Microeconomics competition and monopoly

Introduction There are four market types namely; monopoly, monopolistic competition, pure competition and oligopolistic markets (Peterson 1977). Pure monopolies and pure competition firms represent the two extremes of competition which is not easy to find in practice. The following is a review of an example of an organisation in Maryland operating in a pure competition market and one in a pure monopoly market.Advertising We will write a custom research paper sample on Microeconomics: competition and monopoly specifically for you for only $16.05 $11/page Learn More Example of a firm operating in a pure competition market Pure competitors such as retail operations however have no control of the market and thus no control over prices (O’Sullivan, Sheffrin, and Perez 2009). A firm in such a market could sell any quantities of its products without influencing the market prices. It is quite difficult to get markets that are purely competitive where buye rs have full knowledge, there are no barriers of entry and exit, buyers can easily switch from one seller to the other, and where there are a large number of buyers and sellers. However, retailers of agricultural commodities could provide a good example of a pure competition market. Some traders have sought to differentiate their farm produce thus reducing price competition in this market. For instance, since consumers are becoming more health; conscious, traders of farm produce are venturing into natural foods in place of GMOs whereas packaging is also gaining prominence as a differentiation tool. Market for agricultural products is set to change resulting to a decline in price competition. Traders are seeking other forms of competitive fronts such as packaging and focus of healthy products. Therefore, the market is set to convert into monopolistic competition where differentiation is critical. Suppliers should therefore brace themselves for non-price competition. Example of a pure monopoly Monopolies are organisations operating in a market where a firm has full control of the market. Such markets are characterized by a large single supplier of a product with no close substitutes. Monopolies such as oil producing companies face no competition and can influence market prices by regulating quantity supplied. In practice, it is very difficult to get a pure monopoly since there are very few, if any, products that do not have close substitutes. Berlin Municipal Electric Company is however a good example of a monopoly firm. It is the sole operator in electric supply industry of Berlin Municipal.Advertising Looking for research paper on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More The main factors contributing towards this monopoly is mainly the huge initial investment outlay required to invest in the electric sector and the government restrictions. The Municipal electric companies are therefore mainta ined so as to reduce electricity costs and thus they do not compete with other private producers. They purchase energy in bulk and offer to consumers at cost with no profit motive. Their existence is therefore protected by the government. The market might change with the increased popularity of alternative sources of power and proliferation of private power producers. To ensure that power is still affordable to the citizens, the government should offer subsidies to suppliers of clean energy. Municipal power suppliers should also be allowed to compete with private suppliers so as to ensure power is supplied in an efficient manner. Conclusion Pure competition and pure monopolies might not be sustainable in future. Traders in pure competitive markets will seek to differentiate their products whereas new entrants will cause monopoly powers to cease for pure monopolies. Reference O’Sullivan, A., Sheffrin, S., and Perez, S., (2009). Microeconomics principles, applications and tools , seventh edition. Prentice Hall Peterson, W., (1977). Introduction to economics. New Jersey: Prentice Hall This research paper on Microeconomics: competition and monopoly was written and submitted by user Christina Wagner to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.

Why George W. Bush Should Not Be Reelected essays

Why George W. Bush Should Not Be Reelected essays The decision of any electorate to reelect the current presidential incumbent is usually contingent on his or her performance on important issues such as economic development, social justice, and foreign policy. Though the domestic economy has been the deciding factor in most U.S. presidential races, the Republican Party elevated September 11th and Homeland Security to the top of its political agenda in 2002 congressional campaign, based on which it won the Senate. Given its previous success and the recent increase in poll ratings post Saddam's capture, it is likely to feature prominently in the 2004 elections as well. While one more, unfortunate terrorist incident may well swing public opinion overwhelmingly in favor of Bush and the Republicans, the American public would do well to remember the democratic values it stands for and the fact that the Iraq war has not only undermined those values but taken a heavy toll of American As things stand, it does appear that the American electorate is divided in its opinion. A recent CBS News poll, in fact, shows that the president's overall job approval rating of 50% ties with the lowest ratings he has received since assuming office, and his disapproval rating (45%) is at its highest. Significantly, ratings on his ability to handle an international crisis, and perceptions of the respect he receives from international leaders has fallen back to pre-9/11 levels, after have risen sharply in the wake of the terrorist attacks and the capture of Saddam Hussein. The fall in ratings is attributed to continuing attacks on American troops in Iraq, and the costs of the war (CBS News Polls, Jan. 17, These ratings match similar findings by other polls. The Los Angeles Times poll, for instance, reveals that Americans remained split along lines of gender, race, and cultural values on the issue of Bush's reelection, with 42% stating that Bush...

Design a total rewards program based on the organization that you have Essay

Design a total rewards program based on the organization that you have studied thus far in the course - Essay Example ply goes to the scheme telling that organization wants to obtain productivity and outcome from its employees and in turn it will provide its employees valuable experience and reward. The following paper will represent the total reward program for the certain organization and will recommend changes to it. It will further assess and discuss the risks of implementing the program and the opportunities it can give to the organization. Certain metrics will be provided for evaluating the total rewards program. For the Sport & Health fitness center it is vital to provide the best services for its clients through excellent work of their employees. As it puts into practice different activities that are connected with the health improvement, it should take into an account professionalism in the execution of its employees’ duties. The organization offers affordable services and is aimed on people from all occupations and life styles and involves everyone from children to the elderly. Since modern life cause people to feel stress more often, for some individuals it is also the monotonous and inactive life and going in for various sport and fitness centers will be the way out that will provide them healthy life. These facts put fitness Centre in the forehand as one of the growing industries. However, the modern technologies and improvements in the recruitment spheres require deeper understanding of how such business should conduct its activities. Thus, Sport & Health fitness center experi ences currently certain financial problems, as the technology is advancing and it requires better acquisition of more modern equipment. It is also facing the challenge that is connected with the people’s understanding of fitness and its role in their lives. Along with it, the organization should revise its policy of providing service, as in the future it can face with the competition because health issue is obtaining more attention and thus more fitness establishments open its doors to

Biology Research Paper Example | Topics and Well Written Essays - 500 words

Biology - Research Paper Example Therefore the hypothesis is that "Light deprivation during fetal development and infancy affect the brain function during adulthood". Since this experiment cannot be performed on humans, we need to test this hypothesis in rat model for light deprivation. There will be three sets of experiments, viz., 1. Light deprivation of mother during fetal development (pre-natal). 2. Light deprivation after birth (post natal) for 6 weeks. 3. Light deprivation during fetal development and after birth (both pre-natal and post-natal). Pregnant mothers will be either reared in dark. The pups born to these mothers will be either grown in dark (group 3) or normal light cycle, i.e., 12 hours light followed by 12 hours dark (group 1) for six weeks. Alternatively, pregnant mothers will be reared in normal light and the pups born to these mothers will be reared in dark for six weeks (group 2). All other variables like room temperature, humidity, access to food, quality of food and water will remain constant. After six weeks, the animals will be tested for learning behavior, by a T-maze. In a T-maze, the reward (food) can be placed at on e end and the hungry rat is allowed to choose the arm several times. The number of trails it takes the animal to choose the correct arm gives a measure of its learning capability. Atleast 6-8 animals will be tested in each group and the number of trails recorded.

Domino's pizza case study Example | Topics and Well Written Essays - 1000 words

Domino's pizza - Case Study Example This analysis presents the elemental constructs of the new information strategy, the digital technologies used in the implementation of the strategy as well as the qualification of such technology to be part or reminiscent of a digital ecosystem. Domino’s revolutionary information system stems primarily from operation innovation complimented by technology-enabled processes, and more specifically the store design. Since the basic steps of making pizza available entail placement of the order by the customer followed by an immediate order preparation that takes into consideration the waiting time duration balanced against quality maintenance, the need for store managers to monitor the rate of order preparation became imperative. Consequently, the business based on its operational design and available technology rolled out a program, the leaderboard that provides store managers with real-time information on performance analytics and operational metrics. Through this platform, store managers are able to monitor the performance of their respective stores relative to that of neighboring ones. In addition to providing information to the store managers, the leaderboard also relayed the same information to regional managers and to the headquarters, which implies that remote monitoring of store became possible. It also increased transparency in the operations of the stores since employees were able to track key performance indicators and make corrections whenever a situation arose that warranted such.

Effect of Early Numeracy Learning on Numerical Reasoning

Effect of Early Numeracy Learning on Numerical Reasoning FROM NUMERICAL MAGNITUDE TO FRACTIONS Early understanding of numerical magnitude and proportion is directly related to subsequent acquisition of fraction knowledge Abstract Evidence from experiments with infants concerning their ability to reason with numerical magnitude is examined, along with the debate relating to the innateness of numerical reasoning ability. The key debate here concerns performance in looking time experiments, the appropriateness of which is examined. Subsequently, evidence concerning how children progress to reasoning with proportions is examined. The key focus of the debate here relates to discrete vs continuous proportions and the difficulties children come to have when reasoning with discrete proportions specifically. Finally, the evidence is reviewed into how children come to reason with fractions and, explicitly, the difficulties experienced and why this is the case. This is examined in the context of different theories of mathematical development, together with the effect of teaching methods. Early understanding of numerical magnitude and proportion is directly related to subsequent acquisition of fraction knowledge Understanding of magnitude and fractions is crucial in contemporary society. Relatively simple tasks such as dividing a restaurant bill or sharing cake at a birthday party rely on an understanding of these concepts in order to determine how much everyone requires to pay towards the bill or how much cake everyone can receive. Understanding of these concepts is also required to allow calculation of more complex mathematical problems, such as solving equations in statistical formulae. It is therefore evident that a sound understanding of magnitude and fractions is required in everyday life and whilst most adults take for granted the ability to calculate magnitudes and fractions, this is not so for children, who require education to allow the concepts to be embedded into their understanding. De Smedt, Verschaffel, and Ghesquià ¨re (2009) suggest that children’s performance on magnitude comparison tasks predicts later mathematical achievement, with Booth and Siegler (2008) further arguing for a causal link between early understanding of magnitude and mathematical achievement. Despite these findings, research tends to highlight problems when the teaching of whole number mathematics progresses to teaching fractions. Bailey, Hoard, Nugent, and Geary (2012) suggest that performance on fraction tasks is indicative of overall mathematics performance levels, although overall mathematical ability does not predict ability on these tasks. This article reviews the current position of research into how young children, between birth and approximately seven years of age come to understand magnitude and how this relates to the subsequent learning of fractions. By primarily reviewing research into interpretation of numerical magnitude, the first section of this paper will have a fairly narrow focus. This restriction is necessary due to the large volume of literature on the topic of infant interpretation of magnitude generally and is also felt to be appropriate due to the close link between integers, proportions and fractions. An understanding of magnitude is essential to differentiate proportions (Jacob, Vallentin, Nieder, 2012) and following the review of literature in respect of how magnitude comes to be understood, the paper will review the present situation in respect of how young children understand proportions. Finally, the article will conclude with a review of where the literature is currently placed in respect of how young children’s understanding of magnitude and proportion relates to the learning of fractions and briefly how this fits within an overall mathematical framework. Is the understanding of numerical magnitude innate? There are two opposing views in respect of the innateness of human understanding of number and magnitude. One such view suggests that infants are born with an innate ability to carry out basic numerical operations such as addition and subtraction (Wynn, 1992, 1995, 2002). In her seminal and widely cited study, Wynn (1992) used a looking time procedure to measure the reactions of young infants to both possible and impossible arithmetical outcomes over three experiments. Infants were placed in front of a screen with either one or two objects displayed. A barrier was then placed over the screen, restricting the infants’ view, following which an experimenter either â€Å"added† or â€Å"removed† an item. The infants were able to see the mathematical operation taking place due to a small gap at the edge of the screen which showed items being added or subtracted, but were not able to view the final display until the barrier was removed. Following the manipulation and r emoval of the barrier, infants’ looking times were measured and it was established that overall infants spent significantly more time looking at the impossible outcome than the correct outcome. These results were assumed to be indicative of an innate ability in human infants to manipulate arithmetical operations and, accordingly, distinguish between different magnitudes. The suggestion of an innate human ability to manipulate arithmetical operations is given further credence by a number of different forms of replication of Wynn’s (1992) original study (Koechlin, Dehaene, Mehler, 1997; Simon, Hespos, Rochat, 1995). Feigneson, Carey, and Spelke (2002) and Uller, Carey, Huntley-Fenner, and Klatt (1999) also replicated Wynn, although interpreted the results as being based on infant preference for object-based attention as opposed to an integer-based attention. Despite replications of Wynn (1992), a number of studies have also failed to replicate the results, leading to an alternative hypothesis. Following a failure to replicate Wynn, Cohen and Marks (2002) posit that infants distinguish magnitude by favouring more objects over less and also display a preference towards the number of objects which they have initially been presented, regardless of the mathematical operation carried out by the experimenter. This suggestion arises from the results of an experiment where Wynn’s hypothesis of innate mathematical ability was tested against the preference hypothesis noted above. Further evidence against Wynn (1992) exists following an experiment by Wakeley, Rivera, and Langer (2000), who argue that no systematic evidence of addition and subtraction exists, instead the ability to add and subtract progressively develops during infancy and childhood. Whilst this does not specifically support Cohen and Marks, it does cast doubt on basic arithme tical skills and, accordingly, the ability to work with magnitude existing innately. How do children understand magnitude as they age? By six-months old, it is suggested that infants employ an approximate magnitude estimation system (McCrink Wynn, 2007). Using a looking-time experiment to assess infant attention to displays of pac-men and dots on screen, infants appeared to attend to novel displays with a large difference in ratio (2:1 to 4:1 pac-men to dots, 4:1 to 2:1 pac-men to dots), with no significant difference in attention times to novel stimuli with a closer ratio (2:1 to 3:1 pac-men to dots, 3:1 to 2:1pac-men to dots). These results were interpreted to exemplify an understanding of magnitudes with a degree of error, a pattern already existing in the literature on adult magnitude studies (McCrink Wynn, 2007). Unfortunately, one issue in respect of interpreting the results of experiments with infants is that they cannot explicitly inform experimenters of their understanding of what has happened. It has been argued that experiments making use of the looking-time paradigm cannot be properly understood as exp erimenters must make an assumption that infants will have the same expectations as adults, a matter which cannot be appropriately verified (Charles Rivera, 2009; K. Mix, 2002). As children come to utilise language, words which have a direct relationship to magnitude (eg., â€Å"little,† â€Å"more,† â€Å"lots†) enter into their vocabulary. The use of these words allows researchers to investigate how they come to form internal representations of magnitude and how they are used to explicitly reveal understanding of such magnitudes. Specifically isolating the word â€Å"more†, children appear to develop an understanding of the word as being comparatively domain neutral (Odic, Pietroski, Hunter, Lidz, Halberda, 2013). In an experiment requesting children aged 2.0 – 4.0 (mean age = 3.2) to distinguish which colour on pictures of a set of dots (numeric task) or blobs of â€Å"goo† (non-numeric task) represented â€Å"more†, it was established that no significant difference exists between performance on both numeric and non-numeric tasks. In addition, it was found that children age approximately 3.3 years and above performed significantly above chance, whereas those children below 3.3 years who participated did not. This supports the assertion that the word â€Å"more† is understood by young children as both comparative and in domain neutral terms not specifically related to number or area. It could also be suggested that it is around the age of 3.3 years when the word â€Å"more † comes to hold some sort of semantic understanding in relation to mathematically based stimuli (Odic et al., 2013). It is difficult to compare this study to that of McCrink and Wynn (2007) due to the differing nature of methodology. It would certainly be of interest to researchers to investigate the possibility of some sort of comparison research, however, as it is unclear how the Odic et al. (2013) study fits with the suggestion of an approximate magnitude estimation system, notwithstanding the use of language. Generally, children understand numerical magnitude on a logarithmic basis at an early age, progressing to a more linear understanding of magnitude as they age (Opfer Siegler, 2012), a change which is beneficial. It is suggested that the more linear a child’s mental representation of magnitude appears, the better their memory for magnitudes will be (Thompson Siegler, 2010). There are a number of reasons for this change in understanding, such as socioeconomic status, culture and education (Laski Siegler, in press). In the remainder of this section, the understanding of magnitude in school age children (up to approximately seven years old) is reviewed, although only the effect of education will be referred to. The remainder of the reasons are noted in order to exemplify some issues which can also have an impact on children’s development of numerical magnitude understanding. As children age, the neurological and mental representations of magnitude encompass both numeric and non-numeric stimuli in a linear fashion (Opfer Siegler, 2012). On this basis, number line representations present a reasonable method for investigation of children’s’ understanding of magnitude generally. One method for examining number line representations of magnitude in children uses board games in which children are required to count moves as they play. Both prior to and subsequent to playing the games, the children involved in the experiment are then presented with a straight line, the parameters of which are explained, and requested to mark on the line where a set number should be placed. This allows researchers to establish if the action of game playing has allowed numerical and/or magnitude information to be encoded. In an experiment of this nature with pre-school children (mean age 4 years 8 months), Siegler and Ramani (2009) established that the use of a linea r numerical board game (10 spaces) enhanced children’s understanding of magnitude when compared to the use of a circular board game. It is argued that the use of a linear board game assists with the formation of a retrieval structure, allowing participants to encode, store and retrieve magnitude information for future use. Similar results have subsequently been obtained by Laski and Siegler (in press), working with slightly older participants (mean age 5 years 8 months), who sought to establish the effect of a larger board (100 spaces). In this case, the structure of the board ruled out high performance based on participant memory of space location on the board. In addition, verbalising movements by counting on was found to have a significant impact on retention of magnitude information. A final key question relating to understanding of magnitude relates to the predictive value of current understanding on future learning. When education level was controlled for, Booth and Siegler (2008) found a significant correlation between the pre-test numerical magnitude score on a number line task and post-test scores of 7 year-olds on both number line tasks and arithmetic problems, This discovery has been supported by a replication by De Smedt et al, (2009) and these findings together suggest that an understanding of magnitude is fundamental in predicting future mathematical ability. It is also clear that a good understanding of magnitude will assist children in subsequent years when the curriculum proceeds to deal more comprehensively with matters such as proportionality and fractions. From numerical magnitudes to proportions Evidence reviewed previously in this article tends to suggest that children have the ability to distinguish numerical magnitudes competently by the approximate age of 7 years old. Unfortunately, the ability to distinguish between magnitudes does not necessarily suggest that they are easily reasoned with by children. Inhelder and Piaget (1958) first suggested that children were unable to reason with proportions generally until the transition to the formal operational stage of development, at around 11-12 years of age. This point is elucidated more generally with the argument that most proportional reasoning tasks prove difficult for children, regardless of age (Spinillo Bryant, 1991). However, more recent research has suggested that this assertion does not strictly hold true, with children as young as 4 and 5 years old able to reason proportionally (Sophian, 2000). Recent evidence suggests that the key debate in terms of children’s ability to reason with proportions concerns t he distinction between discrete quantities and continuous quantities. Specifically, it is argued that children find dealing with problems involving continuous proportions simpler than those involving discrete proportions (Boyer, Levine, Huttenlocher, 2008; Jeong, Levine, Huttenlocher, 2007; Singer-Freeman Goswami, 2001; Spinillo Bryant, 1999). In addition, the â€Å"half† boundary is also viewed as being of critical importance in children’s proportional reasoning and understanding (Spinillo Bryant, 1991, 1999). These matters and suggested reasons for the experimental results are now discussed. Proposing that first order relations are important in children’s understanding of proportions, Spinillo and Bryant (1991) suggest that children should be successful in making judgements on proportionality using the relation â€Å"greater than†. In addition, it is suggested that the â€Å"half† boundary also has an important role in proportional decisions. Following an experiment which requested children make proportional judgements about stimuli which either crossed or did not cross the â€Å"half† boundary, it was found that children aged from approximately 6 years were able to reason relatively easily concerning proportions which crossed the â€Å"half† boundary. From these results, it was drawn that children tend to establish part-part first order relations to deal with proportion tasks (eg. reasoning that one box contains â€Å"more blue than white† bricks). It was also suggested that the use of the â€Å"half† boundary formed a fi rst reference to children’s understanding of part-whole relations (eg. reasoning that a box contained â€Å"half blue, half white† bricks). No express deviation from continuous proportions was used in this experiment and, therefore, the only matter which can be drawn from this result is that children as young as 6 years old can reason about continuous proportions. In a follow up experiment, Spinillo and Bryant (1999) again utilised their â€Å"half† boundary paradigm with the addition of continuous and discrete proportion conditions. Materials used in the experiment were of an isomorphic nature. The results broadly mirrored Spinillo and Bryant’s (1991) initial study, in which it was noted that the â€Å"half† boundary was important in solving of proportional problems. This also held for discrete proportions in the experiment despite performance on these tasks scoring poorly overall. Children could, however, establish that half of a continuous quantity is identical to half of a discrete quantity, supporting the idea that the â€Å"half† boundary is crucial to reasoning about proportions (Spinillo Bryant, 1991, 1999). Due to the similar nature of materials used in this experiment, a further research question was posited in order to establish whether a similar task with non-isomorphic constituents would have any impac t on the ability of participants to reason with continuous proportions (Singer-Freeman Goswami, 2001). Using models of pizza and chocolates for the continuous and discrete conditions respectively, participants carried out a matching task where they were required to match the ratio in the experimenters’ model with their own in either an isomorphic (pizza to pizza) or non-isomorphic (chocolate to pizza) condition. In similar results to the previous experiments, it was found that participants had less problems dealing with continuous proportions than discrete proportions. In addition, performance was superior in the isomorphic condition compared to the non-isomorphic condition. An interesting finding, however, is that problems involving â€Å"half† were successfully resolved, irrespective of condition, further adding credence to the importance of this feature. Due to participants in this experiment being slightly younger than those in Spinillo and Bryant’s (1991, 1999) experiments, it is argued that the â€Å"half† boundary may be used for proportional reasoning tasks at a very early age (Singer-Freeman Goswami, 2001). In addition to the previously reviewed literature, there is a vast body of evidence the difficulty of discrete proportional reasoning compared to continuous proportional reasoning in young children. Yet to be identified, however, is a firm reason as to why this is the case. Two specific suggestions as to why discrete reasoning appears more difficult than continuous reasoning are now discussed. The first suggestion is based on a theory posited by Modestou and Gagatsis (2007) related to the improper use of contextual knowledge. An error occurs when certain knowledge, applicable to a certain context, is used in a setting to which it is not applicable. A particular problem identified with this form of reasoning is that it is difficult to correct (Modestou Gagatsis, 2007). This theory is applied to proportional reasoning by Boyer et al, (2008), who suggest that the reason children find it difficult to reason with discrete proportions is because they use absolute numerical equivalence to explain proportional problems. Continuous proportion problems are presumably easier due to the participants using a proportional schema to solve the problem, whereas discrete proportions are answered using a numerical equivalence schema where it is not applicable. An altogether different suggestion for the issue is made by Jeong et al, (2007), invoking Fuzzy trace theory (Brainerd Reyna, 1990; Reyna Brainerd, 1993). The argument posited is that children focus more on the number of target partitions in the discrete task, whilst ignoring the area that the target partitions cover. It is the area that is of most relevance to the proportion task and, therefore, focussing on area would be the correct outcome. Instead, children appear to instinctively focus on the number of partitions, whilst ignoring their relevance (Jeong et al., 2007), thereby performing poorly on the task. From proportions to fractions In tandem with children’s difficulties in relation to discrete proportions, there is a wealth of evidence supporting the notion that fractions prove difficult at all levels of education (Gabriel et al., 2013; Siegler, Fazio, Bailey, Zhou, 2013; Siegler, Thompson, Schneider, 2011). Several theories of mathematical development exist, although only some propose suggestions as to why this may be the case. The three main bodies of theory in respect of mathematical development are privileged domain theories (eg. Wynn, 1995b), conceptual change theories (eg. Vamvakoussi Vosniadou, 2010) and integrated theories (eg, Siegler, Thompson, Schneider, 2011). In addition to the representation of fractions within established mathematical theory, a further dichotomy exists in respect to how fractions are taught in schools. It is argued that the majority of teaching of fractions is carried out via a largely procedural method, meaning that children are taught how to manipulate fractions with out being fully aware of the conceptual rules by which they operate (Gabriel et al., 2012). Discussion in this section of the paper will focus on how fractions are interpreted within these theories, the similarities and differences therein, together with how teaching methods can contribute to better overall understanding of fractions. Within privileged domain theories, development of understanding of fractions is viewed as secondary to and inherently distinct from the development of whole numbers (Leslie, Gelman, Gallistel, 2008; Siegler et al., 2011; Wynn, 1995b). As previously examined, it is argued that humans have an innate system of numerical understanding which specifically relates to positive integers, he basis of privileged domain theory being that positive integers are â€Å"psychologically privileged numerical entities† (Siegler et al., 2011, p. 274). Wynn (1995b) suggests that difficulty exists with learning fractions due to the fact that children struggle to conceive of them as discrete numerical entities. This argument is similar to that of Gelman and Williams (1998, as cited in Siegler et al., 2011) who suggest that the knowledge of integers presents barriers to learning about other types of number, due to distinctly different properties (eg. assumption of unique succession). Presumably, priv ileged domain theory views the fact that integers are viewed as being distinct in nature from any other type of numerical entity is the very reason for children having difficulty in learning fractions, as their main basis of numerical understanding prior to encountering fractions is integers. Whilst similar to privileged domain theories in some respects, conceptual change theories are also distinct. The basis of conceptual change theories is that concepts and relationships between concepts are not static, but change over time (Vamvakoussi Vosniadou, 2010). In essence, protagonists of conceptual change do not necessarily dismiss the ideas of privileged domain theories, but allow freedom for concepts (eg. integers) and relationships between concepts (eg. assumption of unique succession) to be altered in order to accommodate new information, albeit that such accommodation can take a substantial period of time to occur (Vamvakoussi Vosniadou, 2010). Support for conceptual change theory is found in the failure of children to comprehend the infinite number of fractions or decimals between two integers (Vamvakoussi Vosniadou, 2010). It is argued that the reason for this relates to the previously manifested knowledge of integer relations (Vamvakoussi Vosniadou, 2010) and that it is closely related to a concept designated as the â€Å"whole number bias† (Ni Zhou, 2005). The â€Å"whole number bias† can be defined as a tendency to utilise schema specifically for reasoning with integers to reason with fractions (Ni Zhou, 2005) and has been referred to in a number of studies as a possible cause of problems for children’s reasoning with fractions (eg. Gabriel et al., 2013; Meert, Grà ©goire, Noà «l, 2010). Siegler et al, (2011) propose an integrated theory to account for the development of numerical reasoning generally. It is suggested by this theory that the development of understanding of both fractions and whole numbers occurs in tandem with the development of procedural understanding in relation to these concepts. The theory claims that â€Å"numerical development involves coming to understand that all real numbers have magnitudes that can be ordered and assigned specific locations on number lines† (Siegler et al., 2011, p. 274). This understanding is said to occur gradually by means of a progression from an understanding of characteristic elements (eg. an understanding that whole numbers hold specific properties distinct from other types of number) to distinguishing between essential features (eg. different properties of all numbers, specifically their magnitudes) (Siegler et al., 2011). In contrast to the foregoing privileged domain and conceptual change theories, the inte grated theory views acquisition of knowledge concerning fractions as a fundamental course of numerical development (Siegler et al., 2011). Supporting evidence for this theory comes from Mix, Levine and Huttenlocher (1999), who report an experiment where children successfully completed fraction reasoning tasks in tandem with whole number reasoning tasks. A high correlation between performances on both tasks is reported and it is suggested that this supports the existence of a shared latent ability (Mix et al., 1999). One matter which appears continuously in fraction studies is the pedagogical method of delivering fraction education. A number of researchers have argued that teaching methods can have a significant impact on the ability of pupils to acquire knowledge about fractions (Chan, Leu, Chen, 2007; Gabriel et al., 2012). It is argued that the teaching of fractions falls into two distinct categories, teaching of conceptual knowledge and teaching of procedural knowledge (Chan et al., 2007; Gabriel et al., 2012). In an intervention study, Gabriel et al, (2012) segregated children into two distinct groups, the experimental group receiving extra tuition in relation to conceptual knowledge of fractions, with the control group following the regular curriculum. The experimental results suggested that improved conceptual knowledge of fractions (eg. equivalence) allowed children to perform better when presented with fraction problems (Gabriel et al., 2012). This outcome supports the view that more ef fort should be made to teach conceptual knowledge about fractions, prior to educating children about procedural matters and performance on fractional reasoning may be improved. Conclusion and suggestions for future research In this review, the process of how children come to understand and reason with numerical magnitude, progressing to proportion and finally fractions has been examined. The debate concerning the innateness of numerical reasoning has been discussed, together with how children understand magnitude at a young age. It has been established that children as young as six months old appear to have a preference to impossible numerical outcomes, although it remains unclear as to why this is. The debate remains ongoing as to whether infants are reasoning mathematically, or simply have a preference for novel situations. Turning to proportional reasoning, evidence suggests a clear issue when children are reasoning with discrete proportions as opposed to continuous ones. Finally, evidence concerning how children reason with fractions and the problems therein was examined in the context of three theories of mathematical development. Evidence shows that all of the theories can be supported to some ext ent. A brief section was devoted to how teaching practice effects children’s learning of fractions and it was established that problems exist in terms of how fractions are taught, with too much emphasis placed on procedure and not enough placed on conceptual learning. With the foregoing in mind, the following research questions are suggested to be a good starting point for future experiments: How early should we implement teaching of fraction concepts? Evidence from Mix et al, (1999) suggests that children as young as 5 years old can reason with fractions and it may be beneficial to children’s education to teach them earlier; Should fractions be taught with more emphasis on conceptual knowledge? References Bailey, D. H., Hoard, M. K., Nugent, L., Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113, 447–455. Booth, J., Siegler, R. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79, 1016–1031. Boyer, T. W., Levine, S. C., Huttenlocher, J. (2008). Development of proportional reasoning: where young children go wrong. Developmental Psychology, 44, 1478–1490. Brainerd, C. J., Reyna, V. F. (1990). Inclusion illusion: Fuzzy-trace theory and perceptual salience effects in cognitive development. Developmental Review, 10, 363–403. Chan, W., Leu, Y., Chen, C. (2007). Exploring Group-Wise Conceptual Deficiencies of Fractions for Fifth and Sixth Graders in Taiwan. The Journal of Experimental Education, 76, 26–57. Charles, E. P., Rivera, S. M. (2009). Object permanence and method of disappearance: looking measures further contradict reaching measures. Developmental Science, 12, 991–1006. Cohen, L. B., Marks, K. S. (2002). How infants process addition and subtraction events. Developmental Science, 5, 186–201. De Smedt, B., Verschaffel, L., Ghesquià ¨re, P. (2009). 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Edgar Allan Poe :: Essays Papers

Edgar Allan Poe2 Edgar Allan Poe’s life had a profound effect on the technical style of his writing. Poe spent most of his life raised by foster parents who did not contribute to or encourage his writing. His first work was published in 1827, at the young age of 18, but his story in 1833, â€Å"MS Found in a Bottle,† marked the beginning of his writing career. Poe uses darkness and death in many of his stories. In his poems he was able to illustrate moods of mystery very well. Edgar Allan Poe was a unique writer who was not afraid to do something different from all the authors, while his adulthood was short and depressing. Born to traveling actors David and Elizabeth Poe on January 19, 1809, Edgar Poe was the middle child of three children. His father, David Poe, was from a Baltimore family. He was an actor by profession and a heavy drinker. Edgar was never very close with his older brother, William Henry Leonard Poe, because he had been left with his paternal grandparents around September 1807 for what began as an undetermined amount of time. In July of 1810 David Poe deserted his family and died shortly after. His death was most possibly alcohol elated. Elizabeth was still pregnant with their youngest child, Rosalie, who was born that December, at this time. Approximately a year after her daughter was born, in December of 1811, Elizabeth Poe died of tuberculosis. As a result of her death, William Henry Leonard stayed with his grandparents, Edgar was adopted by a couple of wealthy merchants from Richmond, Virginia, John and Fanny Allan, who offered him a better education than his grandparents could , while Rosalie was adopted Mr. and Mrs. William Mackenzie. In 1815, John Allan moved the family to England to try to make Allan and Ellis prosper. While there, Edgar went to private schools where his creative writings were discouraged. In 1820 the Allan’s returned to Virginia as a result of the collapse of John’s business venture. Shortly after the Allan’s return to the United States, Edgar began to support himself as he moved to Boston and worked in a merchandise house. Edgar Allan Poe :: Essays Papers Edgar Allan Poe2 Edgar Allan Poe’s life had a profound effect on the technical style of his writing. Poe spent most of his life raised by foster parents who did not contribute to or encourage his writing. His first work was published in 1827, at the young age of 18, but his story in 1833, â€Å"MS Found in a Bottle,† marked the beginning of his writing career. Poe uses darkness and death in many of his stories. In his poems he was able to illustrate moods of mystery very well. Edgar Allan Poe was a unique writer who was not afraid to do something different from all the authors, while his adulthood was short and depressing. Born to traveling actors David and Elizabeth Poe on January 19, 1809, Edgar Poe was the middle child of three children. His father, David Poe, was from a Baltimore family. He was an actor by profession and a heavy drinker. Edgar was never very close with his older brother, William Henry Leonard Poe, because he had been left with his paternal grandparents around September 1807 for what began as an undetermined amount of time. In July of 1810 David Poe deserted his family and died shortly after. His death was most possibly alcohol elated. Elizabeth was still pregnant with their youngest child, Rosalie, who was born that December, at this time. Approximately a year after her daughter was born, in December of 1811, Elizabeth Poe died of tuberculosis. As a result of her death, William Henry Leonard stayed with his grandparents, Edgar was adopted by a couple of wealthy merchants from Richmond, Virginia, John and Fanny Allan, who offered him a better education than his grandparents could , while Rosalie was adopted Mr. and Mrs. William Mackenzie. In 1815, John Allan moved the family to England to try to make Allan and Ellis prosper. While there, Edgar went to private schools where his creative writings were discouraged. In 1820 the Allan’s returned to Virginia as a result of the collapse of John’s business venture. Shortly after the Allan’s return to the United States, Edgar began to support himself as he moved to Boston and worked in a merchandise house.