Effective Teaching of Abstract Algebra :: Mathematics Education Papers

Effective Teaching of Abstract Algebra Abstract Algebra is one of the important bodies of knowledge that the mathematically educated person should know at least at the introductory level. Indeed, a degree in mathematics always contains a course covering these concepts. Unfortunately, abstract algebra is also seen as an extremely difficult body of knowledge to learn since it is so abstract. Leron and Dubinsky, in their paper  ¡Ã‚ §An Abstract Algebra Story ¡Ã‚ ¨, penned the following two statements, summarizing comments that are often heard from both teacher and student alike. 1."The teaching of abstract algebra is a disaster, and this remains true almost independently of the quality of the lectures." (Leron and Dubinsky agree with this statement.) 2."There's little the conscientious math professor can do about it. The stuff is simply too hard for most students. Students are not well-prepared and they are unwilling to make the effort to learn this very difficult material." (Leron and Dubinsky disagree with this statement.)(Leron and Dubinsky, p. 227) Thus the question is raised: if there is something the "conscientious math professor can do about" the seemingly disastrous results in the learning of algebra, what is it that we can do? As a teacher of undergraduate mathematics, I want and need to know what these effective methods of teaching abstract algebra are. Leron and Dubinsky's paper referred to above and papers resulting from their research contain the bulk of literature that I reviewed. In this paper, they summarize their experimental, constructivist approach to teaching abstract algebra. Among the classroom activities are computer activities, work in teams, individual work, class discussion, and sometimes a mini-lecture summarizing the results of student work (which by this time is familiar to them), providing definitions, theorems, and proofs in their abstract forms. The computer activities use the ISETL programming language. As an example of its use, students write a program implementing the group axioms. They then can enter what they consider to be a group, and the computer will give as output a true or false response. They can use the same process to determine whether their proposed group is closed, has an identity, etc. They choose their answer and then let the computer respond. In this way, students  ¡Ã‚ §construct ¡Ã‚ ¨ the group process, with the view that they will also have a  ¡Ã‚ §parallel construction ¡Ã‚ ¨ occurring in their minds. Students have an experience on which to base their learning of group theory. The method proposed here by Leron and Dubinsky certainly seems patterned after Dubinsky's theoretical foundation for student learning laid out in his work  ¡Ã‚ §Reflective Abstraction In Advanced Mathematical Thinking.

Wuthering Heights, Chapters 11-23 :: Free Essay Writer

Wuthering Heights, Chapters 11-23 Chapters 11-12 After her long absence from Wuthering Heights, Nelly decides to return in order to speak with Hindley. However, instead she meets Hareton who does not remember her and greets her with a hail of stones and curses. No doubt these actions have been copied from Heathcliff. Nelly runs away. The next day, Heathcliff comes to the Grange and embraces Isabella, much to the annoyance of Cathy. Heathcliff tells her ‘I’m not your husband, you needn’t be jealous of me.’ Edgar challenges Cathy and Heathcliff regarding their relationship. Heathcliff takes the position that Cathy has wronged him and that he will be revenged. Cathy taunts Edgar encouraging him to fight with Heathcliff. Edgar strikes Heathcliff and then goes to get assistance in order to have him removed from the house. Heathcliff, realizing that he will be outnumbered, leaves. Cathy is asked to choose between Heathcliff and Edgar, but Cathy will not answer her husband. Instead, she locks herself in her room refusing to eat. Edgar then decides to persuade his sister Isabella to pursue Heathcliff, as their relationship would end the link between Cathy and Heathcliff. After a few days without food, Cathy calls for Edgar begging forgiveness. She is delirious and talks about her childhood with Heathcliff and she has a foreboding of her death. Nelly insists on keeping the windows in her bedroom closed, but Cathy staggers to them and throws them open claiming she can see Wuthering Heights. She goes on to speak about her death, but that she will wander the world until she is with Heathcliff. Edgar is appalled to find Cathy in such a weakened state and scolds Nelly for not telling him sooner. That night Isabella runs away with Heathcliff and Edgar disowns his sister for this scandal. The doctor arrives and predicts that Cathy will not survive the illness. Chapter 13-15 Cathy is in fact pregnant and Edgar tries to nurse her back to health. He hopes for a male heir. Isabella has married Heathcliff and writes to Edgar begging his forgiveness, but this is ignored. She then writes to Nelly and asks her to visit Wuthering Heights. She is distraught at the way Heathcliff treats her. In the letter she tells of her loneliness, as Hareton, Joseph and Hindley are rude to her. She regrets having married Heathcliff and cannot see any way for her to escape. When Heathcliff learns of Cathy’s illness he blames Edgar for this. Nelly visits Wuthering Heights, but she can give no words of comfort to Isabella from Edgar who still will have no contact with her. Heathcliff is eager to learn about Cathy’s situation, clearly hurting

Case Study: Developing Chinks in the Vaunted “Toyota Way”

Introduction Since 2005 Toyota has dominated the car industry but when people spoke of Toyota is was never to say that it had the best fuel efficiency, faster or even more luxurious. They always spoke about how solid the car was, how good it was on gas and how they really never had a problem with the Toyota they bought. Everyone that spoke about Toyota always said that it was a great car for a great price. Toyota has always focused on making a quality car for a fair price and had the reputation as a great company to work for.The people that worked for Toyota always felt they were making a difference and part of a team. They felt their work mattered and problems were not swept under a rug in order to turn a profit†¦until recently. Over the last couple of years it seems that Toyota has run into more than their fair share of problems. Now when people talk about Toyota they mention mechanical problems or problems with the quality of the product. What has changed? What has taken Toyo ta off the path of a great car for a great price?Has Toyota sacrificed quality for quantity in order to turn a larger profit or was something behind all of this? Was part of the plan to recover the United States auto industry to put into question the quality of the foreign automobile? Issues Addressed What has taken Toyota away from â€Å"The Toyota Way (Nelson and Quick, 2011-586)? † The Toyota way is, according to Toyota, a set of principles that have, until recently, set the standard for all other auto makers to follow. Toyota listens to the employee’s suggestions and even implements them if they make sense.Toyota recently conducted a study of the their products against the competitors, component by component only to find that just over half of all of their products were superior. This type of findings found Toyota was suffering from mediocrity and maybe Toyota’s pursuit of profit and becoming number one caused the loss of focus of the original fourteen princ iples that was the very core that got them to the top? Answering the Questions 1. Nelson and Quick describe espoused values as â€Å"what members of an organization say they value (Nelson and Quick, 2011-560)† and â€Å"enacted values are values reflected in the way individuals actually behave (Nelson nd Quick, 2011-560). † So one has to think that there is a strong possibility that Toyota’s employees are no longer feeling valued as employees. With the economy suffering, cuts are being made in almost every corporation in the world and Toyota is not exempt from this. Since 2009 Toyota has been suffering from the massive lawsuits of the braking problems of their vehicles and the vehicles unable to stop. With massive recalls and millions of dollars being paid out because of a quality issue the money had to come from somewhere.Since 2009 Toyota made huge cuts in manufacturing and production came to crawl and thus laying off a lot of employees. With employee layoffs comes the uncertainty of a future and with that the employees are no longer feeling like a family but now feeling like a number and numbers are easy to cut. 2. Toyota has always tried to stick with the original fourteen principles they simply label as the Toyota way. These fourteen basic principles are â€Å"a pattern of basic assumptions that are considered valid and that are taught to new members as the way to perceive, think, and feel in the organization (Nelson and Quick, 2011- 740). The Toyota Way lends in the way management decision are made, process flows, amount of production and bringing problems to the surface vice sweeping them under a rug. 3. Up until the last few years The Toyota Way was preached, taught, and embedded into the way all employees acted and thought. Now the CEO of Toyota, Katsuaki Watanabe, is thinking that Toyota has strayed from the path of the Toyota Way and the quality of the product and the efficiency of the production companies are suffering because of this. 4.As virtually every company in the world is trying to figure out how to survive and make it through the recession, Toyota is no different. The CEO of Toyota faces new challenges as well as trying to get back to the core principles that brought them to the top of every auto manufacturing envy list. Toyota is trying to expand their operations, recover from the damaging reputation and instill the Toyota Way back into the entire corporation. Toyota is spending millions of dollars in an attempt to give Toyota the public confidence it once had.This challenge, in today’s economy seems almost impossible but Toyota is committed and believes they will prevail. Conclusions I have always considered myself an open minded individual and have tried to look at only the facts before coming to a conclusion. While America’s auto industries were on the verge of collapse and the United States government having to bail them out, I have to wonder why the United States government w as so involved with the problems of the Toyota products.At the peak of the auto industry crises in the United States our government ensured the problems with the quality and reliability of the Toyota products were questionable and always in the headlines of all the news. With the United States trying to recover what was left of the auto industry and ensure the American people had faith in the quality of the American automobile they always made sure the quality of the import was in question. One has to think that something was behind all this to ensure the American people went back to buying American automobiles.Has Toyota really left the path of the Toyota Way or did they get pushed off the path? ? References Isidore, Chris. CNN Money. February 9, 2001. http://money. cnn. com/2011/02/08/news/companies/toyota_cost_cutting/index. htm Nelson, D. & Campbell-Quick, J. , (2011). Organizational Behavior: Science, the Real World and You. (7th ed. ). Canada: South-Western Cengage Learning. P ace, Joe. The Workplace: Today and Tomorrow. The Professional Development Series, Book One.

Unit 9 P4

Unit 9:exploring creative product promotion P4: explain the reasons behind the choice of media in a successful promotional campaign. Brandon Baumgart IBS 1c P4 Version 3 30 may 2012 Mrs. Daymond From mouth-to-mouth to TV and Internet. In 1886 when coca cola started they didn’t had TVs, radios and Internet to tell people they have invented something new. So everything was from mouth-to-mouth, through the flyers, the newspapers or big wall paintings on high buildings.Later they could add the radio in this list. And that status they still have but how do they do that now a day? They do that most through the TV will al the happy people who drink Coke and with the happy and bright colours and their slogan: OPEN HAPPINESS. Why one the TV and Internet and not on the radio for example? Because if you hear a commercial on the radio you only HEAR and not see the commercial but on TV you SEE and HEAR the commercial and because of that you want a Coke.The number one reason is that almost everybody has now a day a TV, a computer and a smartphone with internet, so Cola has to go with their time and now they have a general site about all the different kinds of beverage the have, they also have a Coca Cola web shop, a Cola diet site, a Cola goes green site and many more. All these sites are for people want to know more about Coca Cola or buy their stuff. Coca-Cola uses direct marketing in many ways. First, the company partners with various restaurants, movie theatres, etc. to carry its product.Unit 9: exploring creative product promotion P5: design a promotional campaign for a given product/service to meet the needs of a given campaign/creative brief @ Fair trade Max Havelaar products Brandon Baumgart IBS 1c P5 Version 1 27 January ‘12 Mrs. Daymond Table of contents 1. Introduction 2. Campaign brief 3. Creative brief 4. Budget and time lining 5. Mood board 6. Conclusion Introduction In this task you design a promotional campaign for a given product/service to meet the needs of a given campaign/creative brief @ Fair trade Max Havelaar. Fairtrade since 1988Max Havelaar Foundation was founded in 1988 by Nico Roozen and Frans van der Hoff in response to an urgent call of coffee farmers in Mexico. â€Å"Aid is good, but a fair price for our coffee is better. Then we don’t need to hold or hand,† they argued. With a fair price for coffee beans, small farmers take matters into their own hands. I hope you will learn as much I will with typing this report. Campaign brief Background to the proposed campaign The Max Havelaar Foundation grants since 1988 in the Netherlands, a hallmark of coffee at a fair price for producers in the market.The initiative was developed in consultation between Mexican coffee farmers and a Dutch aid organization. The organization is further supported by ICCO, an interchurch organization for development. The initiative was copied: Max Havelaar is now also the name of the only independent fair trade label for food s whose producers in Latin America, Africa and Southeast Asia by buying a higher price than the world price is paid. On top producers receive a premium as an extra.The name comes from the book Max Havelaar (1860) by Multatuli, which injustice is made of coffee farmers in the former Dutch East Indies. The mark guarantees that organizations of small farmers or plantations in developing countries receive a fair price for their products. Although the mark, partly because of his name, especially evokes associations with coffee, it is also found in ice cream, tea, chocolate, honey, cocoa, fruit juice, rice, wine, beer, sugar and fruit. Include the make â€Å"Oke†, under that name bananas, oranges, pineapples and mangoes sold, may Fairtrade / Max Havelaar label.In addition there are other brands such as Ben & Jerry's (ice world 100% fairtrade), Verkade, Swiss Noir (chocolate), Penotti (chocolate spread) and Fair Trade Original (an array of products). There are also several supermark ets (such as Albert Heijn â€Å"Pure and Honest† and Lidl â€Å"Fair Globe†) that choose to sell fruit to sell under their own brand of course Fairtrade / Max Havelaar label. In January 2010, the supermarket chain PLUS the largest commitment to fair trade made. From this date all bananas Plus sells Fairtrade / Max Havelaar certified. In 2011, the SPAR supermarket organizations and ALERT followed suit.The foundation itself is acting in any of these products, it provides only the label that guarantees a fair trade. In 2004, 3% of the Dutch coffee and 2% of the Belgian coffee certified under the Max Havelaar label. In many countries there are foundations that same goal and same working method. The Max Havelaar label is now (2009) in some 23 countries and used products come from some 55 countries. Of these, approximately a half million farmers directly (and workers) benefit. These organizations have joined the international Fairtrade Labelling Organizations (FLO).The Fairt rade mark (the international version of the Max Havelaar label), with 2006 revenue growth of 40%, the largest increase was in the United States where coffee sales quadrupled. In January 2006, the Max Havelaar label a big campaign in the Netherlands to focus on products with its brand to establish. The advertising slogan â€Å"no discount, but advantage,† with a wink referring to the price war between the Dutch supermarkets, wanted the label to highlight that the products are more expensive, but that a portion of the proceeds benefit the producers them. we are going to do it big than in 2006.We want more people to be aware about the prodcuts they buy. We are going to show in our commercials small movies about were their â€Å"cheap† coffee comes from and where our coffee comes from. Also we are making a FaceBook page and a Twitter page to keep them updated. Objectives To increase awareness of the product through advertising from 36% to 46% by the end of the year 2012. A nd that more people buy our products. Target markets Is everybody who does the grocery and â€Å"anyone who knowingly lives and want to meet others with the same respect that you take yourself expect from others†.Product/service specification Nowadays you can find the Max Havelaar Fairtrade Mark not only coffee but a wide range of products such as chocolate, fruit, wine, tea, spices and even on ice and peanut butter. Also adorns the label on products such as cotton bath towels, blankets, shirts and curtains and flowers. The Max Havelaar Fairtrade Mark is the only standard that the ‘Triple P' of sustainable development – People, Planet and Profit – completely covers. Through a guaranteed fair price creates the label space for both economic development and environmental improvement and social progress.Fairtrade system that makes it a unique model with the highest standard for sustainable development. People The identity of the Max Havelaar label is primarily associated with social justice. Respect for human rights and labor standards, according to the Charter and Conventions of the United Nations, are the starting point. But social progress is not as the basis for prosperity and ecological health is destroyed. Planet Farmers realize that is why many organizations turn to organic farming. Part of the products with the Max Havelaar Fairtrade Mark also has an organic label.But the Max Havelaar label itself represents a healthy environment. Dealing with soil, water, air and biodiversity in Fairtrade bound by rules. Basic standards to be met as a condition for certification. The system also offers guidelines for further improvement. Profit And the financial area, because that's not without. The space created by a fair reward for goods supplied. Through better trading conditions to improve poor farmers Fairtrade gradually their living standards. They have tools at hand to invest in their operations and their environmental performance, with o rganic certification often represents the pinnacle.Fairtrade in the third P belongs right there. He suggests farmers are able to trust the future to work on sustainable development. Creative brief Background/introduction We are Cherry Redâ„ ¢, one of the most efficient advertising agencies. Established in 1991 we strive to offer the greatest service possible putting the client at the centre of business. Target markets Is everybody who does the grocery and â€Å"anyone who knowingly lives and want to meet others with the same respect that you take yourself expect from others†. Women respond most favourably to social responsibility messages.Design marketing materials aimed at women. The age group 25-34 respond more favourably to socially responsible messaging. People identify with fair wages and employee treatment. Wealthy people and people who buy gifts often tend to do it online and in boutiques. A great website, product reviews, and well-trained sales people will help you sell. Promotional/advertising objectives Create consumers demand and awareness for the Fair trade products Max Havelaar: proud to be fair. Promotional/advertising proposition That the products they buy must stay fair too the farmers and for the customers. Support Fair trade * Empowerment * Poverty * Conservation * Social improvement * Clean environment * Development * Transparency * Co-operation These points will make a better world. Tone of voice Serious, friendly, â€Å"green†, everyday and FAIR. Mandatory inclusions Max Havelaar fair trade logo, Max Havelaar website, available at the better supermarket. Budget and timing Promotional Designs For Campaign| Costs| Logo DesignEmail DesignPostersLeaflet DesignNewspaper Advert DesignWebsite DesignCommercial on TV| â‚ ¬50. 00â‚ ¬160. 00 â‚ ¬395,48 (25 needed at â‚ ¬15,82 each)â‚ ¬140 (2000 needed at 7p each)â‚ ¬900â‚ ¬300 paid for the yearâ‚ ¬ 11. 00| Maximum Budget Of: ? 15. 000,00| Total Cost: ? 12. 945 ,48| We want the ad’s come out in the holiday period because people will give and buy more in this season because it stands for togetherness, joy, giving and caring for fellow creature. Conclusion This was a very interesting task. Now I know more about how too make a simple promotional campaign. And also know more about Max Havelaar Fairtrade products. Such as that Max Havelaar is not a brand. Max Havelaar Foundation is part of an international umbrella: Fairtrade Labelling Organizations (FLO). I hope you have leared as much as I have.

Deprivation as a Result of Poverty Essay

Slums in Mumbai are only a reflection of many facets of poverty. The movie Slumdog Millionaire directed by Danny Boyle is an ideal portrayal of the harsh lives of children on the wrong side of India who experience the bitterness of poverty. Despite the unjust peculiarities and sorrows created by poverty, people are still hopeful on their future and still have lust for life. Dharavi is a perfect example of slum area. Slum area is generally defined as informal and low class settlements often found in the cities. â€Å"Dharavi is a sprawling, chaotic place of precariously-built brick houses, bamboo and corrugated iron-roofed huts, milky cess pits, greasy fried food stalls and noisy, dusty workshops† with unreasonably many number of population (â€Å"Slum in Mumbai† 2009). Their illegal settlements deprived them of public services such as water sewage and medical assistance. Moreover, their massive population encourages fornication, street gangs or other forms of violence, health problems, homelessness and thus poverty. The level of poverty experienced in the Slums of Mumbai is not only manifested in the shortest of common or basic needs such as food, clothing, shelter and safe drinking water. But poverty also deprived them of many opportunities such as the education, high paying careers and updated modernity. Children and youth under the state of poverty instead of participating in community and social services for their individual growth and learning will be forced to work at a very early age to provide for their family. Thus spiritual, emotional and intellectual growth is relatively slower compared to those youngsters expose to different learning communities/ activities. People who live in poverty often perceive themselves as hopeless individuals and unconsciously see themselves as victims of capitalism. They often have a bad impression towards government and social institutions believing that their services are unfairly distributed for the people like them. As a result, they are the one prone to rebellious activities against the government. They are often putted into a situation where they make impulsive decisions for the sake of survival that will only serve to further complicate their lives. This may include considering crime as an acceptable or justifiable alternative for physical survival. Ultimately, their value system and moral standard will be greatly affected. Poverty may cause disunity inside the family and community as a whole. Example of this is the increasing number of single mothers and separated parents because couples can’t live by love alone. Poverty may lead to encountering many mental and psychological problems because and anxieties and different levels of depression. The effects of poverty all over the world especially on slum areas show inequalities and disparities between the rich and the poor. It is not only a reflection of their own wrongdoings but also a reflection of mismanagement in governance and unequal distribution of wealth and resources. Moreover, poverty especially in Asia is also a reflection of cultural causes which exercise their life in conformity to their tradition and religion. The United Nations and various social institutions though are working hand in hand to at least lessen poverty since everybody deserves a decent life. . (2009). â€Å"Slum in Mumbai†. The Star Online. Retrieved on February 17, 2009 from http://thestar. com. my/lifestyle/story. asp? file=/2009/2/16/lifefocus/3092984&sec=lifef

My First Day in the University Essay

My first day at college is an important event of my life. To me it is an unforgettable day. During my school days. I had a glimpse of college life from my elder brothers and sisters. I was most curiously awaiting the day when I would start my college life. I thought that the college life would offer me a free life; here restrictions would be few and threat of teachers would be little. At last the longed for day came in. I was admitted to the Government College of my city. I entered the college premises with new hopes and aspirations. I was glad to see that the college presented a new sight. It was quite different from what I had seen in and around our school. I came across many unknown faces. I had some very strange experiences on the first day of my college life. I was baffled to see students playing indoor and outdoor games and enjoying radio programmes during class-hours. There is no restriction of uniform. I observed that the students are free in their movements. They can do things according to their choice. I found all the newly admitted students in high spirits. They were all happy to make friends. I moved round the college. I was very much delighted to see the grand library of the college where I could find books on very subject. The college laboratory excited my interest on the very first day and I got eager to perform experiments there. I noted down the time-table of my class from the notice board. I attended the classes. I found that the method of teaching in the college is different from that in the school. Each subject is taught by a specialized teacher. Questions are not asked in the classes. Professors do not rebuke the students if they fail to learn their lessons. They simply tell the students to be conscious of their responsibilities. The students find here a homely atmosphere which they lack in the school. For this, they feel easy and comfortable here. I felt a new rhythm of life and returned home with a mixed sense of duty and liberty.

Education in the Middle East in the Last 20 Years Essay

Education in the Middle East in the Last 20 Years - Essay Example Poor governance, political revolutions, poor traditional laws, and high poverty levels have had negative reflections on attitudes towards education, especially for the girl child. However, the reform movements have seen significant changes in the people’s perception of education. The governments are increasingly investing in education as they seek aid from international agencies and industrialized nations. Thus, despite the difficulties that are experienced in the most of the Middle East countries, there have been significant improvements in education in these countries, especially in the last two decades. The level of literacy, especially for women, has improved dramatically with women having more access to institutions of higher learning. Education improving in the Middle East in the last 20 years Introduction Education has been considered as one of the fundamental human rights that are necessary for development in a given society. Every individual in the society has the rig ht to access quality education owing to the benefits that education has to the individual and to the society. Education contributes towards all aspects of development in the society. It provides individuals with the basic knowledge and skills that are appropriate for the development of a career. It provides the medium through which different talents can be identified that are beneficial to the society (Behrman & Stacey, 1997, p.11). Education improves an individual’s general understanding of life as well as how to relate to others morally and responsibly in the society. Through education, one is able to understand his or her fundamental rights and freedom in the society, and the necessary steps to be taken when such rights are infringed. The fights for democratic forms of government that are experienced in different parts of the world can be easily won if the citizens are more educated. The education in the Middle East has been low as compared to the other parts of the world like the West. In many regions in the Middle East, education was not taken seriously by the public as well as the government. It was considered a luxury and its access was limited to few individuals (Editorials, 2005, para.3). The restrictions were extreme on the female children. The political oppression, traditional beliefs, and high levels of poverty greatly contributed to this situation. The Middle East Countries include the Arab nations in South Asia and North Africa like Syria, Yemen, Egypt, Iraq, Afghanistan, Iran, Armenia, and Bahrain among several others. The countries have certain similarities and differences in terms of the system of government, economic activities, and the religious culture. All these countries exhibit the Arab–Muslim relations. Most of these countries and the neighboring countries of North Africa that form the Greater Middle East have experienced civil wars resulting from poor forms of governance as well as terrorist attacks. The North African Ara b nations have experienced rebel movements that have seen most of their long-term leaders hoisted unceremoniously. Similar revolutions continue to be witnessed in the Middle East countries like Syria and Yemen.