Management Information System Research Paper Example | Topics and Well Written Essays - 750 words - 2

The executives Information System - Research Paper Example Web is the interconnection of systems over the world which associates PCs to servers henceforth connecting the billions of individuals around the globe. The web which started during the 1970s has kept on encountering colossal development in innovation and demographic base. Web is given by the web access suppliers which offer association with assigned web spaces. Sending of data however the web is a perplexing procedure that a great many people who are not PC technocrats can't comprehend. In any case, the straightforward clarification is that every PC has an Internet Protocol Address which is novel to that PC. When data is sent through the web, it must be deteriorated sending data to the assigned location and afterward reassembled when it arrives at the assignment and the procedure is rehashed over with data looked for. This procedure happens so quick that individuals don't see (Laudon and Laudon, 2014). Web clients associate with the web through the three distinctive area name framework: top-level, second-level and third-level areas. With every area level, the data is limited to the points of interest of the data looked. The top-level space incorporates government level, authoritative level, and instruction among other which are condensed with .com or .organization among others. It is at the third level that data is refined to the fundamental hunt words. A portion of the normal internet providers incorporate messages, moving records, having news gatherings and utilizing the World Wide Web to send or recover data, for example, illustrations and writings. The most widely recognized web utilization is the visiting and sending of texts usually the online networking (Abbate, 2000). The web with all its brilliance and various points of interest likewise has its own disservices. Individuals have the opportunity to stack in any data on the web which would then be able to be gotten to by others

Roman Empire and Nero

Clarify the job and commitment of Seneca to the rule of Nero Seneca was the individual guide of Nero during his rule. He was an emotionless logician who assumed an imperative job in the running of the realm. Seneca contributed in numerous parts of Nero’s rule by presenting changes, bringing emotionlessness into training and assuming a key job in the senate. Seneca helped in significant dynamic. He drove Nero down a suitable way, especially when Nero turned out to be very whimsical. He served Nero well and made a phenomenal commitment during his reign.Seneca comprehended the issues of Rome so he had the option to present changes, which profited the individuals. He made conditions for slaves progressively empathetic, presented financial change and presented an increasingly illuminated organization in Britain. This emphatically added to the domain as he had the joy of the individuals to his greatest advantage. By presenting changes that satisfied the individuals he picked up ubiq uity for both himself and Nero. This was useful for Nero as the individuals of the domain could think back on Nero’s rule years after the fact and consider the great choices and amazing changes that had occurred during the period.Tacitus says â€Å"Nothing in human issues is more flimsy and shaky than power unsupported by its own quality. † This statement by Tacitus shows us exactly how incredible the effect of Seneca was. It is disclosing to us that without Seneca, Nero may have had the force, however had no help to counsel him to settle on the right choices. Seneca was the solidarity to Nero’s power. Seneca made Nero’s first discourse to the senate. This discourse offered extra capacity to the senate and shows that Seneca was adding to the rule of Nero directly from the very start.The discourse additionally vowed to come back to what life had been similar to under Augustus. Obviously, the realm was viewed as a Republic during the Augustan time frame and the individuals esteemed this time. Seneca and Nero were viewed well when they vowed to come back to a period of satisfaction. In this way Seneca urged an incredible beginning to the rule of Nero. Apathy impacted the composition of Seneca for Nero as he composed â€Å"on clemency† which urged Nero to administer indulgently. Aloofness is especially appeared as he composes â€Å"†¦worthy to do the ork of the divine beings upon the earth† It is realized that the Roman’s were extremely strict, so to accomplish crafted by the divine beings would be viewed as morally and ethically right to Seneca. These qualities are one of the convictions of Stoicism, mirroring his impact. This added to Nero’s rule as it implied that Nero appeared to be a self-controlled, ethically right apathetic man who might run the realm tolerantly and fulfill the individuals of Rome. Fulfilled Romans implied that they would keep on giving their help to Nero during his rule. Seneca w orked proficiently with the senate permitting Nero to stay mainstream inside the senate.A key job that Seneca played was to guarantee that the Neronian government had great relations with the senate. He did this adequately. This was an amazing commitment to his rule as it permitted Nero to stay mainstream inside the senate, just as with the individuals. Staying mainstream among Rome implied that he had the help of its kin and could keep on administering adequately with Seneca close by. Seneca’s impact was especially appeared as he composed the discourse Nero gave where he proclaimed his organization for the senate and his craving that they continue their old function.Seneca’s fruitful addresses added to the sound connection among Nero and the senate as he mentioned to them what they needed to hear. He additionally gives coins, which were a further pointer of the great relations among Nero and the senate. Credit for this fruitful relationship must go to Seneca who put t he words into Nero’s mouth and had the option to fulfill the senate by giving them what they needed. A participating senate implied that the domain had the option to run much better during Nero’s reign.Further on in Nero’s rule, Seneca started to see a change. He developed progressively flighty and extraordinary. From here it turned into the job of Seneca to check his excitement. Tacitus portrays this activity as â€Å"To direct his deviations from excellence into authorized channels of extravagance. † The shows that Seneca satisfied his activity by maintaining a strategic distance from exercises that would bring about outrage. Nero’s disappointment became out of a significant number of his liberal thoughts fizzling and it was the job of Seneca to caution Nero about his arrangements in the event that they were insufficient or terrible policy.Although Seneca couldn't change the character of Nero and his conduct, he had the option to add to the resul t of his activities. Seneca profited the realm by dodging choices, which would outcome in uncovering Nero’s horrendous flighty side. This profited the domain in that Nero was as yet ready to be supported as the Romans didn't see the most exceedingly terrible of his inconsistent and extraordinary character, just as preventing Nero from settling on impulsive choices that would not assist his with ruling by illuminating him when strategies or thoughts were not recommended.Seneca’s commitment was helpful for all parts of Nero’s rule. He had the option to prompt Nero on significant dynamic and had the option to end Nero presenting arrangements and thoughts that would not profit his rule. Seneca gave a voice to Nero and had the option to advise the Roman individuals needed to hear and thusly earned their help. Seneca’s presentation of new approaches and making of aloofness contributed further to expanding the achievement of the domain, just as the accomplishmen t of Nero.Seneca gave the solidarity to Nero’s power and without his commitment the rule of Nero would not have been as superb. Seneca had the option to make individuals long for a â€Å"Republic† which further constrained their help onto Nero. He additionally assumed a job in making and keeping up a sound connection with the senate so that through Nero’s reign they had the option to run the realm in coordinated effort. The job and commitment of Seneca was imperative to the accomplishment of Nero, he went about as a brilliant counsel to the sovereign, especially through giving an aloof voice to Nero.

Cognitive Restructuring and Social Anxiety

Cognitive Restructuring and Social Anxiety Social Anxiety Disorder Treatment and Therapy Print Understanding Cognitive Restructuring Core Part of Cognitive Behavioral Therapy By Arlin Cuncic Arlin Cuncic, MA, is the author of Therapy in Focus: What to Expect from CBT for Social Anxiety Disorder and 7 Weeks to Reduce Anxiety. Learn about our editorial policy Arlin Cuncic Updated on November 16, 2018 Pixelfit/Getty Images More in Social Anxiety Disorder Treatment and Therapy Social Skills Symptoms Diagnosis Coping Work and School Related Conditions Cognitive restructuring is an essential part of cognitive behavioral therapy (CBT). CBT, an intensive form of therapy that requires significant effort on the part of the patient with assistance from a therapist, is considered to be one of the most effective treatment options for mental disorders like social anxiety disorder (SAD). What Is Cognitive Restructuring? Cognitive restructuring is a CBT technique that involves identifying and disputing irrational thoughts and negative automatic thoughts. It draws on several different methods such as thought recording, disputation, and guided questioning. The goal of cognitive restructuring is to replace anxiety-inducing thoughts with more rational and positive ones to reduce anxiety. The theory behind cognitive restructuring is that negative thoughts can be reformulated through practice. This process involves  testing ideas for their accuracy and questioning if they are reality or just your own mistaken perception. Does Cognitive Restructuring Help Social Anxiety Disorder? The results of a 2016 study suggested that cognitive restructuring may positively impact social anxiety in the short-term, not because of changes in the perceived accuracy of negative thoughts, but rather simply due to exposure to a feared situation. This suggests that its not so much replacing negative thoughts that is important, but rather going into situations and gradually having anxiety lessen. However, a 2014 study showed that post-event processing (PEP) was reduced after cognitive restructuring. PEP refers to the ruminative thoughts that you have after a social situation, such as I screwed it all up or Everyone saw how nervous I was. This seems to indicate that changes in thinking are important for anxiety reduction. While we dont know the precise reason cognitive restructuring has an effect, it is likely a combination of these factors: thinking more rationally, facing situations that scare you, and engaging in less ruminative afterthoughts. Each of these aspects will strengthen each other in a positive cycle. How to Practice Cognitive Restructuring On Your Own Cognitive restructuring is an intensive process. It is usually recommended that you work with a therapist who specializes in both social anxiety and cognitive behavioral therapy. However, while its true that you should generally practice cognitive restructuring under the guidance of a trained therapist, you can also get started with some self-help techniques. Below are some tips on how to start practicing cognitive restructuring in your everyday life. There are several steps to cognitive restructuring: Record: Record your thoughts in a journal, including all negative thoughts you have about yourself or self-limiting ideas. Also, note the situation at hand:  was it a large party with people you didnt know? Or, was it a public presentation in front of coworkers? Write down the implications of how you felt. If you were convinced you were going to fail, did that make you more nervous or did you refuse to attend the event?Analyze: With the help of your therapist, review the notes you have written to determine if certain patterns exist. You may find that you are okay in  work settings, but get anxious at parties where you dont know anyone. It might be that public speaking scares you, but not mingling with strangers. Analyzing these triggers can help you and your therapist create a strategy to combat your unique form of social anxiety.Dispute: Review the thoughts about yourself and critique them for accuracy. If you wrote down I always fail at everything, think about times when you did su cceed in your social or professional life. Identify a few examples, and  disprove the thought that you wrote down.Replace: Replace those disproven negative thoughts with accurate and positive affirmations. Instead of I always screw up, replace that thought with Im a very strong researcher or Im a great listener. Tips for Using Cognitive Restructuring Below are some additional tips to make the most of cognitive restructuring. Its best to be in a calm state of mind when doing this process. If you are still anxious from a situation, take some time to calm yourself by using techniques such as deep breathing or meditation. Use a self-help book specifically designed to help you implement CBT techniques. Most of these books will include a worksheet to help you practice cognitive restructuring. Monitor yourself for negative automatic thoughts in the future and replace them with the positive affirmations that you created. Practicing mindfulness meditation can be helpful to learn how to detach yourself from your thoughts or to let them go without fighting against them. It can be used alongside cognitive restructuring as a helpful tool. A Word From Verywell Cognitive restructuring is not an easy skill to learn, even with the help of a healthcare provider. Particularly if you have social anxiety, you likely have spent years thinking negatively about yourself, worsening your anxiety and nervousness. However, cognitive restructuring does get easier with practice. Continue working on it for your different fears with the help of your therapist or doctor. Over time, cognitive restructuring and cognitive behavioral therapy can have a significant impact on your social anxiety. Underlying your negative thoughts is a core belief about yourself and your ability to function in social and performance situations. Once your thoughts and actions are significantly changed, your core beliefs will also eventually shift.

Essay on How Stigma and Discrimination Effect Mental Illness

Mental illness is a term which is used when a persons mind is affected in some way by a group of illnesses (Ministry of Health [MOH], 2012). People with mental health issues have been viewed and treated in a variety of ways within western society throughout time. Historically if an individual displayed behaviours which disrupted their function in society and defied social norms they were viewed as lunatics, insane or even cursed (Cowan, 2008; Elder Evans Nizette, 2009). It is from these past issues that many people still have unreasonable thoughts about mental illness; their misconceptions have created unreasonable fears and negative attitudes toward those who experience it. This negativity brings for many the barriers of not only†¦show more content†¦The effects of self-stigma can lead to a lack of self esteem, lack of confidence, isolation and the increased likelihood of avoiding professional help for their illness. This then has an over all affect on quality of life and where one sees themselves fitting within society (Barney, Griffiths, Jorm Christensen, 2005; Griffiths Christensen, 2004; Newell Gournay , 2000). Legislation in New Zealand such as The Human Rights Act 1993, section 21 and the Employment Rights Act 1997 are in place to prohibit the discrimination on the grounds of mental illness in areas such as housing, training, education and employment. The incidence of stigma and discrimination in these areas is however still continuing to be an issue for those with a mental illness. It has become apparent through large amounts of research that most incidences of stigma and discrimination are usually reported through research studies and surveys (Peterson Barnes Duncan 2008; Newell Gournay, 2000). El-Badri Mellsop (2007) suggest that most research on stigma tends to center on attitudes and beliefs of the public and how they view those with a mental illness. Much less emphasis on research has involved the personal experience, self-stigma and quality of life of the person with the illness and how they fit within the community. Badri Mellsops (2007) study Stigma and quality of life as ex perienced byShow MoreRelatedMental Health Stigma, Discrimination, and Prejudice1712 Words   |  7 PagesMental Health Stigma, Discrimination and Prejudice Karen Bleicher Spring, 2009 Professor Mark Harris Social Problems 2023 To Fight Stigmas, Start with Treatment Last fall, British television broadcast a reality program called â€Å"How Mad Are You?† The plot was simple: 10 volunteers lived together for a week in a house in the countryside and took part in a series of challenges. The amazing thing was that there were no prizes at the end of the challenges. There was a very interestingRead MoreThe Stigma Of Mental Illness1602 Words   |  7 Pagescenturies have seeked to improve care and reduce stigma around those with mental illness. This began in 1942, when Harry Truman signed the National Mental Health Act, which requested the formation of a National Institute of Mental Health. Shortly after this, in 1949, the National Institute of Mental Health was established (â€Å"National Institute of Mental Health†). During the company’s 60 year lifespan they have focused on research about mental illness, educating the public, and improving the lives ofRead MoreMental Health Service Delivery Models1146 Words   |  5 Pages Mental health illness is related to a group of illness, anxiety and stress are the most common health problems. Mental illness affects how a person feels, thinks, behaves, and interacts with other people (Department of Health, 2007). Mental health service delivery models in Australia has significantly changed from institutional care to the community care setting (Frost et al., 2017). This easy will discuss about he changes in services before and post institutional, how recovery model introduced inRead MoreThe Stigma Of Children With Mental Illness1608 Words   |  7 Pagesassociation with mental illness. This stigma creates a negative feedback loop in how society views people with psychiatric disabilities. Media portrays people with mental illness as scary, bad, dangerous, unpredictable, and un-educated. These views cause people to shy away and fear the mentally ill. This stigma also affects a person’s willingness to seek help when they are experiencing a mental illness. Some cultures, such as Hispanic Catholics, may not recognize mental illness as a health problemRead MoreThe Ways Oppressions Are Carried Out1481 Words   |  6 Pagesparticular, the discrimination against the mentally ill becomes an interesting and unique history that has evolved due to Western medicine, and now effects the whole world. In many instances, it has become apparent that the symptoms and stigma surrounding the mentally ill stems from Western ideals as well. This paper explores this stigma, the ways oppressions are carried out, and how they are being dealt with. When society is confronted with those who suffer from a mental illness, people are oftenRead MoreThe Stigma Of Mental Health Care Essay1711 Words   |  7 PagesMental health issues have been an ongoing hot topic in this country for over a century. Though many strides have been made to increase awareness and lessen the stigma, there continues to be a barrier to mental health care, especially for our nations’ youth and young adults. I will be discussing the history behind mental health care, current policies regarding it, how the presence of stigma reduces the likelihood that youth and young adults are receiving the adequate mental health care they requireRead MoreThe Importance Of Mental Disorders In The Prison System1288 Words   |  6 PagesIn addition, persons with mental disorders are clearly overrepresented in the prison system, when compared to rates of persons in the community with mental disorders, studies found â€Å"that prevalence estimates were three to 12 time s higher than in community samples, reaching as high as 64%,† (Prins, S. J., 2014, p. 862) with â€Å"prevalence† being defined as the commonness or occurrence of a mental disorder. The reasoning behind this skewed representation has continually puzzled researchers and led toRead MoreIntroduction.... â€Å"If Mental Illness Could Be Seen On A1255 Words   |  6 PagesIntroduction... â€Å"If mental illness could be seen on a sufferer maybe society wouldn’t say ‘just get over it’ .† Mental illness unlike other diseases or disorders are, for the most part invisible. They are not easily recognised. These instances of being told to â€Å"just get over it† or â€Å"just calm down† or â€Å"It’s all in your head† are direct evidence of the stigma of having mental illness present in some cultures. A mental illness is in fact in your head, but your head is connected to body, they areRead MoreInadequacy Of The United States Mental Health Care System1104 Words   |  5 PagesStates Mental Health Care System: Barriers to Care According to the World Health Organization, mental illness will affect approximately 25% of people at some point in their life (â€Å"WHO Qualityrights†, n.d.). Despite that, the current mental health care system in the United States is inadequate. Many aspects of the system need improving, especially the barriers to service. In fact, approximately 20% of individuals are left without necessary treatment for their mental health disorder (â€Å"Mental Health†Read MoreThe Stigma Associated With Schizophrenia1554 Words   |  7 PagesThe Stigma Associated with Schizophrenia. Jason Branch Fayetteville Tech Community College Author Note This paper was prepared for English 112.02, taught by Mr. Charles King on April 2, 2015 Abstract Mental illness is an area that many people are uncomfortable with. There is something suspicious about people who tend to appear mentally ill. This creates nervousness, fear, while presenting the unknown; therefore, Stigma. Now Stigma is defined as disgrace or public disapproval, which can lead

A Nursing Shortage 2019

All over the U.S., the health care industry has reported a shortage in qualified nurses. Several online colleges and universities, such as The University of Phoenix, are trying to help by offering several health care and nursing degrees. The American Association of College of Nursing said that the in the U.S. alone, there could be a shortage of 340,000 quailified nurses before the year 2020. That is roughly 3 times the current rate. There are multiple reasons for the trend. Many veteran nurses are retiring as the baby boomer generation reach retirement. Compounding the issue is the fact that people live longer now than ever before, all of which creates a greated need for health care. There is also a problem in finding teachers to train new nursing and health care canidates. 150,000 applicants were turned down for nursing programs because of shortages in qualified nursing educators. Part of this was due to keeping qualified faculty. A recent survey of nursing faculty members reported many work close to 60 hour work weeks, due to the shortage. .u973147cb992422e267f728e9ce0b16f1 { padding:0px; margin: 0; padding-top:1em!important; padding-bottom:1em!important; width:100%; display: block; font-weight:bold; background-color:#eaeaea; border:0!important; border-left:4px solid #34495E!important; box-shadow: 0 1px 2px rgba(0, 0, 0, 0.17); -moz-box-shadow: 0 1px 2px rgba(0, 0, 0, 0.17); -o-box-shadow: 0 1px 2px rgba(0, 0, 0, 0.17); -webkit-box-shadow: 0 1px 2px rgba(0, 0, 0, 0.17); text-decoration:none; } .u973147cb992422e267f728e9ce0b16f1:active, .u973147cb992422e267f728e9ce0b16f1:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; text-decoration:none; } .u973147cb992422e267f728e9ce0b16f1 { transition: background-color 250ms; webkit-transition: background-color 250ms; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; } .u973147cb992422e267f728e9ce0b16f1 .ctaText { font-weight:bold; color:inherit; text-decoration:none; font-size: 16px; } .u973147cb992422e267f728e9ce0b16f1 .post Title { color:#000000; text-decoration: underline!important; font-size: 16px; } .u973147cb992422e267f728e9ce0b16f1:hover .postTitle { text-decoration: underline!important; } READ A Master's Degree in Health Care ManagementBoth four-year bachelors degrees and two year associates degrees in the nursing and health care fields provide a future for strong job outlook. The Bureau of Labor Statistics estimated that nurses will create the second largest number of new jobs among all occupations in the future. In addition to the new jobs, many existing positions are expected to open as existing health care providers retire. Related ArticlesHealth Care Employment OpportunitiesAcquiring a Health Care Degree on the InternetAttaining a Health Care Management Masters DegreeEarly Childhood Education Teaching CertificationA Masters Degree in Health Care ManagementGetting Your Health Care Management Education

Domestic International Market Free Essays

Types of resources and capabilities underlie BMW Approach to Innovations. Founded In 1916, Bayberries Motormen Worker GAG, well known as BMW, Is a German automobile company, mall headquarter In Munich, Germany. Well, BMW also known as one of the leading manufacturing of luxury cars. We will write a custom essay sample on Domestic International Market or any similar topic only for you Order Now Nowadays when we are walling form Apple Inc. To launch their new generation innovative cell phone, the same image BMW has in today’s world market regarding their new innovative features luxury cars. BMW has gained the status of innovative luxury cars by utilizing its best resources and provide best qualities to its customer. There are many automobile companies UT there but only few firms in this industry are earned a title of innovations, and BMW comes first in that list. The main reason behind BMW success is their own Research and development center around the world, BMW group spend billions of dollar behind this R to provide best quality and innovative product to its customers. BMW comes In top 25 companies of best brand value in the world, today Its brand value exceeded to 25 Billion dollar because of Its R and Innovative Ideas of luxury cars. There are more than 8500 employees are working at Research and Development center of BMW around the globe. When I look over to the BMW group site, I found many facts about BMW regarding their innovative strategies. When I review their website I found out that currently BMW R teams are working for 2020 product of BMW. The assembly line of BMW is also ranked 1st in the auto industry by their innovative process of manufacturing luxury cars. BMW are more focused on their efficient innovation process by its innovative culture. The structure of company’s culture are more emphasis on differentiate and innovative ideas, and there is no doubt that BMW is holding one of the best talented pools of employees and cosmologies to approach the innovation. As per my opinion BMW will maintain Its title of Innovation because of their advance technologies such as using own optimizing engine, lower emission advance technologies, habitation, electrification and newly developed connected drive technologies. Bum’s Sustainable Production. Bum’s sustainable production has focused on many important factors as it mentioned below. Advanced technology by reducing emission of CO to 50%. BMW is leader in using renewable energy for production and value. Electro mobility. Always ready for future challenge by advanced technology. Continuous improvement in employee motivation for innovation. Less consumption on natural resources in production. Mobility patterns. Raising workforce awareness by providing essential training to the employees. Product Safety. Sustainable construction and process. More focusing on Opportunities Strong Brand Value. As per the current BMW strategic action regarding the future production as well as with advanced innovative technology, BMW is the only firm I found who can survived even after we will out of the fuel energy, BMW had already started working on hydroelectric advanced vehicle production, environment friendly and safety icicles, advanced production process which helps BMW to maintain its title of innovative firm. How do the resources, capabilities, and activities of BMW contribute to its differentiation strategy and unique position in the industry it has achieved? By using advanced technology and innovative ideas for production and best quality product, BMW had earned the best brand value in auto industry. BMW is also recognize as leader of innovation in auto industry, I still remember that when I bought Phone AS which had feature of Sir, but I also found out that BMW had developed this feature long back in 2006 in their BMW 7 series Models. None of the firm in auto industry had achieved in advanced technology yet and BMW group is the only company who looks to the future and gears its actions towards the long term. Well, BMW is not only one who is spending large amount on RD, there are many other automobile industry does same, but the uniqueness of BMW is the process and strategy they are using, the different culture of innovation spread in BMW, the status of innovation and advanced technology, the status brand and many other factor are consider to be the uniqueness of BMW. BMW had keep this innovative title form last two decades cause of their uniqueness and differentiate strategy where other automobile companies find hard to adopt it, the main reason behind this uniqueness is the firm’s organization culture of innovation where all employees are allowed to think different and something new that world had never seen. How to cite Domestic International Market, Papers

Pupils Errors and Misconceptions free essay sample

Errors and misconceptions are common place in the classroom especially in mathematics. â€Å"It is important to establish a distinction between an error and a misconception† (Spooner, 2002, p3). An error can be due to a number of different factors, such as lack of concentration, carelessness and misreading a question. On the other hand, a misconception is generally when a student misinterprets the correct procedure or method. â€Å"Students often misunderstand or develop their own rules for deciding how something should be done. This is part of normal development. † (Overall et al. 2003. 127). Whilst many of these invented rules are correct, they may only work under certain circumstances. It is important, when teaching, that error patterns and misconceptions are eradicated and corrected when pupils are learning and that they use procedures and algorithms correctly to obtain the right answer. In this report I am going to focus on the basic errors and misconceptions made by pupils studying algebra, specifically within key stage 3. We will write a custom essay sample on Pupils Errors and Misconceptions or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Algebra is the generalisation of arithmetic, containing a wealth of symbolic notation, in which students have not previously met. It is not surprising that students find the basic concepts hard to grasp, resulting in many errors and misconceptions. I am going to cover ‘what does the equal sign mean? ’ and students’ understanding of algebraic letters. These are the two fundamental concepts in which pupils need to be fully competent in, in order to be successful in working with algebra. Pupils Understanding of Letters in Algebraic Expressions In order for students to be confident in working with algebra they first need to be able to understand algebraic expressions and variables. In a study by Kuchemann (1981), he found less than half the children, in his study, seemed able to use a letter as a numerical entity in its own right, instead the letter was ‘evaluated’ or regarded as an ‘object’. Children can interpret letters in a number of different ways. The first is that the student may refer to the letter as an object. Letters in algebraic expressions are frequently thought of as representing an object. For example when measuring a length a pupil may refer to the side they are measuring as x, rather than the measurement. The idea of seeing letters as labels (truncated words) rather than as a variable might stem from the use of the letters l and b in relation for the area enclosed by a rectangle. l is seen as truncated â€Å"length† and b as the truncated â€Å"breadth†, but l and b are representing the measurements i. e. number of length units and NOT the object (the sides). (Kesianye, 2001, p16). The ‘fruit salad’ approach to teaching algebra can often lead pupils to believe that a letter stands for an object, reinforcing these misconceptions. When explaining what 3a + 2b means, teachers will often say three apples and two bananas. This is especially common when collecting terms; 5c + 2c means 5 cow plus 2 cows which results in 7 cows. However, the ‘fruit salad’ approach is flawed when questions such as: If a = 2 and 6a = 4b find b, arise. If taught the ‘fruit salad’ method, pupils’ immediate thoughts would be â€Å"6 apples don’t equal 4 bananas†. They take 6a to mean 6 things, or objects, rather than 6 multiplied by a value. Issues like this can also be seen in questions such as; if x = 2 what does 3x equal? Students may answer this question with 32 rather than the correct answer, 6. A remedy for this approach would be to consider the letter as the cost of the object, thus the question could be phrased differently; the cost of 6 apples is equal to the cost of 4 bananas. When teaching algebra it is extremely important to emphasise that the letters represent numbers and not objects. Another misconception can be found when students are asked to evaluate a letter. When asked to solve for x in 4x + 25 = 73, a student literally inserted x=8 into the equation, resulting in 48 + 25 = 73. This student has understood the property of the equivalence as he pasted the correct number to make the equivalence work, although he did not follow the normal equation solving procedures†. (Egodawatte, 2011, p95). This misconception can be stemmed back to the ‘fruit salad’ approach where pupils do not recognise that 4 is multiplied by the x. Many children will try and avoid having to solve pr oblems with a specific unknown. Instead they will give the unknown a value. Kuchemann (1981) presented a group of children with the question â€Å"what can you say about a if a+5=8? 92 percent of the group answered the question correctly however he found that most of them relied on their knowledge of a â€Å"familiar number-bond or counting from 5 until they reach 8†. In classes I have observed I have also found that this is the case. When a class was presented with the question 50m=100, they automatically knew that 50 x 2 = 100. They did not think about the algebraic process in order to determine the correct answer. The procedures pupils learn may be correct or they may be full of misconceptions. It is important or teachers to ensure pupils understand the correct mathematical procedures and algorithms for solving such equations. What Does the Equals Sign Mean? Another misconception I have come across, whilst observing in the classroom, was the misconceptions students make a bout the meaning of the equals sign. Does it mean ‘equivalent to’ or ‘the answer is’? Students interpret equals as an instruction to do something to determine a result rather than as a symbol that indicates the equivalence of two expressions. This arises in a natural way through the use of equals in numerical calculations. It is also encouraged by the presence of a key labelled with an equals sign on many calculators (French 2002, pp 13-14). â€Å"When two algebraic expressions are combined together with an equals sign, it is called an equation† (Egodawatte, 2011). In an equation the equals sign is used to express the equivalence between two sides of an equation whereas in arithmetic, normally students are given an operation to act upon on the left side of the equals sign and they are to write their answer on the right hand side of the equals sign. When presented with a question such as simplify x + x + 3 students may be able to collect the x terms together resulting in 2x+3 however they become baffled as to what to do next. Many students will over simplify this and write x + x + 3 = 2x + 3 = 5x as they will recognise the equals sign as a symbol asking them to compute something instead of a relationship. This is because in arithmetic the equals sign is the symbol to announce a result containing no operational signs. â€Å"The presence of the operator symbol, +, makes the ‘answer’ appear unfinished† (Lovell, n. . p13) therefore students are reluctant to accept 2x + 3 as their final answer because the expression seems incomplete. This can be very confusing for students who have learned that the equals sign means ‘the answer is’. The idea of a balanced scale can be introduced to students to help them understand the meaning of the equals sign when it is used in equations. â€Å"Students can connect representations of a balanced scale with operations that preserve equalities in an equation. The equals sign is synonymous with the centre of the scale† (Foster 2007, p166). If a weight is added to one side of the balanced scales, then it must be added to the other to maintain the balance. Foster illustrates the question â€Å"solve 3x + 5 = 11 for x† through the use of a diagram, shown below. On the left side of the scales are three boxes each representing the unknown value x and 5 marbles. On the right hand side of the scales are eleven marbles. To get the unknown value by itself 5 marbles may be removed from the left side of the scales. To keep the scale balanced, 5 marbles must be removed from the right side. This illustrates the process of subtracting equal quantities from each side of an equation. Now we are left with the three unknown values, which are equal to each other, on the left side of the scales and 6 marbles remain on the right side of the scales. We may separate the blocks so we can see the 3 separate values. We can also share the 6 marbles into three groups. This can be shown in the illustration below. It is easy to see from the diagram that one block is equal to 2 marbles. Thus x = 2. Depicting a set of scales is only a useful tool for students if they understand that an equation works in the same way as a set of balanced scales, where both sides are equal to each other, i. . have the same value. Students must understand the correspondence between the arithmetic operations and their scale counterparts of adding objects, removing objects, or partitioning objects. With these understandings, students can solidify meanings of solving equation. (Foster, 2007. p166). The scales demonstrate that if you add or subtract the same value from both sides of an equation then eq uality is conserved. This representation allows students to understand that the equals sign means ‘equivalent to’ as well as ‘the answer is’. Conclusion My research has identified a number of different meanings that can be given to the letters in algebra and to the equals sign. This can often be very confusing and cause misunderstanding when pupils are problem solving in algebra. It is therefore extremely important for teachers to explain these varied definitions to prevent misconceptions from developing. It is necessary for students to grasp these different meanings as algebra appears in different parts of the key stage 3 and 4 curriculums; in mathematics and science. Further review is needed to cultivate a clear assessment of what factors help students to fully grasp all aspects of algebra. We already know that even very basic mathematical concepts such as addition of whole numbers involve complicated cognitive processes. Since teachers are already familiar with those basic concepts, this leads them to ignore or underestimate the complexity by taking a naive approach to teaching those concepts (Schoenfeld, 1985; Edgodawatte, 2011. p22). Regardless of the previous knowledge students have from studying general processes in arithmetic; they will still find it bewildering when coming across symbols for the first time. If students are unfamiliar with algebraic expressions, notation and symbols then the students understanding and method may not be what the teacher intends. Research on student errors and misconceptions can provide support for both teachers and students. Whilst it is not always possible to teach in a way that eradicates all errors and misconceptions, it will allow teachers to come up with methods of overcoming these problems. Teachers must be able to apprehend pupils thought processes and their understandings in order to provide lessons which reduce pupils’ errors and misconceptions and support them in their learning.