Tuesday, October 29, 2019

Sedimentary or metamorphic rocks and engineering issues Essay

Sedimentary or metamorphic rocks and engineering issues - Essay Example der, 2001).   Given the ability of engineers to measure all these, an emphasis on the latter is quite important in order to provide insight that would at least help in reducing earthquake intensities in the society. Particularly, the understanding of sedimentary rocks and their contribution to earthquakes intensities is necessary. To start with, earthquake shaking starts from the rupturing fault and then continues at other distances away from the fault. Earthquake shaking intensity is supposed to decrease as the distance from the rupturing fault decreases. However, it has been observed that shaking in one site is sometimes stronger than shaking in another site. Sometimes, this shaking can be ten times higher or stronger than shaking in another site (Ammon, 1997). Geologists have come up with information relating sedimentary rocks with earthquake shaking intensities. Geologists argue that shaking is always high in areas of softer rocks. In addition, shaking is amplified in areas of thicker sediments compared to areas of thin sediments. As it has been observed, the major reason why sedimentary rocks are associated with shaking intensities is because they are soft (Denecke & Series, 2003). An explanation of the relationship between sedimentary rocks and earthquakes shows that seismic waves’ speed is much higher in hard rocks when compared to sedimentary rocks. This is because the latter are soft as it has been explained earlier. In areas with different rock types, waves tend to pass through harder rocks to the softer rocks, they slow down. However, in order to carry the same energy carried in the hard rocks, they tend to get bigger than before. Therefore, shaking at sites that have soft rock layers is stronger since the seismic waves tend to move slowly as shown in Figure 1 and 2 (SCEC, 2014). The loss of life and properties associated with earthquake intensities can actually be controlled by avoiding buildings in area of soft sedimentary rocks. If this is not

Sunday, October 27, 2019

Employee Attitude And Performance Management

Employee Attitude And Performance Management Employees are the major drivers of any form of business and good employee performance is the most important need for the current competitive business environment to run successfully. Many organisations have started to attach a great emphasis towards the knowledge workers as claimed by Armstrong and Baron (1998) which makes it even more essential to understand the various practices of performance management. Performance Management and Performance Appraisal are very important tools; it helps to motivate employees to work hard and improves overall companys productivity Based on the study of Armstrong (2000) , performance management aims at improving the current results of the organisation or individuals or a group. A simple way to describe performance Management it is A process that significantly affects organizational success by having managers and employees work together to set expectations, review results and reward performance (Bowen, J. 2007). Performance appraisal is a way of giving employees feedback about their performance at work. According to ACAS (2003)  ¿Ã‚ ½Performance appraisal is an assessment of employees performance, potential and development needs. Performance appraisal is an opportunity to take an overall view of work content, loads and volumes, to look back on what has been achieved during the reporting period and agree objectives for the next( ACAS, 2003). 1.1 Background Study Research Question Performance Management , regular, balanced and systematic appraisals must be administered consistently in order to evaluate the performance of each individual in the organization. This allows human resources to pinpoint the weaknesses of an individual ¿Ã‚ ½s work style and the strengths. They can then share this information with the employee in order to affect a change in performance. This in turn will lead to more productivity and potentially better returns on human investment. Design of Organization, Analyze the work processes and recommends improvements when necessary. HRM also need to scan the world environment and identify emerging trends that will affect the organization and the management of people therein. In this role, the HR person contributes to the development of and the accomplishment of the organization-wide business plan and objectives. The HR business objectives are established to support the attainment of the overall strategic business plan and ob jectives. performance appraisal method that  ¿Ã‚ ½ranks individuals performance by counting the number of times any one individual is the preferred member when compared with all other employees in an organization ¿Ã‚ ½ (Decenzo, D and Robbins, S. 2001) According to Rue and Byars (2003) they illustrate the Paired Comparison Method using an example  ¿Ã‚ ½Suppose a manager is to evaluate six employees. The manager firstly compares the first employee with the second employee on a chosen performance criterion, such as quantity of work. If the manager thinks the first employee has produced more work then the second employee, he or she gets a higher rating. The first employee is then compared to the third, fourth, fifth and sixth employee on the same performance criterion. A better rating is given to the employee who produced the most work in each of these paired comparisons. The process is repeated until each employee has been compared to every other employee on all the chosen performance criteria. The employee with the best rating is considered to be the best performer. Likewise, the employee with the lowest rating is the lowest performer ¿Ã‚ ½. The main drawback of this method is that it can be used only in small organizations, wit h small numbers of employees, but in large organizations with large number of employees, it is difficult to compare each employee with every other employee in the organization. An appraisal method in which the employee ¿Ã‚ ½s performance feedback comes from such sources  ¿Ã‚ ½as self assessment, peers, team members, managers in the organizational hierarchy, and also from external sources such as customers, suppliers and other interested stakeholders has become very popular in contemporary organizations ¿Ã‚ ½ (Decenzo, D and Robbins, S. 2001) 360-Degree appraisal is a very useful tool, the data for appraisal is collected from a wide range of resources and it provides a very through picture of how an individual ¿Ã‚ ½s performance is viewed and can be an extremely powerful tool in analyzing performance. According to Foot and Hook. (2005) they state.  ¿Ã‚ ½To have any genuine value or meaningful impact, 360? feedback must be far more than a standalone activity. It should involve managing the individual ¿Ã‚ ½s expectations, aligning questionnaires to competency frameworks, setting goals to integrate the exercise into personal development plans and providing feedback from trained facilitators. The process surrounding the 360? process itself is complex, and how well HR and learning managers plan that process will determine what impact it will have ¿Ã‚ ½ this shows that while 360? feedback is not an easy process to introduce into an organization,  ¿Ã‚ ½it does nevertheless provides a powerful tool that fits well with t he performance management and performance appraisal approach ¿Ã‚ ½ (Foot, M. and Hook, C. 2005) Career Management, managing people is one of the most difficult aspects of organizational management .It means dealing with people who differ physical and psychologically. HR need to always talk with employees to find out what are individual assessments of abilities, interests, career needs and goals or all kinds negative feedback. 1.2 Research Questions 1. What is the relationship between performance appraisal and Employee attitude? 2. What is the attitude of employees towards goal setting? 3. What is the attitude of employees towards agency relations? 4. What is the attitude of employees towards dynamic capability? 5. What is the employee attitude towards relevant resources? 1.3 Research Objective 1. To investigate the relationship between performance Management and employee attitude 2. To investigate the employee attitude towards goal setting 3. To investigate the employee attitude towards Agency relations 4. To investigate the employee attitude towards Dynamic capability 5. To investigate the employee attitude towards Relevant resources 1.4 Problem Statement Many SME ¿Ã‚ ½s in Malaysia are facing numerous problems in the current business world which comprise of the information age, development of the technological factors at a rapid pace and globalisation are some examples, these changes are very rapid and highly unpredictable and the only department which manages this pressure is the HR department and the polices of the department which have equipped themselves to overcome these situations and volatile changes in the business environment and such policies include manpower planning performance plans and development performance plans and frequent appraisal of employees and performance guidance. Many organisations fail at this level which is a major concern, and the organisations which have overcome these obstacle have gone a long way bringing in many revolutionary changes in the business world and HR practices. (Becker et al., 2001; Zairi, 1998). 1.5 Significance of the study SME ¿Ã‚ ½s represent the major group of business organisations in Malaysia based on the Malaysia SME ¿Ã‚ ½s Report (2008) which contributes to a total of 99.2% , which in itself has its own significance and lays emphasis behind conducting this research study . The research paper also aims at establishing the relationship that exists between performance management practices and employee attitude. The purpose of this paper is to establish the relationship between performances 1.6 Research design and research context: The research philosophy which the researcher thinks is suitable is the positivist philosophy of research. The method used will be a survey method with questionnaires with both primary and secondary sources of data. This will include questionnaires, interviews and document analysis. The data analysis technique for the proposed research will be multiple regression analysis to find the relationship between the variables. In terms of the research context, the proposed research is based on Ahsan Ullah and Routray ¿Ã‚ ½s (2007) research employee attitude and performance management in Malaysian SME ¿Ã‚ ½s. The research will be carried in Malaysian SME ¿Ã‚ ½s. The reason for choosing Malaysian SME ¿Ã‚ ½s for this research purpose is largely due to their representation in Malaysian business as claimed by the Malaysian SME ¿Ã‚ ½s Report (2008). 1.7 Structure of Dissertation The dissertation is laid out in five chapters; the first chapter introduces the reader to the concept of Mutual funds and describes the aims and objectives of the study. The actual study begins from chapter two with Review of Literature analyzing the concept of mutual funds and assessing the previous research carried in analysing the mutual fund performance. The contents in the research report can be elaborated briefly as shown under the following headings. Chapter One: Introduction The first chapter of the research study as the name suggests the chapter introduces the study and the major area of focus in the research. The chapters clearly describe the aims and objectives of the study giving the reader glimpse about overall research. It also gives out the scope of the research and spells out the rationale behind the study. Chapter Two: Literature Review This chapter primarily prepares the study for empirical work by looking at evaluations and conclusions drawn on certain theories and concepts to check for similarities and difference made by past writers on similar or related studies. It ¿Ã‚ ½s on this basis, that later stages in the research are developed. In particular, academic journals, websites and textbooks that articulate models and related theories are used as a reference. Chapter Three: Research Methodology The Chapter three reviews a range of research methods and highlights the strength and weakness and also research design discussion. Chapter Four: Research Findings and Analysis Chapter four discusses the main research findings and provides critical evaluation of primary and secondary data ¿Ã‚ ½s about the leadership behaviors in the engineering organization. Chapter Five: Conclusions and Recommendations After careful examination, evaluation, assessment and analysis of data, in this chapter, the study points out how the aims and objectives of the research are met. It points out how the respective objectives are realized and tries to give an answer to the research question. 1.8 Limitations 1. The Research Study will be based only in Malaysian SME ¿Ã‚ ½s in Kuala Lumpur due to time constraint. 2. The research study will be cut short to just the evaluate the relationship between employee attitude and performance management 3. The research study will be carried out in Limited number of organisations only. 1.9 The Research Framework Adapted from James Kagaari (2010)

Friday, October 25, 2019

The Awakening :: essays research papers

The short novel, The Awakening, begins at a crisis in Edna Pontellier's life. Edna is a free-spirited and passionate woman who has a hard time finding means of communications and a real role as a wife and a mother. Edna finds herself desperately wanting her own emotional and sexual identities. During one summer while her husband, Leonce, is out of town on business, her frustration and need for emotional freedom leads to an affair with a younger man. Her search for identity and love leads her on a wild ride against society and tests her strengths to the end. The book raises issues about the role of women in society, not only in the time period in which it is set, but also in the modern world. Edna was truly brave in the way that she slowly began to defy society's conventions. She was never unfaithful to her husband because he had betrayed her by seeing her as an object. This contributed to her yearning for truth and freedom. Her husband was a well-meaning man, but Edna had no real trust in him. She felt empty with him and their children. Once Leonce was gone and Edna had been with Robert, she felt like she had found true and passionate love, but she had not. Robert was like Leonce. Robert speaks of her being "set free and given to her" and she realizes that Robert also viewed women as possessions. This was a trouble that she could not get away from. Robert loved her, but the way that he thought was still being controlled by the society and time that they lived in. Edna realizes that her loving and lusty relationship with R obert would still be repressed by the society that they were in. That is not what Edna wanted. She could not hold back her feelings and continue living the way that she was. Edna did not want to live a life that would have her lying to her children, and raising them would have been painful to her without truth. She felt that if she were to follow through with being with Robert, she would be taking away their expression and personal freedom. Edna was a very strong woman in the light that she did not want to give herself away. She strove to be an independent and self-sufficient individual. In the time period which Edna was in, women had few choices in the case of divorce, and men took the sole custody of their children.

Thursday, October 24, 2019

Band of Brothers by Stephen Ambrose

This book report is written in fulfillment of the requirements for (class subject e. g. Hist. 108) under Professor (professor’s name). Band of Brothers is a novel based on the events of World War II, emphasizing more on the lives of the soldiers, particularly the paratroopers of Easy company, 506 regiment of the 101st Airborne Division of the United States Army. Paratroopers are trained soldiers launched into battle by parachute into areas inaccessible by aerial bombing.Written by Stephen Ambrose and published by Simon and Schuster in 2001, Band of Brothers, has been an all time best seller which was made into a mini series by HBO in association with Dreamworks, edited by Billy Fox and directed by Phil Alden Robinson. Life in the military has always been a fascination of many young men. All the amazing weapons and gears that they use in battle, the handsome uniforms, not to mention the recognition and accolade that one can receive sounds like a promising career. A priceless ho nor which brings pride that lasts beyond your lifetime.If one decides to pursue a career in the armed forces, one must be ready to make all the adjustments and face the challenges, not only that of a rigorous training, but a life in the battle field. A soldier’s life, activity and relationships literally changes the moment training commences. The armed forces is a stratified society full of rigidity. A soldier has to understand the hierarchy and chain of command and must learn to obey first before complaining (not that one is allowed to complain). The inability to perform a particular duty, due to whatever reason, is inexcusable, therefore punishable. A soldier’s life is full of misconceptions.Civilians mostly view them as fortunate individuals who enjoy a lot of privileges both from the government and the private sector. Stephen Ambrose used a lot of characters to portray the lives of soldiers in Easy company. Captain Herbert M. Sobel was the commanding officer of Eas y company in the 2nd battalion 506th parachute infantry regiment of the 101st airborne division. He was very strict and usually rude, squeezing the energy of his soldiers during training. He doesn’t tolerate anything that he feels like not tolerating to the point of just simply finding errors on his soldiers just for the heck of it.Although disliked by most of his soldiers, his attitude towards training and his ways of implementing training schedule and activities helped in the honing of his soldiers’ skills and intelligence. In the mini series, David Schwimmer played the role of Captain Sobel. Lt. Richard D. Winters, played by actor Damian Lewis, was the second in command of Captain Sobel. Lt. Winters outdo Captain Sobel in the field. Although a Jew, he was respected and well-liked by the soldiers. Scott Grimes played the role of technical sergeant Donald Malarkey who was refused admission to the Marines due to dental issues.He also tried Army Air Corps, but due to ma th requirements, still he was not admitted. He only became a member of E company (Easy company) when he volunteered to be a part of the paratroops of the United States Army. He was awarded the Bronze star medal for his participation on D-Day’s Brecourt Manor Assault in Normandy. Captain Ronald Speirs was initially company D’s (Dog company) platoon leader. During the end of the Battle of the Bulge in Bastogne, Captain Speirs was reassigned to command Easy company. 2nd Lt. Clifford Carwood Lipton a. k. a Lip, joined E company in 1942.From Private he was promoted to company first sergeant, then to second lieutenant. Band of Brothers is a historical documentary novel telling the story of the lives and experiences of airborne soldiers during World War II. 1942 marked the year when the United States Army Airborne Division formed the second battalion of the 506th parachute infantry regiment in Toccoa, Georgia (Ambrose 2001). The story began in Toccoa, Georgia when the U. S. a rmy is preparing for battle against the Germans. Under the command and rigid training of Captain Herbert M.Sobel, the soldiers of E company endured rigorous and severe training. Their company was known to be the best in the regiment and Captain Sobel prided himself on that; and because of their reputation, they were always given the toughest assignments. E company trained for ninety days which included lectures, physical exercises, obstacle courses and field simulations after which, they were deployed to England on board a ship in preparation for the invasion of Hitler’s Third Reich. Their task is to penetrate enemy lines and subjugate German Artillery.On June 6, 1944 in Normandy, the soldiers had their first jump which did not go as planned. Due to heavy firing on the ground, planes carrying the paratroopers flew at high speeds with only a short distance from the ground (Ambrose 2001). One of the planes got hit, went on fire and crash to the ground. Nevertheless, the troop w as able to arrive at Carentan, gained control of the area then they flew back to Aldbourne. On September 17, 1944, the troops made their second jump in Holland which was executed perfectly. After completing their mission in the area, they also fought in the Battle of the Bulge.The paratroopers arrived in Germany on the second day of April, 1945 where the enemies finally surrendered. They celebrated their victory in Austria where they drank alcohol and took a lot of things from the Germans like jewelry and lugers. When the war was over, they parted ways and took different paths. As often as possible, a reunion is made in New Orleans where they all could catch up while remembering the years they spent at war. My impression on the book is positive. Stephen Ambrose was able to make World War II a more relatable event to ordinary people.He was able to show two perspectives of the story – officers’ point of view and the soldiers’ point of view. The story was able to s how that an army officer is not perfect. He might be very good at one thing, but he still has his flaws, like Captain Sobel who was very good at training men but performs poorly on the field. Soldiers are also human beings who feel fear, stress, anxiety and bleeds inside out; but the important thing is ones ability to endure whatever hardships that one has to face in carrying out his duty to the country and the people. They are always together and yet, they feel alone in the battle field.War means death, and these men had to psyche themselves up to be ready in all aspects – physically, emotionally, spiritually and mentally. Focusing on one particular battalion like Easy company, the author was able to present the lives of soldiers in the battlefield. Their ‘humanness’ were more felt and their bond as brothers in their cause was strongly established. However, Ambrose’s exposure of their ‘humanness’ can be a downside as this could lead to debate s and issues regarding the deployment of soldiers to war in support of allied nations under fire.But then again, the personal approach employed by Ambrose in writing the story made the events of World War II more relevant in the lives of people. Band of Brothers enabled us to understand, at a deeper level, the struggles and hardships that soldiers face. True, recognitions and accolades are given, but such can only be enjoyed by them if they are lucky to be alive. Bibliography Stephen Ambrose (2008). â€Å"Band of Brothers. † 123 Helpme. com. 04 January 2006. 05 January 2008. . Stephen E. Ambrose (2001). â€Å"Band of Brothers. † Simon and Schuters. ISBN: 0743216385 Band of Brothers by Stephen Ambrose Airborne Division of the United States Army was formed in Toccoa, Georgia. They were trained under Capt. Sorbel.. Members of the battalion voluntered for the job for the money, thrill, honor and to be the best among the ordinary infantry men. Because the Band of Brothers was narrated from the points of view of the soldiers of Company E or the Easy Company, the story is unique for the narration was so vivid that a reader would feel that he is there fighting with the band of brothers. Because of the physical requirements during the training only few made it to their graduation day.Here the story is significant for a soldier because the story is about the everyday life of a soldier in the boot camp and in the field—not a story about generals and admirals usually made by most movie companies. It tells a soldier that even how much he has suffered while training it doesn’t guarantee that he would survive in war. From Toccoa the company was sent to Fort Benning for their jumpi ng course. Their earlier training at the boot camp hardened them physically that they even outlasted the physical fitness trainers at the fort.This is the reality about soldiery. There are soldiers who are better than the trainers themselves. After only five jumps, ironically they were made as parachutists, and after nine months of training were sent to England on board a transport ship to prepare themselves for the invasion against the Third Reich of Hitler. The writer narrates the daily regimen of the company while in training in England. The narration was from the points of view from both the officers and men of the Easy Company.Both the movie and the book depict the confusion, heroism and struggle during the time the company jumped into the countryside where they were separated from each other. Many landed on buildings, trees, farm houses, fences, carts, houses, rafters and in the middle of enemies since they jumped behind enemy lines at dawn. There was chaos all around but many maintain their composure as hardened soldiers of Easy Company. Their job was to silence the German artillery and neutralize the enemy soldiers guarding the guns. They effectively put their hard training into practice.The highlight of the Band of Brothers is how Lt. Richard Winters achieved the mission. The book narrates: â€Å" By this time, about 0700, E company consisted of two light machine guns, one bazooka (no ammunition), one 60 mm†¦. † But with less than 100 men from the original 139 jumpers, Lt. Winters’s men were able to accomplish the mission. The mission was done without heroic deeds of a few. They fought as a team and with the right maneuvers attacked the German platoon guarding the battery emplacement. This is also about the best aspect on soldiery.As a soldier, you have also to protect not your life but also your brothers in arms. In this kind of situation, a soldier usually has to consider that everyone in his group as his brother. Why? Because the y shed blood and tears together or suffer pain together. They are blood brothers, so to speak. The book quotes one of the men: â€Å" We fought as a team†¦we were like machine†¦We knocked it out or made it withdraw by maneuver and teamwork†¦We were smart†¦we had learned that heroics was the way to get killed without getting the job done†¦.† Easy Company continued to fight in Normandy until it was pulled out and deployed to Utah beach. They were about 139 when they exited from the plane’s door. And ended the battle with only 79 remaining men. In the movie, you can feel the struggle of private Albert Blithe. He has to overcome fear, as every soldier has experienced fear. Winters, on his part, has suffered anguish after he shot a German teenage soldier. The company jumped into Holland under Operation: Market Garden and fought until November 1944.The company also heroically defended Bastogne almost to the last man. . In the movie, the German Army s ent couriers to relay offer the message of the German commander of Bastogne for them to surrender or perish. Winters made a succinct reply: â€Å"Nuts. † They held their trenches until reinforcements arrived. Then the men of Company E fought in the famous Battle of the Bulge, which marked the defeat of the German Panzer division. Winters’ men continued fighting and were the first to occupy Hitler’s mountain retreat known as the Eagle’s Nest.From Austria the battalion was redeployed to a town near Paris and on November 30, 1945, the 101st Airborne Battalion was deactivated. What’s the significance of the story to a plain infantry man? I can say that the Band of Brothers is one of the few stories written from the testimonies of actual combatants without fanfare or garnishment for use in movies. The book tells the story of leadership amid blood, guts and tears and about overcoming fear by soldiers and officers alike. It tells the credo of an American general who says â€Å" The more you sweat in peace and less you bleed in war. † But many die in war.

Wednesday, October 23, 2019

Hamlet Soliloquies and Their Analysis

HAMLET’S SOLILOQUIES & THEIR ANALYSIS In the course of the play, Hamlet has seven long soliloquies. The first of these occurs before he has seen the Ghost. In this soliloquy, Hamlet reveals the grief that has been gnawing at his mind. He wishes that religion did not forbid suicide so that he could kill himself and be rid of this grief. He feels disillusioned with the world. â€Å"How weary, stale, flat and unprofitable, Seem to me all the uses of this world†. He deplores (condemns) the fact that his mother should have remarried barely two months after the death of her first husband. This soliloquy shows Hamlet’s meditative nature. It also reveals his filial attachment to his dead father whom he speaks highly, and his scorn of his uncle to whom he refers in disparaging terms. His references to Hyperion, Niobe and Hercules show him to be well versed in classical literature. We also note his generalizing tendency when says: â€Å"Frailty thy name is woman;† Resolution to avenge his father’s murder. Hamlet’s second soliloquy comes just after the Ghost leaves him, after charging him with the duty of taking revenge upon the murderer of his father. Hamlet resolves to wipe out everything else from his memory and to remember only Ghost’s command. The manner in which Hamlet here speaks of never forgetting into action and carry out the behest (request) of the Ghost. The Ghost’s revelation has stunned him and he refers to his mother as â€Å"a most pernicious woman† and to his uncle as a â€Å"smiling damned villain†. We again note his generalizing tendency when he says that â€Å"one may smile, and smile, and be a villain†. Self reproach: In his third soliloquy, Hamlet bitterly scolds himself for having failed to execute his revenge so far, he calls himself â€Å"a dull and muddy mettled rascal† for his failure, accusing himself of being â€Å"pigeon livered†, an ass who â€Å" like a whore† can only unpack his heart with words and â€Å"And fall a-cursing, like a very drab†. He refers to his uncle as a â€Å"bloody bawdy villain; remorseless, treacherous, lecherous, kindles illain†. He then dwells upon his plan to stage a play (The Mouse Trap), saying: â€Å"the the play ‘s the thing Wherein I'll catch the conscience of the king† In other words, Hamlet now seeks a confirmation of the Ghost’s charge against Claudius. This is rather strange, because it has taken him long to doubt the authenticity of the Ghost’s version. It is obv ious that Hamlet is more a philosopher and less a man of action. On the Horns of Dilemma. Hamlet fourth soliloquy, his most famous and most celebrated, is the most philosophical of all. To be, or not to be: that is the question†. Hamlet asks himself whether it is noble to suffer the cruelties of fate silently or to put up a fight against the misfortunes of life. It would be better perhaps â€Å"to commit suicide† if death were to mean a total extinction of consciousness. But the fear of what may happen to us after death, make us endure the ills and injustices of life. This soliloquy, more than any other reveals the speculative temperament of Hamlet, his irresolute and wavering mind, and his incapacity for any premeditated action of a momentous nature. His catalogue of the misfortunes of life once again shows his generalizing habit of thought. This soliloquy partly explains Hamlet’s delay in carrying out his purpose, and shows at the same time the mental torture that he has been undergoing because of that delay. We here see a sensitive, reflective person compelled to face situation with which he unable to cope. Decision to â€Å"speak daggers† to his motherIn his fifth soliloquy, Hamlet describes his mood as one in which he could â€Å"drink hot blood, an do such bitter business as the day would quake to look on†. In this mood he can even kill his mother, but he would not follow Nero’s example: â€Å"Let me be cruel, not unnatural†. He therefore decides to â€Å"speak daggers† to his mother but use none. We can well realize Hamlet’s story resentment against his mother but we also know that the man who has not been able to kill his uncle will be incapable of killing his mother because, apart the fact of her marriage, she has done nothing to deserve that punishment. Evading the responsibility. Hamlet’s sixth soliloquy shows him shrinking from an act for which he has long been preparing and for which he now gets an excellent opportunity. Hamlet’s reason for not killing his uncle at this moment is that the uncle is at prayers and that by killing him at such a time Hamlet would be sending him straight to heaven. Hamlet decides to wait for an opportunity when his uncle is â€Å"drink asleep, or in his rage, or in the incestuous pleasure of his bed, at gaming, swearing, or about some act that has no relish of salvation in it†. Obviously, Hamlet is evading a responsibility which he has fully accepted. His reasoning here is nothing but a piece of casuistry (misleadingly subtle reasoning). Thus Hamlet’s tendency to procrastination is further emphasized in this soliloquy Self Reproach Again. Hamlet’s last soliloquy is again full of self reproach: â€Å"How all occasions do inform against me, And spur my dull revenge! † Three part of his failure, he says are due to cowardice, and only one part due to wisdom. It is to be deplored (condemned) that he only lives yet to say: â€Å"This thing’s to do (meaning his purpose is yet to be accomplished). A man is no better than a beast, if he is content with feeding and sleeping. Hamlet’s dilatoriness is due to â€Å"bestial oblivions†, or to â€Å"some craven (cowardly) scruple (hesitation) of thinking too precisely on the event†. Having rebuke himself in strong terms, Hamlet forms the following resolve: â€Å"O, from this time forth, My thoughts be bloody, or be nothing worth! † This soliloquy, once again emphasizes Hamlet’s irresolution and his meditative temperament. His conscience keeps pricking him and urging him to revenge, but a natural deficiency always obstructs him. His generalizing and universalizing tendency too is seen here once again † What is a man, If his chief good and market of his time Be but to sleep and feed? a beast, no more. † The idea of delay emphasized by the soliloquies. Hamlet’s soliloquies are foremost in bringing the idea of his delay to our notice. The stress on delay shows also Hamlet’s preoccupation with his role. His life is one to be lived under the imposition (burden) of a great task which he seems unable to fulfill. Excessively speculative, irresolute, scholarly poetic. The soliloquies of Hamlet undoubtedly throw a flood of light on his character and personality. A soliloquy is a device by which Shakespeare reveals to us the inner working of a character’s mind, the secret thoughts and cogitations (meditations) of a character’s mind, the deepest recess of a character’s soul. Hamlet’s soliloquies surely serve that purpose. These soliloquies not only reveal that Hamlet is given to excessive speculations and that he is therefore unfit to carry out the task assigned to him, but also unable to understand his reasons for delaying his revenge. Furthermore, these soliloquies show Hamlet's poetic eloquence. Each soliloquy by him is a masterpiece, not only as regards its philosophic content but also as regards its style and expression. They show Hamlet to be a scholar, a philosopher, and a poet. . Nothing about his relations with Ophelia in these soliloquies. Introspective as he is, Hamlet is constantly analyzing himself inwardly. He is for even looking into himself, delving into his own nature, to seek an explanation' for this or for that, and giving vent to his dissatisfaction, discontent, or frustration. In one important respect, however, these soliloquies do not express Hamlet's mind. In none of these soliloquies does he speak of his feelings or thoughts about Ophelia. While he speaks a good deal about his uncle and, his mother, he says nothing about Ophelia. The result is that so far as his relations with Ophelia arc concerned, we have to depend only on external evidence. Three powers of the soul dramatized. According to one critic, the first six soliloquies of Hamlet' dramatize the three powers of the soul – namely , memory; understanding, and will – and show how his memory and understanding are opposed to his will, while the seventh soliloquy is concerned with all three powers of the soul though-â€Å"the battle in Hamlet's mind is never decided at a conscious level. Over-analysis of motives. The soliloquies of Hamlet deepen Hamlet's tragic character by portraying him as a â€Å"thinking† man. His excessive introspection checks action by too curious a consideration of the need and justice of . the action contemplated. The soliloquies contain an over-analysis  ·of the motives of the action that is required of him. His mind weighs all that may conceivably be said for and against the course proposed.

Tuesday, October 22, 2019

Mourning Colonialism and Globalization Essay

Mourning Colonialism and Globalization Essay Mourning: Colonialism and Globalization Essay Globalization – Chapter 5 Notes Historical Globalization Chapter Issue: To what extent did early globalization affect peoples of the world? How did Globalization Begin? There are many different ideas about when globalization began: 1. 325 BCE – Buddhist leader Chandragupta Maurya combined religion, trade and military to create a vast trade empire in India 2. 1100’s when Ghengis Khan introduced the idea of fighting from horseback, which allowed him to create an empire stretching from the Adriatic Sea to China. 3. 1492 – when Columbus made his first trip to the Americas 4. 1800’s – when low-cost goods from farms and factories poured into markets around the world and access increased to these goods. One theory suggests that globalization evolved in three distinct rounds: a. First Round – Goods and ideas were exchanged along ancient trade routes. Knowledge of Indian science, medicine, literature and mathematics were introduced to Europe b. Second Round - grew out of the first round and began in the late 1400’s. Europeans developed new technology that allowed them to travel farther, allowing Imperialism to take place. c. Third Round – we are now in this phase. It began after World War II. A time of rapid growth and nearly instant communication. No matter the timeline you agree with, it is unarguable that globalization exists. Here are some reasons why: 1. Early Trade Routes As early as the third century a trade route existed from China through the Byzantium Empire (now the middle east) called the Silk Road (because of the beautiful cloth made in China from silkworms). Goods as well as ideas like the Indo-Arabic number system were passed from culture to culture along this road. 2. Books The printed word spread ideas about science, religion, politics and philosophy across Europe. 3. Rise of the Middle Class Historically society was organized into classes, determined by birth, social power was based on how much land you owned and the economy was based on the Landlord / peasant relationship. As cities were growing, trades people, entrepreneurs, artists, scholars, etc†¦ were attracted to the area, accumulating more wealth from developing their skill. This rise in wealth and social status created a new middle class. As they grew larger and more influential, trade became even more important to their profits, and accumulation of material goods. New ideas emerged and then technologies that helped lay the foundations of historical globalization. 3. Innovations like the large, square sail and gunpowder influenced how travel, trade, exploration, and conquest were conducted, therefore aiding in globalization. 4. Trade Competition for trade between colonial empires was increasing. Countries were racing to colonize other nations in order to obtain their raw materials for use in their own factories back home. This is also known as imperialism. Mercantilism – the strict controlling of trade between the mother country and the colony did help to increase globalization due to new goods being imported into other countries. When mercantilism started to disband due to rebellions etc†¦ globalization of goods was expanded even more. Cultural Imperialism – non-violent form of imperialism, in which one country imposes its values and beliefs on another. Due to (mainly European) colonization, the Indigenous peoples were forced off their land, disrupting their way of life and often other groups’ ways of life as they encroached on new territory. They also faced new types of disease, which could be argued, wiped out extreme numbers of their populations, they were enslaved by the colonizers, forced out of their traditional territories and some were forced

Monday, October 21, 2019

Idioms Phrasal Verbs in English Business Writing [common mistakes]

Idioms Phrasal Verbs in English Business Writing [common mistakes] As businesses become more international, so must our writing. Most of the time, good business writing skills transfer very well to global audiences, but there are some confusing verbs that global business writers should try to avoid. These are called phrasal verbs. First, let’s take a look at the different types of verbs. There are two main types of verbs: Action verbs, such as run, jump, talk, negotiate, etc. Stative verbs, such as be, have, like, love, etc. (We don’t really â€Å"do† these verbs. They are more descriptive verbs than doing verbs.) As I’m sure you can guess, there are far more action verbs that stative verbs, and there are a lot that are particular to business. You can find a great list of business related action verbs here from Pepperdine University: Now that we have reviewed some background information on verbs, what exactly is a phrasal verb? A phrasal verb is phrase made up of a verb and a preposition that means something other than what the two words mean independently. If we made this into a formula, it would look like this: verb + preposition = new meaning Phrasal verbs are common in English, but they are difficult for global audiences. They are often concidered idioms. You cannot deduce the meaning based on the two words alone, they can be difficult to find in a dictionary, and they are different from one English speaking country to another. (Ever notice that the British call to-go food â€Å"take away† while in the U.S. it’s called â€Å"take out?†) Let’s take a look at a couple of examples, and the synonymous one-word verbs you could use instead: The markets are blowing up right now. In this example, no one is literally blowing air up into the sky, so this could be hard to decode. Instead, say: The markets are exploding right now. The use of the synonymous one-word verb exploding makes the sentence accessible for all readers, not just those who speak a particular variety of English. hbspt.cta._relativeUrls=true;hbspt.cta.load(41482, 'bf4ee473-8e6b-46bf-b9e3-368d74d60b44', {}); Here’s another example: We need to look into that option. In this example, we are not literally looking into a box or the refrigerator, so this also could be hard to understand. Instead, we should say: We need to research that option. In both examples, there is a one-word verb that means the same thing as the phrasal verb. When writing for a global audience, it is always better to use the synonymous one word verb because it is easier to understand and far easier to look up if your reader doesn’t understand it. If you enjoyed this article, you may also enjoy our full list of business writing tips. For readers looking to improve their English business writing skills we offer a full business writingcourse for non-native speakers.

Sunday, October 20, 2019

How to Become President of the United States

How to Become President of the United States With the primary election coming to an end, only two candidates (if you’re not counting the independent candidates) will remain. While that seems simple enough, the path to becoming the President of the United States can be rather confusing and difficult to understand. After all, our system involves us voting for who we want as our leader, but we technically vote for representatives who then vote for the person we want as our leader, in which the representatives don’t always abide by the wishes of the voter. Make sense? No? Yeah, it’s pretty  convoluted but to make things easier to digest, we’ve compiled a very short and basic infographic on what it takes to become the President of the United States.

Saturday, October 19, 2019

(power relations) in Greco-Roman myth Essay Example | Topics and Well Written Essays - 1250 words

(power relations) in Greco-Roman myth - Essay Example This is again reflective of issues we continue to deal with today. By analyzing these issues within the plays of the ancients, such as the power struggle women fought against the exercise of power men had over them, it may be possible to learn something about how we deal with these issues now. One shining example of this exploration into power struggles can be found in Sophocles’ play Antigone. This play tells the story of one of Oedipus’ daughters, Antigone. It opens just after her two brothers have killed each other in a battle to see who would be king of Thebes, one having held the throne for the past year and the other marching on the city to enforce an earlier agreement regarding who will rule Thebes for the following year. While one brother is given a lavish and honorable burial, the other is ordered to be left rotting in the sun under punishment of law. Even though both brothers had reasonable claims, King Creon only acknowledges the letter of the law in the case, foreshadowing the trouble to come. Antigone, however, feels both brothers were wrong and both should be given the god-ordered rites of burial. Completely defying the law as set forth by Creon, and thus rejecting the power he is supposed to have over her, Antigone chooses to act instead in ke eping with her deep-seated and widely accepted religious beliefs that dictate all bodies should be buried. The trouble with trying to determine which character, Creon or Antigone, should have the right of power is made difficult by the very real and present flaws found within Antigone herself. She enters the first scene already raging regarding Creon’s decree and his nerve in believing he has any power over her. She is seen as bold, rash and passionately incapable of tempering her behavior, thus reinforcing the then-prevailing belief that women needed the steady guidance of men to

Friday, October 18, 2019

An Examination of Means of Application and Core Function in Predicting Assignment

An Examination of Means of Application and Core Function in Predicting Crime - Assignment Example Using the example of the New York City Police Department, given in the prompt for this essay, one understands that the key inputs that the police department interfaces with in regards to building the outputs and feedbacks that are generated is made available through a weekly process of data input. In this way, personnel from New York City Police Department’s precincts, service areas, and transit districts compile a statistical summary or overview of the week’s crime data. In this way, crime patterns, arrests, complaints, and other verifiable and measurable data of significance are collated and entered into a database. This process represents the input phase, or data gathering phase that forms the very backbone of the process of CompStat. It is important to note that this process itself is the most important as it is the only stage in the process where human inputs can directly affect and oftentimes skew the results that are reported. For this reason, an individual depar tment has been set up within the Chief of Police’s office; labeled as the CompStat Unit. As such, the unit is directly responsible for winnowing, sorting, and inputting in the correct fashion, any and all pertinent information that could be of use with reference to developing a type of predictive policing to ultimately reduce the level of crime displayed within the city’s regions and precincts. ... For this reason, an individual department has been set up within the Chief of Police’s office; labeled as the CompStat Unit (Willis et al 2012). As such, the unit is directly responsible for winnowing, sorting, and inputting in the correct fashion, any and all pertinent information that could be of use with reference to developing a type of predictive policing to ultimately reduce the level of crime displayed within the city’s regions and precincts. Once the inputs have been entered into the system, the second phase of analysis then takes place; that of processing of the determinant data. This stage is reliant not upon the level of analysis that individual humans would otherwise perform; rather, it is entirely dependent upon the algorithms and likelihood matrixes that CompStat itself can infer from the inputs it has been given. As with the old cliche with regards to a computer program only being as good as the programmers that programmed the code, the same is true with relation to CompStat as it is but a tool and should not be seen as a perfect representation truth or overall infallibility. As has been stated with the input stage that has previously been discussed, the processing of the data and the outputs that it ultimately yield is solely reliant on the quality and voracity of the information that is loaded into the system. In other words, only a quality level of inputs will be processed and related into a quality level of outputs from which a degree of reasonable and actionable inference could foreseeably be drawn. The heart of the CompStat process therefore relies on each step of the process; however, for purposes of evaluation, the third step, or the outputs, is of perhaps the most interest. Within this step, a team of

Clever Marketing for Luxury Goods in the Fashion Industry Essay

Clever Marketing for Luxury Goods in the Fashion Industry - Essay Example The essay "Clever Marketing for Luxury Goods in the Fashion Industry" concerns the clever fashion marketing. It first looked into the number of years that the number of years by which the latter are working as members of the marketing industry within the luxury fashion industry. Seven respondents (11.7%) reported to have been in the luxury fashion industry for less than five years. Meanwhile, twenty two (36.7%) said that they have been employed by the said industry for five to six years. In the same manner, fifteen (25.0%) noted to have been working in such for seven to ten years. Finally, sixteen (26.7%) said that they are within the luxury fashion industry for more than ten years. Aside from determining the number of years that the respondents have stayed within the luxury fashion industry, the researcher also determined which among of the three groups being studied are they a member of. Since this research is aimed towards ensuring the proper representation of the three groups, tw enty respondents (33.3%) were obtained from each. These results are graphically presented in Table 2. As established in the previous chapters of this study, the era wherein fashion was characterized as super exclusive and could only be afforded by the elite has ended (Agins, 2000). In fact, designers are now taking their cues from consumers from the mainstream and creativity has been channeled to the mass-marketing clothes. As a result, members of the industry were seen to have joined financial groups.

Keyword Critique Research Paper Example | Topics and Well Written Essays - 1750 words

Keyword Critique - Research Paper Example In sociology, persons are normally classified into groups according to their socio-economic conditions. Social stratification tries to understand political, social, ideological, cultural, and economic dimensions of social inequality. However, stratification is not homogenous concepts. It is by definition has multiple meanings and the meanings changes when placed against different contexts and different actors. In sociology, the use of the term stratification has changed from time to time. It even substantially changes in terms of meaning and practice in different schools such as Marxism, functionalism and structuralism. II. The Conceptualization of Stratification When someone tries to find answer of poverty in any society the concept of stratification becomes important. If we try to locate reasons behind the backwardness of Black people or women vis-a-vis White people or we try to gauge chances of a child born into working class family to climb the social ladder, we will lend into ou rselves into the study of social stratification. The methodological analysis of stratification seeks ‘to discover social gulfs- to find the gaps in people’s social relations and experience- which might explain the fissures in people’s perception of each other. ... Max Weber has tried to elaborate the concept of social stratification wherein he studies stratification in traditional societies or we could call them status-based societies and of modern societies. According to him in traditional societies, person’s social status was depended upon his ascribed status wherein a person possesses qualities, which are beyond his control like sex, class at birth ethnicity, race, caste, or religion. Whereas in modern society element of achievement or personal qualities defines persons social status. Max Weber has made distinction between social class, which is defined according to material wealth, and status class, which depends upon social honor, prestige and links to the religious institutions. Studies of social stratification try to understand at what extends class or status system affects modes of social action. It analyses class and status structures and its reproduction in the society. Social stratification tries to understand how inequality of condition and opportunities affects outcome and what are the methods used by groups to protect their class or status boundaries. In simple word, how people maintain their class privileges and how other sections try to get access to it, these are the issues which get importance in the study of social stratification. Social stratification investigates various ways through which class, status-groups are formed in the society, and through it sociologist understand the society. While fiercely criticising the empirical sociology dominated in the United States, Anderson and Massey points out that â€Å"as the status attainment model came to dominate American sociology, the study of stratification became progressively despatialized. Socio-economic outcomes were conceptualized as individual-level

Thursday, October 17, 2019

UK Construction Industry Essay Example | Topics and Well Written Essays - 1250 words

UK Construction Industry - Essay Example Currently, this industry is faced with a shortage of skills as well as safety and health issues. The relationship between contractors and clients, together with the supply chains are very complex. Additionally, a number of firms are moving towards a modern manufacturing approach but others are still traditional. Among the main factors driving the construction sector is the government's Public Private Partnership (PPP) for main infrastructure projects. Private Finance Initiatives (PFI) have also been widely adopted. These projects include prisons, schools, and hospitals. The private sector then takes responsibility in running these projects. PPP and PFI have brought in the discipline of private sector management, ownership and financing. This has greatly improved efficiency and value in the public sector. There is an acute shortage of houses particularly in South East of England. It requires a big infrastructure and housing projects emphasising on brown field sites and high density houses. The UK construction industry will continue to grow. Its output is expected to rise to about 12.7 per cent by 2010. The construction industry in the UK is growing very fast. Experts expect construction to shift from the North to the South and East. This is driven by the strong growth in the housing sector including 36 billion pounds of big projects. East London is expected to undergo a high employment rate at about 18.6 per cent by 2010. London's will be 11 per cent while the South East will be at 14 per cent (Weaver, 2002). Growth in the North is expected to be slower. Construction employment in the North West is estimated to grow by 5 per cent from 2006 to 2010, Scotland by eight per cent, Humberside by six per cent, Yorkshire and Humberside by six per cent and the North East by 6 per cent. Northern Ireland and Wales will also experience strong growth. The construction sector employment in Wales is expected to increase by 12 per cent. This is attributed to the 3.2 billion pound Welsh Quality Standards Scheme. Northern Ireland's 13 per cent growth is associated mainly with the public investment programme planned for the next ten years. Generally, the future of the construction industry in the UK is expected to show the following characteristics: Private output growth will exceed publicly funded construction programmes Public housing is expected to experience the biggest growth since private and government housing developers will seek deliverance of affordable and key worker housing, specifically in the South East and London. The commercial sector is also expected to grow due to the continued recovery for offices market and also further increases in PPP/PFI education and health projects. Infrastructure output is expected surpass the industry average. This will be due to projects like widening of M1 and M25 among other projects. The problems The construction industry in the UK is currently faced with many problems. These problems are threatening to lead this industry into a crisis. Meeting the industry Challenges In spite of its drawbacks, the UK construction sector experiencing increased demand and growth. This offers good employment opportunities. However, the rapidly changing environment has placed a lot of challenges in its bid to deliver new developments. Skills Shortage The construction industry has forecasted that 348,000 more workers will be required by 2010 to

The Main Features and Problems Faced by Service organisations In Essay

The Main Features and Problems Faced by Service organisations In pursuing this Technique(Banks in the UK) - Essay Example More than 74% of the United States work force for example is employed on this sector (Li H. & Smith L.2001).With a dramatic fall in labour cost, the cost of processing information, overheads has become far more important in the present age of advanced manufacturing technology (AMT) with direct labour representing 5%. Thus, it therefore now appears difficult to justify the use of direct labour or direct material as the basis for absorbing overheads.ABC was developed to overcome some of the major problems of the traditional cost accounting. The 80s witnessed an influx of research in to this concept. Activity based costing involves the identification of the factors which cause the costs of an organisations major activities (Lewis; J.R., 1993). In this regard overhead are charged on the basis of their usage of factor causing the overhead. In the UK and the US, information and manufacturing technology are widely used in both manufacturing and the service sector, with both sectors experiencing different degree of the usage (Palmer, A.2000). The four main characteristics inherent to services provide an answer to the main problem of ABC in the service industry. ... There is a strong possibility that the same enquiry would be answered slightly differently by different people. 1.2 Activity based costing and the service industry in the UK (Banking Sector). By the end of the 1980s, ABC became the focal point within the realms of academic researchers, consultants and managers as a means of overcoming the disadvantages of traditional cost allocation methods. Cost accounting was limited to it s usage of one volume sensitive driver (Cooper & Kaplan 1991). By 1990 initial followers of ABC in the manufacturing sector were able to reduce cost, identify opportunities for improvement and determine a more profitable product mix (Cooper & Kaplan 1991). Thus, the concept gradually gain grounds and became popular in the manufacturing sector. In the service sector, the adoption of ABC has been relatively slow, and the concept was rarely used apart from the health and banking sector. A recent study however, by Schultz & Rostocki (2004) concluded that, the rate of adoption of ABC in service and manufacturing industry was now similar. An essential part of managing and ensuring the long term competitiveness of banking institutions in the United Kingdom will be to configure, manage the service deliveries and their chain of distribution processes. The financial sector in the UK, like in any other country is characterised with the following characteristic Banking institutions and other financial houses are price takers. This is so because the prevailing market price has to be accepted. Large number of institutions offering the same services with none of these institutions being able to influence price. However, their actions are not negligible. As a move by institution A will trigger a whole chain of event, in the form of competitive service

Wednesday, October 16, 2019

UK Construction Industry Essay Example | Topics and Well Written Essays - 1250 words

UK Construction Industry - Essay Example Currently, this industry is faced with a shortage of skills as well as safety and health issues. The relationship between contractors and clients, together with the supply chains are very complex. Additionally, a number of firms are moving towards a modern manufacturing approach but others are still traditional. Among the main factors driving the construction sector is the government's Public Private Partnership (PPP) for main infrastructure projects. Private Finance Initiatives (PFI) have also been widely adopted. These projects include prisons, schools, and hospitals. The private sector then takes responsibility in running these projects. PPP and PFI have brought in the discipline of private sector management, ownership and financing. This has greatly improved efficiency and value in the public sector. There is an acute shortage of houses particularly in South East of England. It requires a big infrastructure and housing projects emphasising on brown field sites and high density houses. The UK construction industry will continue to grow. Its output is expected to rise to about 12.7 per cent by 2010. The construction industry in the UK is growing very fast. Experts expect construction to shift from the North to the South and East. This is driven by the strong growth in the housing sector including 36 billion pounds of big projects. East London is expected to undergo a high employment rate at about 18.6 per cent by 2010. London's will be 11 per cent while the South East will be at 14 per cent (Weaver, 2002). Growth in the North is expected to be slower. Construction employment in the North West is estimated to grow by 5 per cent from 2006 to 2010, Scotland by eight per cent, Humberside by six per cent, Yorkshire and Humberside by six per cent and the North East by 6 per cent. Northern Ireland and Wales will also experience strong growth. The construction sector employment in Wales is expected to increase by 12 per cent. This is attributed to the 3.2 billion pound Welsh Quality Standards Scheme. Northern Ireland's 13 per cent growth is associated mainly with the public investment programme planned for the next ten years. Generally, the future of the construction industry in the UK is expected to show the following characteristics: Private output growth will exceed publicly funded construction programmes Public housing is expected to experience the biggest growth since private and government housing developers will seek deliverance of affordable and key worker housing, specifically in the South East and London. The commercial sector is also expected to grow due to the continued recovery for offices market and also further increases in PPP/PFI education and health projects. Infrastructure output is expected surpass the industry average. This will be due to projects like widening of M1 and M25 among other projects. The problems The construction industry in the UK is currently faced with many problems. These problems are threatening to lead this industry into a crisis. Meeting the industry Challenges In spite of its drawbacks, the UK construction sector experiencing increased demand and growth. This offers good employment opportunities. However, the rapidly changing environment has placed a lot of challenges in its bid to deliver new developments. Skills Shortage The construction industry has forecasted that 348,000 more workers will be required by 2010 to

Tuesday, October 15, 2019

What are the most important factors that contribute to job Research Paper

What are the most important factors that contribute to job satisfaction What are challenges to improving job satisfaction - Research Paper Example In pursue of career our dreams and aspirations are one thing and practicalities are another. If an employee can have both – that is a treasure job to pursue. However, often times the two does not go together. Yet, it is possible to be getting job satisfaction even doing menial tasks. It can be greatly influenced by a variety of factors. Work plays a significant role in our lives. In our quest to be happy and productive, having a strong sense of job satisfaction is important. When you are dissatisfied with your job, this tends to have an influence on your overall outlook on life. While you may not be in the career of your dreams right now, it is still your responsibility to make sure that what you are doing is satisfying to you.( †Creating Job Satisfaction. Getting the most from your job.†) Why is it important anyway? What difference does it make if one is satisfied with his job or not? There are many answers, yet one thing is sure – when stress mounts, job s atisfaction lowers, which leads to more stress and then it becomes a vicious circle. But, fortunately, there is a way to break that routine. The first thing to evaluate is an attitude employee has for his job. He might see his job as a carrier, or a job or, perhaps, a calling. If the job is only a way to get money, the employee would be moderately satisfied receiving his monthly salary for a fair number of tasks completed. If it is a carrier the employee pursues, he will be looking for position advancement and will be working harder to get it; and if it is a calling – the employee will work passionately, finding a sense in the fulfilling of the job itself. There are not so many people, though, who would not want to advance in their job at least in some way. For some of them it would only be important to grow in their skills and performance, others would prefer additional knowledge and growth in hierarchy. In either case, advancement is one key element in job satisfaction. Of course, it is not possible for all the workers to be completely satisfied with their job all the time and increasing job satisfaction is a challenge faced by managers. There is no across the board solution to the problem that would work well for everybody, since each company is different and must find their own unique and efficient way. But let’s take a look at different factors that contribute to job satisfaction. Besides personal motivation for the job, another factor in employee being more satisfied is positive working environment. According to Fran Tarkenton â€Å"you  have to find what turns people on† then you will know how to motivate them. Motivating working environment means caring for the needs of workers. That includes benefits for the workers, such as health care, childcare etc, as well as retirement benefits rising with the experience and age of the employee. Also, it really stiffens people’s productivity and satisfaction when they have many cumbe rsome and difficult policies and rules. Working place set-up and its comfort has a positive effect on workers’ job satisfaction, so it has to be considered how comfortable and ergonomic desks and chairs are and if there is a proper lighting etc. Another challenge is personal recognition and financial compensation for the job. All the employees have a need for recognition in some ways. While receiving salary is something the employee expects, his skills being noticed, or achievements, or personality etc, is something that comes as a bonus, and, though often it is not tangible, it can significantly improve employee’s self-esteem and job satisfaction. Simple acts, like a greeting, a pat on the back, approving smile etc, do wonders. Yet, though it is simple, it

Monday, October 14, 2019

History of Mathematics Teaching in the National Curriculum

History of Mathematics Teaching in the National Curriculum This research paper is to discuss about the nature and history of mathematics, how it has taken its place within the National Curriculum; the framework for teaching Mathematics in Secondary and finally investigation on a series of three lessons designed for Year 7 on Algebra. INTRODUCTION Education has made a difference in my life, the knowledge I have gained has given me the potential to explore, think and make decisions accordingly. In other words, Education is a powerful tool and plays a vital role to shape up a strong economy of a country. As a Mathematics teacher, I clearly understand my key role in imparting knowledge and skills to the younger generation to make full use of their potential. The perception of mathematics has been changed over the years. Hence, it is important to look back at the nature of mathematics, how it has taken its place within the national curriculum; how the teaching and learning of mathematics has been guided by the National Strategies Framework. LITERATURE REVIEW Nature of Mathematics Even though mathematics is one of the many subjects in schools, there is a greater pressure on pupils to succeed in Mathematics other than subjects like History, Geography; why is that so? As part of my investigation into the nature of Mathematics I referred to two sources that gave substantial evidence towards the nature of Mathematics. The Enquiry Committee: A Major Enquiry Committee was set up in 1978 to consider the teaching of Mathematics in Primary and Secondary schools. After 4 years of study and research the committee came out with a report called The Cockcroft Report. It would be very difficult perhaps impossible to live a normal life in very many parts of the world in the twentieth century without making use of mathematics of some kind. (The Cockcroft Report (1982), Mathematics counts) This fact itself for a thought is sufficient to reason out the purpose of importance given in teaching and learning mathematics in Schools. The usefulness of Mathematics can be perceived in different ways; as arithmetic skills needed to use at Home and Office, as basis for development of Science and Technology and usage of Mathematical techniques as management tool in commerce and industry. Therefore, the Enquiry Committee in their report (The Cockcroft Report) concluded that all the perceptions on usefulness of mathematics arise from the fact that mathematics provides a mean of communication which is powerful, concise and unambiguous. Hence, providing a principal reason for teaching mathematics at all stages in the curriculum. According to American Association for the Advancement of Science (AAAS), mathematics is closely related to Science, Technology and being greatly used in real life. The association has launched a program called Project 2061 where they relate mathematics into Science and Technology. Project 2061 is an ongoing project that was launched in 1985 in America, where its main objective is to help all Americans to literate in Science, Mathematics and Technology. As part of the project, it has been clearly defined that mathematics does play an important role in developing Science and Technology in real life. Besides communication, Mathematics can be used to present information by using charts, graphs and diagrams. As what AAAS has mentioned about the Mathematical representation, manipulation and derivation of information based on a mathematical relationship formed; the enquiry committee as well does mention in its report the usage of figures and symbols in mathematics for manipulation and to deduce further information from the situation the mathematics relate to. They gave 3 scenarios; A car that has travelled for 3 hours at an average speed of 20 miles per hour; we can deduce that it has covered a distance of 60 miles. To find the cost of 20 articles each costing 3p, the area of carpet required to cover a corridor 20 metres long and 3 metres wide In the 3 scenarios, we made use of the fact that: 20 x 3 = 60; hence it provides an illustration of the fact that the same mathematical statement can arise from and represent many different situations. This fact has important consequences. Because the same mathematical statement can relate to more than one situation, results which have been obtained in solving a problem arising from one situation can often be seen to apply to a different situation. Thus this characteristic of Mathematics does show its importance in the study of science and Technology as mentioned by both the Enquiry committee and the programme Project 2061 (AAAS). History of Mathematics By looking at the history of Mathematics; it has been further proven how the development of mathematics had impact on development of Science and Technology. The 17th century saw an unprecedented explosion of mathematical and scientific ideas across Europe. Galileo, an Italian, observed the moons of Jupiter in orbit about that planet, using a telescope based on a toy imported from Holland. Tycho Brahe, a Dane, had gathered an enormous quantity of mathematical data describing the positions of the planets in the sky. His student, Johannes Kepler, a German, began to work with this data. In part because he wanted to help Kepler in his calculations, John Napier, in Scotland, was the first to investigate natural logarithms. Kepler succeeded in formulating mathematical laws of planetary motion. This explains the relationship between mathematics and science or another word, how knowledge of mathematics has been used to develop science over the years. The 19th century saw the beginning of a great deal of abstract algebra. Hermann Grassmann in Germany gave a first version of vector spaces, the British mathematician George Boole devised an algebra that soon evolved into what is now called Boolean algebra, in which the only numbers were 0 and 1 and in which, famously, 1  +  1  =  1. Boolean algebra is the starting point of mathematical logic and has important applications in computer science. Abel and Galoiss investigations into the solutions of various polynomial equations laid the groundwork for further developments of group theory, and the associated fields of abstract algebra. In the 20th century physicists and other scientists have seen group theory as the ideal way to study symmetry. The 20th century saw mathematics become a major profession. Every year, thousands of new Ph.D.s in mathematics was awarded, and jobs are available in both teaching and industry. Therefore, from the 20th Century is where importance has been given to teaching of mathematics. National Curriculum of Mathematics This further explains how the national curriculum for Mathematics has been formed in Britain. Lets look at the various views of Mathematics usage in Industry before the Enquiry Committee was set up; From 1973 to 1976 there were a large volume of complaints which seemed to be coming from employers about lack of mathematical competence on the part of some school leavers; In his speech made at Ruskin College, Oxford in October 1976, Mr James Callaghan, at that time Prime Minister, said: I am concerned on my journeys to find complaints from industry that new recruits from the schools sometimes do not have the basic tools to do the job that is required. There is concern about the standards of numeracy of school leavers. Is there not a case for a professional review of the mathematics needed by industry at different levels? To what extent are these deficiencies the result of insufficient coordination between schools and industry? Indeed how much of the criticism about basic skills and attitudes is due to industrys own shortcomings rather than to the educational system? (The Cockcroft Report (1982) In written evidence to the Parliamentary Expenditure Committee, the Confederation of British Industry (CBI) stated: Employers are becoming increasingly concerned that many school leavers, particularly those leaving at the statutory age have not acquired a minimum acceptable standard in the fundamental skills involved in reading, writing, arithmetic and communication. This shows up in the results of nearly every educational enquiry made amongst the CBI membership, and is backed up by continuing evidence from training officers in industry and further education lecturers that young people at 16+ cannot pass simple tests in mathematics and require remedial tuition before training and further education courses can be started. (The Cockcroft Report (1982) In oral evidence to the Expenditure Committee a CBI representative stated: Mathematics, I think or arithmetic, which is really the primary concern rather than mathematics themselves is the one area which is really brought up every time as a problem. It seems that industrys needs are greater in this respect than almost any other. This is the way, certainly, in which shortfall in the education of children makes itself most manifest immediately to an employer. (The Cockcroft Report (1982) Written evidence to the Expenditure Committee from the Engineering Industry Training Board (EITB) stated: The Engineering Industry Training Board, over the last two years, received from its industry increasing criticism, with supporting evidence, of the level of attainment, particularly in arithmetical skills, of school leavers offering themselves for craft and technician training In the view of the Engineering Industry Training Board the industry needs a higher level of attainment in basic mathematics among recruits than it is now getting and believes that, with closer cooperation between school and industry, children can while still at school be motivated to achieve this Mathematics is, however, not simply a question of basic manipulative skills. An understanding of the concepts is also needed and these are better taught by innovative methods, which also appear to enhance the ability to acquire planning and diagnostic skills, of great importance to craft and technician employees. The Cockcroft Report (1982) These are the examples of complaints received and the main reason for the enquiry committee to set up in 1978 to investigate complaints about low levels of numeracy among young entrants to employment and the need for improved liaison between schools and industry. Hence we could deduce that due the mathematical knowledge demand in the work force has brought mathematics an important place in the national curriculum to promote numeracy skills among the young people. Programme of Study (POS) The national curriculum through the Mathematics Programme of Study (POS) aims to develop; Successful learners where pupils should be numerate, creative and able to tackle problems with more than one approach and to solve open-ended problems. Confident Individuals Pupils are given the opportunity to express their ideas using strategies that they are familiar and secure with. Responsible citizens the emphasis on analyzing and justifying conclusions in mathematical situations helps prepare pupils for taking critical and analytical approaches to real-life situations. The framework has set out a number of key concepts that pupils need to know in order to deepen and broaden their knowledge, skills and understanding of Mathematics; Competence should be able to apply a range of mathematical techniques to assess risk, problem solving and decision making Creativity Able to combine understanding, experiences, imagination and reasoning to construct new knowledge and usage of existing mathematical knowledge to create solutions Application and Implication of Mathematics Able to understand that mathematics is used as a tool in a wide range of contexts, such as for Financial issues, Engineering, computer security and so on Critical Understanding Recognizing the limitations and scope of a model or representation. For example, mathematical skills are required to compare different methods of borrowing and paying back of money but the final decision may rely on other factors like comparing the merits of using a credit card that might offer the lowest overall costs. The framework has a set of key processes for both Key Stage 3 and 4 that are essential skills that pupils need to learn to make progress within the Subject. Representing Identify the mathematical aspects of a situation or problem, able to choose between representations to simplify a situation or problem in order to represent it mathematically, using appropriate variables, symbols, diagrams and models to select mathematical information, methods and tools to use. Analysing Use mathematical reasoning, pupils should be able to: make connections within mathematics use knowledge of related problems visualise and work with dynamic images identify and classify patterns; make and begin to justify conjectures and generalisations, considering special cases and counter-examples; explore the effects of varying values and look for invariance and covariance; take account of feedback and learn from mistakes; work logically towards results and solutions, recognising the impact of constraints and assumptions; appreciate that there are a number of different techniques that can be used to analyse a situation; reason inductively and deduce. Use appropriate mathematical procedures Pupils should be able to: make accurate mathematical diagrams, graphs and constructions on paper and on screen; calculate accurately, selecting mental methods or calculating devices  as appropriate ; manipulate numbers, algebraic expressions and equations and apply routine algorithms; use accurate notation, including correct syntax when using ICT; record methods, solutions and conclusions; estimate, approximate and check working. Interpreting and evaluating Pupils should be able to: form convincing arguments based on findings and make general statements; consider the assumptions made and the appropriateness and accuracy of results and conclusions; be aware of the strength of empirical evidence and appreciate the difference between evidence and proof ; look at data to find patterns and exceptions; relate findings to the original context, identifying whether they support or refute conjectures; engage with someone elses mathematical reasoning in the context of a problem or particular situation; consider the effectiveness of alternative strategies. Communicating and reflecting Pupils should be able to: communicate findings effectively; engage in mathematical discussion of results; consider the elegance and efficiency of alternative solutions; look for equivalence in relation to both the different approaches to the problem and different problems with similar structures; make connections between the current situation and outcomes, and situations and outcomes they have already encountered. The framework sets out an outline for teachers to follow in teaching the key concepts and key processes. The range and content for both Key stages are as follow: Key Stage 3: Number and algebra rational numbers, their properties and their different representations rules of arithmetic applied to calculations and manipulations with rational numbers applications of ratio and proportion accuracy and rounding algebra as generalised arithmetic linear equations, formulae, expressions and identities analytical, graphical and numerical methods for solving equations polynomial graphs, sequences and functions Geometry and measures properties of 2D and 3D shapes constructions, loci and bearings Pythagoras theorem transformations similarity, including the use of scale points, lines and shapes in 2D coordinate systems units, compound measures and conversions perimeters, areas, surface areas and volumes Statistics the handling data cycle presentation and analysis of grouped and ungrouped data, including time series and lines of best fit measures of central tendency and spread experimental and theoretical probabilities, including those based on equally likely outcomes.Rules of arithmetic: This includes knowledge of operations and inverse operations and how calculators use precedence. Pupils should understand that not all calculators use algebraic logic and may give different answers for calculations such as 1 + 2 X 3. Calculations and manipulations with rational numbers: This includes using mental and written methods to make sense of everyday situations such as temperature, altitude, financial statements and transactions. Ratio and proportion: This includes percentages and applying concepts of ratio and proportion to contexts such as value for money, scales, plans and maps, cooking and statistical information (eg 9 out of 10 people prefer). Accuracy and rounding: This is particularly important when using calculators and computers. Linear equations: This includes setting up equations, including inequalities and simultaneous equations. Pupils should be able to recognise equations with no solutions or an infinite number of solutions. Polynomial graphs: This includes gradient properties of parallel and perpendicular lines. Sequences and functions: This includes a range of sequences and functions based on simple rules and relationships. 2D and 3D shapes: These include circles and shapes made from cuboids. Constructions, loci and bearings: This includes constructing mathematical figures using both straight edge and compasses, and ICT. Scale: This includes making sense of plans, diagrams and construction kits. Compound measures: This includes making sense of information involving compound measures, for example fuel consumption, speed and acceleration. Surface areas and volumes: This includes 3D shapes based on prisms. The handling data cycle: This is closely linked to the mathematical key processes and consists of: specifying the problem and planning (representing) collecting data (representing and analysing) processing and presenting the data (analysing) interpreting and discussing the results (interpreting and evaluating). Presentation and analysis: This includes the use of ICT. Spread: For example, the range and inter-quartile range. Probabilities: This includes applying ideas of probability and risk to gambling, safety issues, and simulations using ICT to represent a probability experiment, such as rolling two dice and adding the scores. Key Stage 4 Number and algebra real numbers, their properties and their different representations rules of arithmetic applied to calculations and manipulations with real numbers, including standard index form and surds proportional reasoning, direct and inverse proportion, proportional change and exponential growth upper and lower bounds linear, quadratic and other expressions and equations graphs of exponential and trigonometric functions transformation of functions graphs of simple loci Geometry and measures properties and mensuration of 2D and 3D shapes circle theorems trigonometrical relationships properties and combinations of transformations 3D coordinate systems vectors in two dimensions conversions between measures and compound measures Statistics the handling data cycle presentation and analysis of large sets of grouped and ungrouped data, including box plots and histograms, lines of best fit and their interpretation measures of central tendency and spread Experimental and theoretical probabilities of single and combined events. Functional Skills in Mathematics The revised mathematics programme of study has given importance in embedding Functional Maths into teaching. Functional Mathematics requires learners to be able to use mathematics in ways where it make them effective and involve as citizens, able to operate confidently in life and to work in a wider range of contexts. The framework has divided the functional skill into two levels, where level 1 is linked to key stage 3 and level 2 to key stage 4. (Please refer to Appendix 1) The key concept of competence emphasises the need for students to be able to adapt and apply their understanding in a widening range of contexts within the classroom and beyond. This is also at the heart of functional skills. In this way functional skills are much more than a set of technical competencies in mathematics; students have to use mathematics to tackle tasks and problems. All teaching needs to be designed in a way that contributes to the development of functional skills. When planning opportunities for students to develop and understand functional skills you should consider whether you have: provided opportunities for different skills you are focusing on in representing, analysing and interpreting to be developed in combination ensured that students understand that they are learning skills that they will use and apply in a variety of contexts given students the chance to select the skills and tools (including ICT) they need for a particular task provided opportunities for students to apply these skills for real purposes and contexts beyond the classroom. For example, a year 10 project asked students to recommend to school managers a method for electing representatives for the school council. Students explored methods used in politics, including first past the post and different methods of proportional representation. They collected data about different voting methods and carried out simulations, which enabled them to produce a clear recommendation with justification. This project has the potential to be developed in conjunction with ICT, English and citizenship colleagues as it addresses wider curricular issues and also offers opportunities to develop functional skills in ICT and English as well as mathematics. The following are case studies on Functional skills taken from the National Curriculum website (http://curriculum.qcda.gov.uk); Wellacre Technology and Vocational College Objective: To help learners understand the relevance of mathematics in real life Year 9 science project and a Year 7 design and technology project. Both required pupils to solve real-world product design problems; In the year 9 science project, skiing was used as a context for developing learners understanding of pressure, mass, surface area and speed. Pupils had to work out how wide skis would need to be for individual pupils to ensure that their skis did not sink into the snow. This required pupils to rearrange formulae and calculate the surface area of their feet and pressure. For the year 7 design and technology project, pupils were given a budget and challenged to raise as much money as they could for  their partner school in Newcastle, South Africa. Pupils considered a range of products before settling on key fobs. Maximising the amount of profit was the main design criterion and pupils were encouraged to use tessellation to ensure their designs minimised waste. As part of the project they also use formulae to calculate break-even points, profit and loss. In both projects, working with real figures proved both an incentive and a challenge pupils were not able to fall back on a set of answers in a textbook. This generated discussion as pupils collaborated to check their calculations. The nature of the tasks also encouraged learners to think independently and creatively to solve problems. Opened ended mathematical Enquiries- Lancaster Girls Grammar School Objective: to develop pupils functional mathematics and problem-solving skills Introducing open-ended projects that required pupils to use mathematics to solve real-life problems Mobiles and Mathematics in year 8 and Music and Mathematics in year 10. Both projects were based around open-ended problems without a right answer. Pupils were given the broad topic areas and told to devise their own projects. Pupils were given two months to prepare, which encouraged them to make their own choices about how they would work and what they would explore. The range of investigations devised by pupils was broad. Year 8 pupils explored different tariffs, compared costs between pay as you go contracts and investigated different usage patterns of people over and under 30. In year 10 pupils were encouraged to make links between mathematics and music. Some considered what kinds of functions might be used to model sound waves. Others explored the connections between the Fibonacci sequence and the layout of a keyboard. In both projects, pupils defined their own problem, decided on the data to collect and how to collect it, gathered information from a number of sources, including their parents or other pupils, considered how to analyse their data, used and applied mathematics skills and drew conclusions. At the end of the projects, they presented their findings and evaluated how successful they had been. Staff and pupils embraced the new way of working. The head of department acknowledged that it was a considerable risk to introduce this way of teaching but it paid off. Initially, staffs were concerned about setting problems when they didnt know the answers but once the work was underway they enjoyed a different way of teaching. The projects offered opportunities to stretch pupils and encourage them to make connections between different parts of their learning. Many of the pupils were nervous about working on a project when they didnt have an indication of what type of project to make. However they soon began to enjoy the freedom of the approach. At the end of the project, a year 8 pupil reflected: This was a break from everyday work and we can use our imagination as we arent being spoon fed the information. We could decide what we wanted to do I have learnt to make decisions. There were different ways to present information on this project and this made it even more exciting. I could be creative with my choices as I didnt have to do exactly what the teacher said. ASSESSING PUPILS PROGRESS IN MATHEMATICS (APP) Finally, in my literature review, I am going to look into embedding APP guidance into teaching and learning of mathematics. Assessing Pupils Progress (APP) is a structured approach to periodic assessment, enabling teachers to: track pupils progress over a key stage or longer; use diagnostic information about pupils strengths and weaknesses to improve teaching and learning Using APP materials, teachers can make more consistent level-related judgements in National Curriculum The APP focuses on how as mathematics teacher can use AFL (Assessment for learning) strategy in lessons in order to generate evidence pupils learning. The diagram shown below tells how the APP cycle works. Review a range of evidence for periodic assessment (APP) Collect and feedback to pupils evidence of their progress during day to day teaching and learning Plan for progression from learning objectives (Secondary Framework and Planning toolkit) Make level related assessment using APP Criteria Adjust Planning, Teaching and learning by referring to Secondary Framework The focused assessment materials are on the APP assessment criteria and organised in National Curriculum levels. There is a set for each level from 4 to 8. The materials include examples of what pupils should know and able to do and some probing questions for teachers to initiate dialogue as to assist in their assessment judgement. The following is an example from the level 6 focused assessment materials. Add and subtract fractions by writing them with a common denominator, calculate fractions of quantities (fraction answers); multiply and divide an integer by a fraction Examples of what pupils should know and be able to do Probing questions Add and subtract more complex fractions such as 11 Ã¢â‚¬Å¾18 + 7 Ã¢â‚¬Å¾24, including mixed fractions. Solve problems involving fractions, e.g.: In a survey of 24 pupils, 1 Ã¢â‚¬Å¾3 liked football best, 1 Ã¢â‚¬Å¾4 liked basketball, 3 Ã¢â‚¬Å¾8 liked athletics and the rest liked swimming. How many liked swimming? Why are equivalent fractions important when adding or subtracting fractions? What strategies do you use to find a common denominator when adding or subtracting fractions? Is there only one possible common denominator? What happens if you use a different common denominator? Give pupils some examples of adding and subtracting of fractions with common mistakes in them. Ask them to talk you through the mistakes and how they would correct them. How would you justify that 4 à · 1 Ã¢â‚¬Å¾5 = 20? How would you use this to work out 4 à · 2 Ã¢â‚¬Å¾5? Do you expect the answer to be greater or less than 20? Why? Probing questions are an important tool in a lesson as it could be used to confirm pupils understanding in a particular topic or their misconceptions. Before we talked about it I always thought if the shape had three numbers you just times them. But now I know that you split the shape into rectangles and I can find the area of a rectangle. Its so easy. I understand it fully now. (Source: APP: Secondary Mathematics Guidance) That was a comment from a pupil after dialogue about understanding and using the formula for the area of a rectangle using the probing questions. KANGAROO MATHS http://www.kangaroomaths.com/index.html Kangaroo Maths is the home page of Bring on the Maths where interactive activities for teachers can be purchased from Key stage 2 to A level. It has an APP page that provides supporting materials for teachers from Key stage 1 to Key stage 3. The assessment policy from the website (Appendix 5) has been rewritten to reflect the APP and to help with the on going development of APP, it has an evaluation tool (Appendix 6) where it allows teachers to self evaluate themselves in focusing, developing and establishing APP criteria with regards to pupils engagement, lesson planning and evidence gathering. Further more, to understand the assessment criteria on the A3 grid, Kangaroo maths has developed the levelopaedias that provide exemplifications and probing questions for each of the assessment criteria. DISCUSSION/FINDINGS: To add on to my findings, I am going to look into the topic Algebra and analyse how it has developed across the levels using the APP criteria (Appendix 7a) and Kangaroo maths Level Ladders( Appendix 7b). Then, based on level 5 work on Algebra, I am going to design 3 series of lesson plans with the guidance of the level ladders. The word ALGEBRA seems to be a put off to most students when unknown numbers or using formulas to real life context. It is a topic that requires accumulative understanding building on from level 2 onwards as shown below (taken from APP guidelines); Algebra Level 5 Construct, express in symbolic form and use simple formulae involving one or two operations. Level 4 Begin to use simple formulae expressed in words Level 3 Recognise a wider range of sequences Begin to understand