he dealt with especially with whites. Troy basically creates a barrier to Lyons because of this fear. Lyons doesnt want to take advantage of Troy but he wants a closer relationship with father. This isnt possible because Troy doesnt support Lyons career and he doesnt give Lyons the same attention he gives Cory. Sadly, Troy doesnt see that Lyons wants more attention instead he looks at Lyons as someone who is trying to take his hard-owned money. Troy later in the play makes another decision that shifts the tone of play where he commits an affair with Alberta. Troy feels trapped in a marriage where he cant display his true self. He doesnt blame Rose but from this scene he looks very unapologetic. He felt like with all the responsibilities of being a father and provider for his family, he needed a way to escape all that. This is his reasoning for committing this fatal decision. Troys selfish act shows that he wanted to break a boundary hes been limited too. Hes been limited from baseball, the status hes been in at work and his marriage. Rose was crushed hearing that the man she gave her life and identity to committed an affair with another woman. It bothered her when he said he needed an outlet from his priorities. She said Dont you think I ever wanted other things? Dont you think I had dreams and hopes? What about my life (Wilson 1071)? She committed herself to the marriage and to repay her, he betrays her by having a baby wi th another woman. Because of this conflict, Troy and Roses marriage is severely jeopardized. Rose is still the mother of his children but she doesnt recognize herself as a wife to Troy. She starts to build her own characteristics and beliefs after this conflict. Rose felt like she wasted her years with Troy so she began to build a life outside of the house she felt trapped in. During the last scene of the play, she tells Cory why the marriage went down the way it did. Rose recognized that she gave up her free will for love. She wanted to have children and be at one with Troy. She accepted that this was her identity. But because of this affair, it woke her up and made her a diverse character because she became independent rather than dependent. Troys decisions distanced himself away from his family as he lost his dominance in the household. Troy Maxson went through a lot in his life. Troy has a singular perspective on the world. He has a strict demeanor because of how society viewed African Americans back in the 1950s. Troy cares a lot about his family even if he doesnt show it. Throughout his life, Racism has been a barrier for him. He was once young and he chased his own dreams but because of his skin color, several ideals got in his way. Racism caused a lot of Troys bitterness towards life. He went to jail and ultimately makes sure he doesnt fall back there. All of his decisions were very influenced by past experiences from racism. Whether it be denying Corys dreams, neglecting Lyons and breaking the barriers of his marriage with Rose. All of these decisions caused tensions around the family and ultimately fenced his family away from him. Works Cited Koprince, Susan. Baseball as History and Myth in August Wilsons Fences.. African  American Review, vol. 40, no. 2, Summer2006, pp. 349-358. EBSCOhost. Wilson, August. Fences Literature: A Portable Anthology. 4th ed. Boston:Bedford/St.Martins, 2016. 1030-1088. Print. What Is Algebra? What Is Algebra? Algebra is a branch of mathematics, as we know maths is queen of science, it plays vital role of developing and flourishing technology, we use all scopes in past and newly, the algebra is not exceptional the maths. Algebra is one of the main areas of pure mathematics that uses mathematical statements such as term, equations, or expressions to relate relationships between objects that change over time.Here is a list of names who have contributed to the specific field of algebra. Algebra is seen by much arithmetic with letters and a long historical precedent the textbooks, stretching back of the 14th century. As such it deepens upon experience and facility with arithmetic calculations. It provides student with skill to carry out algebraic manipulations .many of the which parallel arithmetic computation. At the very least ,school algebra is a collection of mathematical practices and procedure to be internalised and integrated into learners functioning ,at the very most in its tradition form its afford glimpse of a powerful tool for modelling and thus resolving problems, (page 559 jifa cai) Word Algebra The word algebra is a shortened misspelled transliteration of an Arabic titleal-jebr wal-muqabalah (circa 825) by the Persian mathematician known as al-Khwarizmi [words, p. 21]. Theal-jebrpart means reunion of broken parts, the second partal-muqabalahtranslates as to place in front of, to balance, to oppose, to set equal. Together they describe symbol manipulations common in algebra: combining like terms, moving a term to the other side of an equation, etc. In its English usage, in the 14thcentury,algebermeant bone-setting, close to its original meaning. By the 16thcentury, the formalgebraappeared in its mathematical meaning. Robert Recorde (c. 1510-1558), the inventor of the symbol= of equality, was the first to use the term in this sense. He, however, still spelled it asalgeber. The misspellers proved to be more numerous, and the current spellingalgebratook roots. Thus the original meaning ofalgebrarefers to what we today callelementary algebrawhich is mostly occupied with solving simple equations. More generally, the termalgebraencompasses nowadays many other fields of mathematics: geometric algebra, abstract algebra, Boolean algebra, Ã‚ ³-algebra,to name a few. Algebra is an ancient and one of the most basicbranch ofmathematics, invented by Muhammad Musa Al-Khwarizmi, and evolve over the centuries. The name algebra is itself of Arabic origin. It comes from the Arabic word ‘al-jebr.[1] The English invented the world (Kelly 1821-1895) algebra of matrices and the research (Paul 1815-1864) may have emerged since 1854 and from this research Boolean algebra, also appeared in 1881 forms of art to illustrate the Boolean algebra, (availabl History of algebra In history, we find some following mathematicians who have great contributions in development of algebra. Cuthbert Tunstall Cuthbert Tunstall (1474 -1559) was born in Hackforth, Yorkshire, England and died in Lambeth, London, England. He was a significant royal advisor, diplomat, and administrator, and he gained two degrees with great proficiency in Greek, Latin, and mathematics. In 1522, he wrote his first printed work that was devoted to mathematics, and this arithmetic book ‘De arte supputandi libri quattuorwas based on Paciolis Suma. Robert Recorde Robert Recorde (1510-1558) was born in Tenby, Wales and died in London, England. He was a Welsh mathematician and physician and in 1557, he introduced the equals sign (=). In 1540, Recorde published the first English book of algebra ‘The Grounde of Artes. In 1557, he published another book ‘The Whetstone of Witte in which the equals sign was introduced. John Widman John Widman (1462-1498) was born in Eger, Bohemia, currently called Czech Republic and died in Leipzig, Germany. He was a German mathematician who first introduced + and signs in his arithmetic book ‘Behende und hupsche Rechnung auf Allen kauffmanschafft. Thomas Harriot Thomas Harriot (1560 -1621) was born in Oxford, London and died in London England. He was an astronomer and mathematician, and founder of the English school of algebra. William Oughtred William Oughtred (1575-1660) was born in Eton, Buckinghamshire, England and died in Albury, Surrey, England. He was one of the worlds great and formally trained mathematicians. Oughtred, in his book Clavis Mathematicae included Hindu-Arabic notation, decimal fractions and experimented on many new symbols such as ÃÆ'-,::, >, and John Pell John Pell (1611-1685) was born in Southwick, Sussex, England, and died in Westminster, London, England. Pells work was mostly based on number theory and algebra. Pell published many books on mathematics such as Idea of Mathematicsin 1638 and the two page A Refutation of Longomontanuss Pretended Quadrature of the Circle in 1644. Reverend John Wallis John Wallis (1616-1703) was born in Ashford, Kent, England and died in Oxford, England. In 1656, Wallis published his most famous book Arithmetica Infinitorum in which he introduced the formula /2 = ( ( In another of his works, Treatise on Algebra, Wallis gives a wealth of information on algebra. John Herschel John Frederick William Herschel (1792-1871) was born in Slough, England and died in Kent, England. He was a great astronomer who discovered Uranus. In 1822, he published his first work on astronomy, a small work to calculate the eclipses of the moon. In 1824, he published his first major work on double stars in the Transactions of the Royal Society. Charles Babbage Charles Babbage (1791 -1871) was born in London, England and died in London, England. In 1821, Babbage made the Difference engine to compile tables of mathematics. In 1856, he invented Analytical Engine, which is a general symbol manipulator and similar to todays computers. Sir Isaac Newton Sir Isaac Newton (1643-1727) was born in Lincolnshire, England and died in London, England. He was a great physicist, mathematician, and one of the greatest scientific intellects of all time. In 1672, he published his first work on light and color in the Philosophical Transactions of the Royal Society. In 1704, Newtons works on pure mathematics was published and in 1707, his Cambridge lectures from 1673 to 1683 were published. ( How is Algebra used in daily life? Every day in our life and all over the world we use Algebra many places as well as finances, engineering, schools, and universities we cant do most scopes without maths.( It is actually quite common for an average person to perform simple Algebra without realizing it. For example, if you go to the grocery store and have ten dollars to spend on two dollar candy bars. This gives us the equation 2x = 10 where x is the number of candy bars you can buy. Many people dont realize that this sort of calculation is Algebra; they just do it). ( and Other Definitions Algebra is the parts of mathematics where numbers and letters are used like A B or X and Y, or other symbols are used to represent unknown or variable numbers. For examples : inA +5 = 9, A is unknown, but we can solve by subtracting 5 to both sides of the equal sign (=), like this: A+5 = 9 A+ 5 5 = 9 5 A +0 = 4 A = 4 3b+12=15 subtract both sides 12 3b+12-12=15-12 3b=3 divide both sides 3 to get the value of b which is 1 and so on 5x/5x=1 if you substitute x any number not zero the equation will be true (Algebra is branch of mathematics that substitutes letters for numbers. An algebraic equation represents a scale, what is done on one side of the scale with a number is also done to the other side of the scale. The numbers are the constants. Algebra can include real numbers, complex numbers, matrices, vectors etc. Moving from Arithmetic to Algebra will look something like this: Arithmetic: 3 + 4 = 3 + 4 in Algebra it would look like: x + y = y + ) artical Terminology used in algebra to make algebra easy or any other branches of maths, we must understand well all basic sign in all operations and use it right way, these signs are , subtractions ,division, addition ,multiplication. variable is also called an unknown and can be represented by letters from the alphabet letters. Operations in algebra are the same as in arithmetic: addition, subtraction, multiplication and division. An expression is a group of numbers and variables, along with operations. An equation is the equality of two expressions. (Polynomials are often written in descending order, in which the terms with the largest powers are written first (like 92- 3x + 6). If they are written with the smallest terms appearing first, this is ascending order (like 6 3x + 92). equation- An equation is a mathematical statement that contains an equal sign, like ax + b = c. exponent- An exponent is a power that a number is raised to. For example, in 23, the exponent is 3. expression- An algebraic expression consists of one or more variables, constants, and operations, like 3x-4. Each part of an expression that is added or subtracted is called atermFor example, the expression 42-2x+7 has three terms. factor- The factor of a number is a number that divides that number exactly. For example, the factors of 6 are 1, 2, 3 and 6. formula- A formula shows a mathematical relationship between expressions. fraction- A fraction is a part of a whole, like a half, a third, a quarter, etc. For example, half of an apple is a fraction of an apple. The top number in a fraction is called the numerator; the bottom number in a fraction is called the denominator. inequality- An inequality is a mathematical expression that contains an inequality symbol. The inequality symbols are : > greater than (2>1) à ¢Ã¢â‚¬ °Ã‚ ¤ less than or equal to à ¢Ã¢â‚¬ °Ã‚ ¥ greater than or equal to à ¢Ã¢â‚¬ °Ã‚   not equal to (1à ¢Ã¢â‚¬ °Ã‚  2). integer- The integers are the numbers , -3, -2, -1, 0, 1, 2, . inverse (addition)- The inverse property of addition states that for every number a, a + (-a) = 0 (zero). inverse (multiplication)- The inverse property of multiplication states that for every non-zero number a, a times (1/a) = 1. matrix- nth- operation- An operation is a rule for taking one or two numbers as inputs and producing a number as an output. Some arithmetic operations are multiplication, division, addition, and subtraction. polynomial- A polynomial is a sum or difference of terms; each term is: * a constant (for example, 5) * a constant times a variable (for example, 3x) * a constant times the variable to a positive integer power (for example, 22) * a constant times the product of variables to positive integer powers (for example, 2x3y). monomial is a polynomial with only one term. A binomial is a polynomial that has two terms. A trinomial is a polynomial with three terms. prime number- A prime number is a positive number that has exactly two factors, 1 and itself. Alternatively, you can think of a prime number as a number greater than one that is not the product of smaller numbers. For example, 13 is a prime number because it can only be divided evenly by 1 and 13. For another example, 14 is not a prime number because it can be divided evenly by 1, 2, 7, and 14. The number one is not a prime number because it has only one factor, 1 itself. quadratic equation- A quadratic equation is an equation that has a second-degree term and no higher terms. A second-degree term is a variable raised to the second power, like x2, or the product of exactly two variables, like x and y. When you graph a quadratic equation in one variable, like y = ax2+ bx + c, you get a parabola, and the solutions to the quadratic equation represent the points where the parabola crosses the x-axis. quadratic formula- The quadratic formula is a formula that gives you a solution to the quadratic equation ax2+ bx + c = 0. The quadratic formula is obtained by solving the general quadratic equation. radical- A radical is a symbol à ¢Ã‹â€ Ã… ¡ that is used to indicate the square root or nthroot of a number. root- An nthroot of a number is a number that, when multiplied by itself n times, results in that number. For example, the number 4 is a square root of 16 because 4 x 4 equals 16. The number 2 is a cube root of 8 because 2 x 2 x 2 equals 8. solve- When you solve an equation or a problem, you find solutions for it. square root- The square roots of a number n are the numbers s such that s2=n. For example, the square roots of 4 are 2 and -2; the square roots of 9 are 3 and -3. symbol- A symbol is a mark or sign that stands for something else. For example, the symbolà ·meansdivide. system of equations- A system of equations is two or more independent equations that are solved together. For example, the system of equations: x + y = 3 and x y = 1 has a solution of x=2 and y=1. terms- In an expression or equation, terms are numbers, variables, or numbers with variables. For example, the expression 3x has one term, the expression 42+ 7 has two terms. variable- A variable is an unknown or placeholder in an algebraic expression. For example, in the expression 2x+y, x and y are variables. +,- ( Learn algebra Symbolizes the number in the account to a group that contains that number of things, for example, No. 5, always stands for a set containing 5 things.In algebra, the symbols may be replaced by numbers, but it is possible to solve the number one or more replace one icon.To learn algebra, we must first learn how to use symbols replace the numbers.And then how to create a constraint for strings of numbers. Groups and variables.There is a relationship between the symbols in algebra and groups of numbers.It is certain that each of us has some knowledge of groups of objects, such as collections of books, collections of postage stamps, and groups of dishes.And groups of numbers are not different for these groups a lot.One way to describe sets of numbers in algebra is that we are using one of the alphabet, such as the name of her p..Then half of the numbers of this group Bhzaretha brackets of the form {}.For example, can be expressed set of numbers from 1 to 9 as follows: A = {1, 2.3, 4, 5.6, 7, 8.9}. The group of odd numbers under 20 are: B = {1.3, 5, 7.9, 11, 13.15, 17, 19}. These examples demonstrated the models of the groups used in algebra. Suppose that the age of four persons were respectively: 12, 15.20, 24. Then can be written in this age group numbers. A = {12.15, 20, 24}. How is the age of each of them after three years? One way to answer this question is that we write 12 +3.15 +3.20 +3 and 24 + 3.We note that the number 3 is repeated in each of the formulas  ¸ à ¢Ã¢â€š ¬Ã‚ ¢ four.In algebra we can express all previous versions form a single task is m + 3 where m is any number of numbers of a group.That is, it can replace any of the numbers 12, 15, 20 or 24 m are indicated.Is called the symbol m variable, called the group a field of this variable, but No. 3 in the formula m+3 is called hard because its value is always one.Known variable in algebra as a symbol can be compensated for the number of one or more belongs to a group. We can replace any names lead to correct reports or reports the wrong variable.For example: Hungary is bordered by the State of the Black Sea Report of the wrong, as in fact can not be like this report is correct only if compensated by the variable r one of the States: Bulgaria or Romania, or Turkey.The report shall be  ¸ Turkey is a country bordered by the Black Sea for example, the right one called the compensation that makes the report and called the right roots group consisting of all roots with a solution.The solution set is the previous example. {Bulgaria, Romania, Turkey}.And in reparation for not use the names to compensate for variables, but we use the numbers. Equations known as the camel sports is equal to reflect the two formats. Phrase: Q +7 = 12 For example, an easy equation  ¸ mean the sum of the number 7 with the number equal to 12 à ¢Ã¢â€š ¬Ã‚ ¢ To solve this equation, we can do to compensate for different numbers of Q until we get a report of the equation makes the right one.If we substitute for x the equation becomes number five report is correct, and if we substitute for x any number of other reports, the equation becomes wrong.So to solve this equation set is {5}. This group contains only one root. It is possible that the equation more than one root: X  ² + 18 = 9 o. No. 2 highest first variable x means that the number of representative variable Q is the number of box, that number multiplied by itself once.See: box.In this equation, we can make up for X number 3: 3 ÃÆ'- 3 + 18 = 9 ÃÆ'- 3 9 + 18 = 27 27 = 27 We can also compensate for X number 6: 6 ÃÆ'- 6 + 18 = 9 ÃÆ'- 6 36 + 18 = 54 54 = 54 Any other compensation for making the equation Q report wrong.Then 3 and 6 are the root of the equation.Thus, the solution set is {3.6}. There are also equations having no roots: X = + 3 If we substitute for x any number, this equation becomes a false report, and a solution is called the group of free and symbolized by the symbol {}. and some of the equations, an infinite number (for high standards) from the roots. (X + 1)  ² = x  ² + 2 x +1 In this equation if we substitute for x any number we get the right report, the Group resolved to contain all the numbers What is best way to learn and teach algebra? Step-by-step equations solving is the key of teaching and learning. To find fully worked-out answers and learn how to solve math problems, one step at a time. Studying worked-out solutions is a proven method to help you retain information. Dont just look for the answer in the back of the book; There are five laws basic principles of math governing operations: multiplication addition subtract and expressing the variables and can be compensated for any number Algebra is anessential subject. Its the gateway to mathematics. Its used extensively in the sciences. And its an important skill in many careers. Many people think, it is a nightmare and causes more stress, homework tears and plain confusion than any other subject on the curriculum but that is not true. Theimportance of understanding equation Connotation and denotation on extension of a concept two opposite yet complementary aspects is clarified the extension is defined vice versa understanding the concept equation includes its connotation and denotations. This session of observed lessons will show the essential nature or the equation is consolidated by designing problem variation putting emphasis on clarifying the connotation and differentiation the boundary of the set of object in the extension. (Page 559 Jifa cai) Whats the best formula for teaching algebra? Immersing students in their course work, or easing them into learning the new skills or does a combination of the two techniques adds up to the best strategy? Researchers at the Centre for Social Organization of Schools at Johns Hopkins are aiming to find out through a federally funded study that will span 18 schools in five states this fall. The study, now in its second year of data collection, will evaluate two ways to teach algebra to ninth-graders, determining if one approach is more effective in increasing mathematics skills and performance or whether the two approaches are equally effective. Participating schools in North Carolina, Florida, Ohio, Utah and Virginia will be randomly assigned to one of two strategies for the 2009-2010 school year; to be eligible, students must not have previously taken Algebra I. Twenty-eight high schools were studied during the 2008-2009 school year. One strategy, called Stretch Algebra, is a yearlong course in Algebra 1 with students attending classes of 70 to 90 minutes a day for two semesters. This approach gives students a â€Å"double dose† of algebra, with time to work on fundamental mathematics skills as needed. The second strategy is a sequence of two courses, also taught in extended class periods. During the first semester, students take a course called Transition to Advanced Mathematics, followed by the districts Algebra I course in the second semester. The first-semester course was developed by researchers and curriculum writers at Johns Hopkins to fill gaps in fundamental skills, develop mathematics reasoning and build students confidence in their abilities. â€Å"The question is, Is it better for kids to get into algebra and do algebra, or to give kids the extra time so the teacher can concentrate more on concepts started in middle schools?† said Ruth Curran Neild, a research scientist at Johns Hopkins and one of the studys principal investigators. Teachers using both strategies will receive professional development. Mathematics coaches will provide weekly support to those who are teaching the two-course approach; the study will provide teacher guides and hands-on materials for students in Transition to Advanced Mathematics. Johns Hopkins researchers will be collecting data throughout the school year. Findings are expected during the 2010-2011 school year. Learn Algebra, the easy way The key to learn and understand Mathematics is to practice more and more and Algebra is no exception. Understanding the concepts is very vital. There are several techniques that can be followed to learn Algebra the easy way. Learning algebra from the textbook can be boring. Though textbooks are necessary it doesnt always address the need for a conceptual approach. There are certain techniques that can be used to learn algebra the fun and easy way. Listed below are some of the techniques that can be used. Do some online research and you will be surprised to find a whole bunch of websites that offer a variety of fun learning methods which makes learning algebra a pleasant experience and not a nightmare. But the key is to take your time in doing a thorough research before you choose the method that is best for you, or you can do a combination of different methods if you are a person who looks for variety to boost your interest. 1. ANIMATED ALGEBRA : You can learn the basic principles of algebra through this method. Animation method teaches the students the concepts by helping them integrate both teaching methods. When the lessons are animated you actually learn more ! 2. ALGEBRA QUIZZES : You can use softwares and learn at your own pace best of all you dont need a tutor to use it. What you really need is something that can help you with your own homework, not problems it already has programmed into it that barely look like what your teacher or professor was trying to explain. You can enter in your own algebra problems, and it works with you to solve them faster make them easier to understand. 3. INTERACTIVE ALGEBRA : There are several Interactive Algebra plugins that allows the user toexploreAlgebra by changing variables and see what happens. This promotes an understanding of how you arrive at answers. There are websites that provide online algebra help and worksheets. They also provide interactive onlinegamesand practice problems and provide the algebra help needed. It is difficult to recommend better methods for studying and for learning because the best methods vary from person to person. Instead, I have provided several ideas which can be the foundation to a good study program. If you just remember all the rules and procedures without truly understanding the concepts, you will have difficulty learning algebra. (

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