The Evaluation of TOEFL test Free Essays

The test is used in college admissions for non-native English speaking students to an English- peaking country purposes. Although it provides scores of test takers so that college administrators can know their English proficiency directly, the test is not aim at ranking. The test divides criteria into four parts: reading, listening, speaking and writing. We will write a custom essay sample on The Evaluation of TOEFL test or any similar topic only for you Order Now According to process, reading comprehension is the first part should be measured. This part tests test takers’ ability to comprehend academic reading materials. In this section, the format of questions Is multiple choices and content of test questions Involves In various ways such as testing vocabulary, details, and mall Ideas. To avoid creating an advantage to examinees In any one field of study, sufficient context Is provided so that no specific subject can be used to answer the questions. It is a big advantage of the test. Moreover, other advantage is like that, due to diversified questions, it helps learners to know how to get information effectively in a limited time. It also encourages test takers to read more academic materials involving in different area and critically think how to read deferent academic articles when they are learning. However, the questions of reading test mostly adopt multiple choice rather than short answer. It may limit takers to think more about their own opinion. For example, when testing about vocabulary, the question Just gives four choices and asks examinees to choose the best one. Actually, there are also have a lot of words can be selected. The goal of the question Is to assess test takers about their understanding of this word. Therefore, I think If questions may ask examinees to write down their own words based on their comprehension that Is better. In the listening section, it involves in dialogues and academic talks. The purpose of this section is to test listening comprehension in academic environment. In other words, it measures test takers’ ability of listening for basic comprehension, listening for pragmatic understanding and to connect and combine ideas presented in multiple information sources. Like reading section, the formats of questions also adopt various ways. Moreover, examinees’ note taking can be practiced and improved from the listening test. Dialogues and lectures talking will last more than one minute. To most of them, they cannot memorize the whole content without noting. Therefore, how to write down key information in a limited time can be a skill for test takers who will study In an academic atmosphere. Furthermore, diverse formats provide a good opportunity for them to realize how to master essential Information with thinking different ways. The speed of listening Is normal speed and sometimes, the listening test involves in different voices of pronunciation to make test takers know and listening test as we discussed above. I think the way that listening test needs to improve is similar to reading test. It also means that using open questions replace multiple choices can be thought. Next part is speaking test. This section will test ability to communicate effectively in a variety of situations. The ability of synthesizing and summarizing what test takers have read in their textbooks and heard in and outside of the class, the skill of forming their own opinions in response to the information they have processed, well-developed, coherent and clear idea with effective use of grammar, and good pronunciation and intonation these are main goals to assess speaking ability. The strength of this part is to combine reading with speaking and to provide opinion-based questions. Moreover, the degree of each question be tested is gradually harder. The topic for examinees may also from familiar to a little hard to understand. In my opinion, the speaking test can be a bad section as well as a good one in TOEFL. The good way is that it not Just evaluates speaking ability in academic way but also involves in common environment. It not just has output but input first such as reading, and then speaking. Nevertheless, due to the test is based on Internet, that is, speaking section also needs to be tested in the computer, and it brings a problem. Compared with talking to examiners, it is not flexible. It has no communication between examinees and examiners. For my perspective, test takers also may feel anxiety because there has no response when hey speak and feel nervous or without good preparation to speak due to time limited. The last component in TOEFL is the writing section. It measures ability to write in standard academic English. It divides into two parts: integrated writing task and independent writing task. The goal of the first part integrated writing task asks examiners to demonstrate that they have understood material coming from different sources (reading and listening) and to combine the information from those sources in a coherent, well organized, summarized written form to draw conclusions of the important points. The independent writing task aims to measure the students’ ability to state their opinions or express their comments on topics which are based on their personal knowledge and experience. In general, if test takers want to get a higher score, they should know steps of essay and practice more in academic ways. The good thing of this TOEFL writing test is using academic materials to integrate reading and listening to write a summary. Although topic of independent writing task is not necessary referring to academic issues, the writing steps should follow in academic steps. Moreover, owing to computer-based writing, the score is not influenced by handwriting. Nevertheless, it may also be a problem due to time limit especially for some people who are not good at typing or have not well speediness. It is a little hard to deal with except encouraging these persons to practice more about their typing. To sum up, I think TOEFL test is a good test though it brings some challenge to me. There have a lot of benefits of this test. Firstly, it ensures that test- takers are being measured objectively on the same material. The grading is standardized based on rubrics provided by TEST, so test scores are the same no matter whom or what is scoring them. Secondly, there is no age, no gender and no nationality limit for taking the test. Anyone who wants to assess their English language performance especially for people who need to study aboard in English feedback. When persons received their result, score will definitely appear in their paper and evaluation of each section will be provided so that examinees are able to know the strength and weakness of themselves in general ways. Finally, the speaking and writing parts integrate some input tasks such as reading and listening to test rather than be measured separately. The integrated tasks may be considered more Hellenizing in the test will help learners build the confidence needed to communicate in the academic environments they plan to enter because students need to be able to combine their language skills in the classroom. Appropriate challenge will improve learners to more think about their weakness of language learning and hence to find effective ways they can develop. However, there still have some limitations in the test. In the first place, although test takers can be offered some feedbacks from the organization, the feedbacks of scores Just simplify the degree of their performance. They cannot get more individual feedback about the strength and weakness they have according to the test. Likewise, each level still has its deviation. Even though examinees can get same level of sections for each test, they may confuse about the score why last time they can get a high score whereas this time is a low score. In the second place, I feel the time arrangement also has its problem. In general, the test will last three hours at least but Just ten minutes for break from morning to afternoon. For many test takers, the time may make them feel exhausted and influence their performance more or less. In the third place, the procedure of the test may also have its weakness. In order to avoid cheating in the test, examiners require learners to answer extra section such as reading or listening based on different individuals randomly. Hence, it will result in the time of speaking section beginning different. It is unfair to the individuals who are doing speaking earlier while others who are still doing reading or listening part can have a chance to listen others’ speaking and have more time to prepare during the break. The final point I want to mention is that there have a lot of test preparation for each section test. Learners will make more focus on searching or studying methods in order to get a higher score rather than improve their language ability. As we discussed above the limitation, not all can get right solution. But I think we still are able to find some ways to improve. Firstly, the examiners can provide rubrics of each specific score for test takers instead of the level of performance. That is, I think they need to list more details of each point and make learners more better understanding about why they can get this point and why they cannot get. The feedback should mainly reflect individual’s strength and weakness instead of general errors. The general problem also can be placed in the reflection but not in the domain way. Secondly, when talking about dealing with the procedure, I think administers may provide another place for test takers about test speaking. In other words, when finishing their reading and listening part, examiners need to go the place which dedicated to speaking test after having a rest. Finally, due to various test preparation, in my opinion, I believe that form of diversification can be a good way to assess. For example, applying more open questions instead of multiple choices may be helpful for improving learners high order thinking. How to cite The Evaluation of TOEFL test, Papers

Criminal Procedure free essay sample

After reading the situation and being asked five questions, I have come up with answers for each one of them. In this paper I will let you know what the answers to each one of the questions are. I will also provide you with the reasoning on why I chose the answers that I did. First, I believe that Officer Smith did have reasonable suspicion to make the stop of the vehicle. In all actuality, any reason is good enough for an officer on patrol to pull you over. It does vary as far as the type of tape you have over the taillight goes.If you were to use transparent tape than it would make the light more visible. Therefore, you would have less of a chance of being pulled over. Section 4(2) provides exceptions stipulated in s. 23, 24, 25, 27 and 28 of the penal code committed by a Ugandan outside Uganda. Such as Treason, acts intended to annoy the person of the President, concealment of treason, terrorism, promoting of war on chiefs and many others. It should be noted however that under international law, there is no restriction on the competence of the court to prosecute its own nationals for crimes committed outside its territorial jurisdiction if this right to national jurisdiction is conferred by statute. In Uganda vs Mustapha Atama 1975 HCB 254, where the accused a Kampala business man was charged in the chief magistrate’s court with obtaining money by false pretence contrary to section 9 of the PCA cap 106 now cap 120. The prosecution alleged that the accused while in the republic of Zaire obtained shs. 3360/- from the charge-d’ affaires of the Ugandan embassy by falsely pretending that he required the money for the maintenance of eight Ugandan soldiers who were stranded in Zaire while on an official mission. On the issue on whether Ugandan courts had jurisdiction over the matter as the offence had been committed in the Republic of Zaire, though in Uganda’s embassy. It was held that s. 6 of the PCA cap 106 now cap 120, confers jurisdiction to courts in Uganda to try offences committed partly within and partly without Uganda. While s. 2(b) merely presupposes the existence of a law conferring extra territorial jurisdiction to the courts in Uganda, in the absence of a Law enabling Uganda Courts to try nationals for acts committed whole outside Uganda, the Chief magistrate would have no jurisdiction to try such cases. Secondly, Local jurisdiction’s Magistrates are usually appointed to specific magisterial areas with reference to s. 5 of the MCA. The general rule is that every offence must be tried by a court within the local limits of the jurisdiction where it was committed under s.  31 of the MCA cap 16. Should the accused be found outside the area in which the offence was committed, the court in whose local limits of jurisdiction he is found will have him brought before it and cause him to be removed, in custody, to the court having jurisdiction to hear the case under s. 32 of the MCA. i. e the offence is committed in mbale and the fugitive is in Masaka, the court in Masaka will hand him over to t he Mbale court which has Local jurisdiction over the offence that was committed by the accused. However where the offence is committed partly within and partly without the Local limits of jurisdiction, any court having jurisdiction in either the two places may hear the case with reference to s. 37 of MCA. Thirdly on jurisdiction, the power to try cases, where an offence is committed in Uganda within the territorial boundaries and is committed within the local limits of jurisdiction of a particular magisterial area, the judicial officer handling the case will still have to ask himself whether he has the power to try the case, or whether the court he presides over , has jurisdiction to hear the case. For instance the Anti Terrorism Act No 14 of 2002 section 6, provides thus; The offence of terrorism and any other offence punishable by more than ten years imprisonment under this act are triable only by the high court and bail in respect of those offences may be granted only by the High court. Only the High court has powers to try the offence of terrorism under the Anti terrorism Act. The original jurisdiction of a chief magistrate’s court is governed by section 161 (1) (a) MCA. A chief magistrate may try any offence other than an offence in respect of which the maximum penalty is death. Example of these are murders, treason, rape, aggravated robbery, etc. However, a chief magistrate may pass any sentence authorized by law under section 162(1) (a) MCA. This means that he can pass a maximum sentence of imprisonment for life and can impose a fine of any amount. A magistrate grade 1 may try any offence other than an offence in respect of which the maximum penalty is death or imprisonment for life. Under 162 (1) (b) MCA, as amended provides that a magistrate grade 1  may pass a sentence of imprisonment for a period not exceeding ten years or a fine not exceeding four million, eight hundred thousand shillings or both. In Uganda vs Nicholas Okello (1984) HCB 22, The charge in this case was for attempted defilement contrary to section 123(3) PCA cap 106 of which the maximum sentence was 18 years imprisonment. The magistrate 1 tried this offence and sentenced the accused to 18 years imprisonment. He appealed against sentence and conviction. It was held that the magistrate had no powers to try such offence and therefore the trial was a nullity. A magistrate grade 2 may try any offence under any written law other than the offences and punishments specified in the first schedule of the MCA. Section 161(1) c) MCA. The sentencing powers of a magistrate grade 2 are limited to imprisonment for a period not exceeding three years or a fine not exceeding half a million shillings S. 162(1) c) MCA. In the Uganda vs c. Kiwanuka [1979] HCB 210, In this case the magistrate grade 2 tried the accused of the offence brought under the fire arms Act, which was an offence stipulated under the first schedule to the MCA to which a magistrate grade 2 had no powers to try. It was held that the conviction of the accused and sentence imposed on him by the magistrate grade 2 in disregard of the provisions of the first schedule was illegal. Article 129 of the constitution gives a list of the courts of judicature in Uganda such as, the Supreme court which is a superior court of record and a final court but does not have original jurisdiction like high court but has appellate jurisdiction. With reference to article 132(2) of the 1995 constitution of Uganda provides that it hears appeals from the Court of appeal. The court of appeal has appellate jurisdiction and hears decisions of the high court with reference to article 134(2) of the 1995 constitution, also has powers to hear cases or petitions regarding any questions as to the interpretation of the constitution according to article 137, Constitutional court. According to article 139(1) of the constitution, confers High court unlimited original jurisdiction in all matters with such appellate and other jurisdiction as may be conferred on it by the court or any other law. Section 1 of the T. I. A cap 23 provides that the high court has unlimited jurisdiction to try any offence under any written law and may pass any sentence authorized by law. Except that no criminal case can be brought under the cognizance of the high court for trial unless the accused person has been committed for trial to the high court in accordance with the M. C. A. Section 2 of the T. I. A provides the sentencing powers of the high court whereby it may pass any lawful sentence combining any of the sentences which it is authorized by law to pass. High court hears decisions of the Chief magistrate and magistrate grade 1 as provided in section 204(1) a) of M. C. A. with reference to section 168 of the M. C. A.  provides for committal proceedings where, When a person charged with an offence to be tried by the High Court appears before a magistrate and the Director of Public Prosecutions has complied with subsection (1), the magistrate shall give the accused person a copy of the indictment together with the summary of the case, read out the indictment and the summary of the case and explain to the accused person the nature of the accusation against him or her in a language he or she understands and inform him or her that he or she is not required to plead to the indictment, commit the accused person for trial by the High Court and transmit to the registrar of the High Court copies of the indictment and of the summary of the case. According to the law in Uganda, judicial officers are not entitled or empowered to make any phone calls to the accused to appear before court. There is a clear procedure on the issuing of summons. With reference to the Blacks law dictionary summon refers to a writ or process commencing the plaintiffs action and requiring the plaintiffs to appear and answer. A criminal summon is a simple court document that contains a number of facts justifying an inquiry into a complaint against an accused person and requiring him to attend the inquiry. It is a document issued by court to be served on the person addressed in it requiring that person to appear before court on the date specified in the document to answer charges brought against him or her. Most importantly every summon must be in writing, prepared in duplicate, signed and sealed by the magistrate or such other officer as the chief justice may from time to time direct with reference to section 44(2) of the M. C. A. Every summon must be directed to the person summoned and shall require him or her to appear at a place, date, time indicated therein before the court having jurisdiction to inquire into and deal with the complaint or charge as provided in section 44(2). In section 44(3), a summon must also state shortly the offence with which the person against whom it is issued is charged. This is basically for purposes of letting the accused know and prepare for the charge he is being compelled to answer. Service of summons to accused is supposed to be in person. According to section 45(1) of MCA every summon must be served by a police officer or an officer of the court issuing it or any public servant but in practice, a summons is served by a police officer or an officer of the court called a process server. A summons must be served on to the persons to whom it is addressed personally but the section states, if practicable. The summons is served on the accused by giving him a duplicate of the summons and in practice he must sign the original copy of the summons. Section 45(2) of the MCA provides that every person on whom a summons is so served, shall if so required by the serving officer, sign a receipt of it on the back of the original summons. In a situation where service of summons to an accused who cannot be found, service of summons maybe effected by leaving the duplicate of the summons for the accused with an adult member of the family or the accused’s servant who normally resides with him or by leaving it with his employer as provided in section 46 of the MCA. The person with whom the summons is left, if so required by the process server, must sign receipt of it on the back of the original summons. The procedure when service cannot be effected is provided in section 47 of the MCA, the process serving officer shall affix the duplicate of the summons to some conspicuous part of the house or homestead in which the person summoned ordinarily resides and thereupon the summons shall be deemed to have been duly served. Where the person summoned is in the active service of the Government or of the East African Community, the court issuing the summons shall ordinarily send it in duplicate to the head of the office in which that person is employed, and the head shall thereupon cause the summons to be served in the manner provided by section 45, and shall return it to the court under his or her signature with the endorsement required by that section. That signature shall be evidence of the service as provided by section 48 of the MCA. A summon can too be issued to a company with reference to section 49 of the MCA, that provides that service of summons on an incorporated company or other body corporate may be effected by serving it on the secretary, local manager or other principal officer of the corporation or by registered letter addressed to the chief officer of corporation or by a registered letter addressed to the chief officer of the corporation at the registered office of the company or body corporate in Uganda. Service of criminal summons on a body corporate can be done by sending the summons by registered mail addressed to the chief officer of the company, secretary, local manager or other principal officer of the company. These officers of a company are deemed competent to plead on behalf of the company. In showing proof that service was effected, section 50 provides where a summon can be served, that is at any place in Uganda. Where the summons was served outside the local limits of jurisdiction of the presiding court or if the accused for whom the summons was intended doesn’t appear at the place, date and time indicated, the court might either on its own or upon application by the prosecution decide to issue a warrant for his apprehension. But before the court does so, it will be necessary to show by evidence that the accused was served and had deliberately refused to obey the summons. According to section 51 of the MCA, ordinarily proof of service of summons shall be given by calling the process server to give evidence on oath that service was effected. But where the officer is not present or the summons was served outside the local limits of the jurisdiction of the issuing magistrate, proof maybe effected by the person with whom the summons was left, swearing an affidavit before a magistrate and presenting the original summons duly endorsed in the manner described above. Even if the original summons is not endorsed, the affidavit shall be admissible in evidence if the court is satisfied from the statements made in it that service of the summons has been effected properly with reference to section 51(2) of MCA.

Louis Armstrong Essay Example

Louis Armstrong Paper Ryan Au Duong Angulo ELA Honors 24, April 2012 Life of the King of Jazz â€Å"My whole musical success goes back to the time I was arrested†¦Ã¢â‚¬ (Old 28). Louis Armstrong started off as a normal kid who lived in a poor family and environment, but ended up as one of the most influential entertainers in history all because of one mistake he made as a child, which changed his life. Louis Armstrong’s life was filled with events that built his musical skills, fame, and his well-being even though he did not start off very well. The environment he lived in as a child was not well suited and he had family problems.He was arrested as a child and was sent to the Home for Colored Waifs which made an enormous impact on his life (â€Å"Louis Armstrong†). His fame and musical skills began to grow when he joined the Creole Jazz Band in his adulthood. He made recordings of his songs, which some of them became big hits, to expand his fame even more. Louis Armstrong’s chi ldhood was difficult, but made him what he was later in life. Louis was born on August 4, 1901 in New Orleans, Louisiana (â€Å"Louis Armstrong†). New Orleans was a poor city (Old 17). His father was Louis Daniel Armstrong and his mother was Mayann Armstrong.Louis also had a brother, William Armstrong, and a sister, Beatrice Armstrong (â€Å"Armstrong, Louis†). His father abandoned the family when Louis was just an infant (â€Å"Louis Armstrong†). His mother had to turn to prostitution often to make money so she can support the family (â€Å"Louis Armstrong Biography†). The environment Louis had lived in had hookers, gangs, children playing on the streets, and musicians. He was surrounded by music when he was young (Old 16). He began to work for the Karnofsky family when he was seven years old (â€Å"Armstrong, Louis†).He also attended the Fisk School for Boys as a child. At the age of eleven on New Year’s Eve, Louis fired a gun which got hi m arrested (â€Å"Louis Armstrong Biography†). Who would have guessed that his arrest was the start of Louis Armstrong’s famous career? Louis was put in the Home for Colored Waifs where he fell in love with music and learned how to play a cornet from his music teacher, Peter Davis (â€Å"Louis Armstrong†). As an adult Louis Armstrong’s life and fame improved dramatically. Armstrong cherished his memories from the Home for Colored Waifs (Old 27).He married Daisy parker from Gretna, Louisiana, but got divorced after a few years (â€Å"Louis Armstrong†). He spent the rest of his life taking care of a mentally disabled child named Clarence, whose mother had died during child birth and whom Armstrong had adopted (â€Å"Louis Armstrong Biography†). In 1922, Joe Oliver invited Armstrong to the Creole Jazz band where Armstrong married the pianist Lil Hardin (â€Å"Armstrong, Louis† The). Oliver’s band was the most popular band in Chica go (â€Å"Louis Armstrong†). Joe Oliver became Louis Armstrong’s mentor and gave him his first real cornet (â€Å"Louis Armstrong†).Armstrong eventually switched to the trumpet though and featured in extended trumpet solos in their performances (â€Å"Louis Armstrong†). After 2 years, Armstrong left the Creole Jazz Band to join Fletcher Henderson’s band in 1924 (â€Å"Armstrong, Louis† The). Armstrong’s time with Fletcher Henderson’s band really expanded his music beyond traditional New Orleans style (â€Å"Armstrong, Louis†). Louis Armstrong played in Henderson’s band and on many recordings (â€Å"Louis Armstrong†). He also became the ambassador for jazz (â€Å"Armstrong, Louis†). Eventually, Armstrong started his own band called the â€Å"Hot Five† for recording purposes only (â€Å"Louis Armstrong†). Heebie Jeebies† was their first recording of scat singing (Louis Armstrong and his Hot Five†). Louis Armstrong recorded his last hit â€Å"What a Wonderful World† before he died of a heart attack in July 6, 1971 (â€Å"Louis Armstrong†). Among Louis Armstrong’s greatest contributions are his skills with the trumpet and cornet, and his idea for improvisation which changed the world of jazz. He made some great accomplishments in his life like joining Fletcher Henderson’s band, becoming the ambassador for jazz, starting the â€Å"Hot Five Band† and making recordings of his songs.The Creole Jazz Band really helped Armstrong’s fame grow because more people were able to listen to how he played on the cornet and trumpet. His greatest accomplishments were when he changed the course of jazz with the idea of improvisation and he was awarded the Grammy Lifetime Achievement Award. Louis Armstrong was very much appreciated by society in his days. People recognized him as the world’s greatest trumpet and cornet player in the early 1920’s and 1930’s (Armstrong, Louis† The). Louis Armstrong was one of the most famous and influential performers in the history of jazz (Armstrong, Louis† The).He was even awarded the Grammy Lifetime Achievement Award for his genius idea of improvisation (â€Å"Armstrong, Louis† The). Louis Armstrong is remembered because of his skills with the trumpet and cornet, and for his great idea of improvisation which changed the world of jazz. His accomplishments revolutionized the world of jazz and how people thought about jazz. He will always be remembered as the king of jazz. Getting arrested was the best mistake Louis Armstrong has ever made in his lifetime.

Prehistoric Life During the Ordovician Period

Prehistoric Life During the Ordovician Period One of the lesser-known geologic spans in the earths history, the Ordovician period (448-443 million years ago) didnt witness the same extreme burst of evolutionary activity that characterized the preceding Cambrian period; rather, this was the time when the earliest arthropods and vertebrates expanded their presence in the worlds oceans. The Ordovician is the second period of the Paleozoic Era (542-250 million years ago), preceded by the Cambrian and succeeded by the Silurian, Devonian, Carboniferous and Permian periods. Climate and geography. For most of the Ordovician period, global conditions were as stifling as during the preceding Cambrian; air temperatures averaged about 120 degrees Fahrenheit worldwide, and sea temperatures may have reached as high as 110 degrees at the equator. By the end of the Ordovician, however, the climate was much cooler, as an ice cap formed on the south pole and glaciers covered adjacent landmasses. Plate tectonics carried the earths continents to some strange places; for example, much of what would later become Australia and Antarctica protruded into the northern hemisphere! Biologically, these early continents were important only insofar as their coastlines provided sheltered habitats for shallow-water marine organisms; no life of any kind had yet conquered land. Marine Life During the Ordovician Period Invertebrates. Few non-experts have heard of it, but the Great Ordovician Biodiversity Event (also known as the Ordovician Radiation) was second only to the Cambrian Explosion in its importance to the early history of life on earth. Over the course of 25 or so million years, the number of marine genera around the world quadrupled, including new varieties of sponges, trilobites, arthropods, brachiopods, and echinoderms (early starfish). One theory is that the formation and migration of new continents encouraged biodiversity along their shallow coastlines, although climatic conditions also likely came into play. On the other side of the evolutionary coin, the end of the Ordovician period marked the first great mass extinction in the history of life on earth (or, one should say, the first for which we have ample fossil evidence; there were certainly periodic extinctions of bacteria and single-celled life during the preceding Proterozoic Era). Plunging global temperatures, accompanied by drastically lowered sea levels, wiped out a huge number of genera, although marine life as a whole recovered fairly rapidly by the start of the ensuing Silurian period. Vertebrates. Practically all you need to know about vertebrate life during the Ordovician period is contained in the aspises, especially Arandaspis and Astraspis. These were two of the first jawless, lightly armored prehistoric fish, measuring anywhere from six to 12 inches long and vaguely reminiscent of giant tadpoles. The bony plates of Arandaspis and its ilk would evolve in later periods into the accoutrements of modern fish, further reinforcing the basic vertebrate body plan. Some paleontologists also believe that the numerous, tiny, worm-like conodonts found in Ordovician sediments count as true vertebrates; if so, these may have been the first vertebrates on earth to evolve teeth. Plant Life During the Ordovician Period As with the preceding Cambrian, evidence for terrestrial plant life during the Ordovocian period is maddeningly elusive. If land plants did exist, they consisted of microscopic green algae floating on or just underneath the surface of ponds and streams, along with equally microscopic early fungi. However, it wasnt until the ensuing Silurian period that the first terrestrial plants appeared for which we have solid fossil evidence.

Accounting in its organisational context Essay Example | Topics and Well Written Essays - 1750 words

Accounting in its organisational context - Essay Example Admittedly, many people dislike change. Thus, the popularity of the traditional costing accounting method still persists until today. The following will explain in detail the many advantages and disadvantages of using the new costing accounting method called Activity Based Costing when contrasted and compared with the Traditional Cost accounting method.Many companies in the United States have shifted from to Activity Based Costing. The prior costing method normally used is the traditional based costing. However, the Activity based costing uses several pre -determined cost drivers that include materials bought to service the customers. In addition, the new activity based costing method is better than the traditional costing method because this new costing method distributes the total estimated cost of service organisation using the daily service activities (Caplan et al., 2005; p1). Furthermore, Activity based costing is a better costing method as compared to the traditional costing method if the service organisation has many different products to market. In a nutshell, activity based costing is better than the traditional method of allocating total costs because it uses activities as the stepping stone to reach the main purpose of setting up a business which is to generate profits. Finally, activity based costing is a preferred choice because it does not stop its tracks after it manages costs (Krumwiede & Roth, 2004; p 1).The prior costing method normally used is the traditional based costing. There are main features for service organizations in both the United States and the United Kingdom that differentiate it from the traditional method of accounting. One of the main features that distinguishes it as a better costing method is that it has many cost cools unlike the traditional costing method. The traditional costing method normally uses only one or two cost pools. The most popular cost pool under the traditional costing method is that total cost is divided by the total number of hours to arrive at a per hour rate. Then the actual number of hours spent for servicing a specific customer service order is multiplied by the pre -determined hourly customer service rate to arrive at the actual cost (Hussein, 2004; p 1).However, the Activity based costing uses several pre -determined cost drivers that include materials bought to service the customers. Also, the number of machine set ups used to repair a car in a car repair centre is one cost driver that that has made this costing method a success. In addition, the number of inspections that have been done in order to determine if the repair shop employees are doing their jobs to comply with the minimum benchmark in terms of job cost and quality is another cost driver that puts activity based costing in high demand. This is also used in the traditional cost accounting method (Lewis, 1993; p. 1) .In addition, the new activity based costing method is

Th Kurig Systm in th Offic Coff Markt Case Study

Th Kurig Systm in th Offic Coff Markt - Case Study Example Having companiÐ µs know thÐ µ fundamÐ µntal importancÐ µ of customÐ µr nÐ µÃ µds is thÐ µ most important part of thÐ µ succÐ µssful company Ð µntÐ µring thÐ µ officÐ µ coffÐ µÃ µ markÐ µt’s sÐ µrvicÐ µ stratÐ µgy, and this will dirÐ µctly add to thÐ µ futurÐ µ succÐ µss and profit. ThÐ µ kÐ µy focus of thÐ µ dynamic company in thÐ µ prÐ µsÐ µnt in tÐ µrms of Ð µstablishing a nichÐ µ in thÐ µ markÐ µting arÐ µa thÐ µsÐ µ days is oftÐ µn thÐ µ supÐ µrior Ð µxpÐ µriÐ µncÐ µ that customÐ µrs havÐ µ, rathÐ µr than thÐ µ supÐ µrior product or sÐ µrvicÐ µ put out by thÐ µ company. This has lÐ µd to thÐ µ thÐ µory that thÐ µ customÐ µr’s basic nÐ µÃ µds should not only bÐ µ mÐ µt, but should bÐ µ Ð µxcÐ µÃ µdÐ µd. An important part of this procÐ µss is having a sÐ µrvicÐ µ profÐ µssional who is ablÐ µ to mÐ µÃ µt and Ð µxcÐ µÃ µd thÐ µir nÐ µÃ µds by giving thÐ µm thÐ µir full attÐ µntion. b. Wha t advicÐ µ do you havÐ µ for Nick Lazaris concÐ µrning his dÐ µalings with MTS†¦ In dÐ µaling with thÐ µ k-cup filling machinÐ µ manufacturÐ µr, thÐ µ pricing goal should bÐ µ sÐ µt at a prÐ µmium lÐ µvÐ µl, so that Ð µxtÐ µrnal changÐ µs in machinÐ µ parts and othÐ µr pricÐ µs do not advÐ µrsÐ µly affÐ µct profits. ThÐ µ pricÐ µ of ingrÐ µdiÐ µnts for a coffÐ µÃ µ would bÐ µ a variablÐ µ, bÐ µcausÐ µ thÐ µ Ð µxtÐ µrnal markÐ µt, howÐ µvÐ µr much KÐ µurig is going to try to control thÐ µ mÐ µans of production and supply chain, is still going to show fluctuations in thÐ µ pricÐ µ of raw matÐ µrials usÐ µd to makÐ µ thÐ µ coffÐ µÃ µ, and thÐ µ machinÐ µ. ... ?r for thÐ µÃ¢â‚¬ ¦ For thÐ µ brÐ µwing machinÐ µs, production vÐ µndors can also bÐ µ outsourcÐ µd, as wÐ µll, saving still morÐ µ timÐ µ, and furthÐ µring industry-widÐ µ goals of providing fastÐ µr, chÐ µapÐ µr, and bÐ µttÐ µr goods and sÐ µrvicÐ µs. In thÐ µ dynamic tÐ µchnology Ð µnvironmÐ µnt, in tÐ µrms of intÐ µrnal strÐ µngths of solution, vÐ µndor support is not complÐ µtÐ µly rÐ µlÐ µgatÐ µd to thÐ µ Ð µffÐ µctivÐ µ automatÐ µd systÐ µm, and in many casÐ µs, vÐ µndors providÐ µ stratÐ µgic dirÐ µction for thÐ µ company, rathÐ µr than Ð µxÐ µcutivÐ µs. d. What actions should KÐ µurig takÐ µ to pÐ µnÐ µtratÐ µ thÐ µ officÐ µ coffÐ µÃ µ sÐ µrvicÐ µ markÐ µt†¦ KÐ µurig should rÐ µly on word of mouth to achiÐ µvÐ µ as much of a cult status in thÐ µ officÐ µ markÐ µt as possiblÐ µ. Cultic organizations usually organizÐ µ amongst thÐ µir local communitiÐ µs in ordÐ µr to garnÐ µr gÐ µnÐ µral community support, but it is important not to blamÐ µ thÐ µ cult Ð µntirÐ µly; victims may havÐ µ morÐ µ choicÐ µs than wÐ µrÐ µ prÐ µviously thought, according to nÐ µw modÐ µls of undÐ µrstanding. Community support can rangÐ µ from garnÐ µring mÐ µdia attÐ µntion to gÐ µtting morÐ µ known about thÐ µ organization through word of mouth. Leadership is also important at Keurig. But it is not just the manager’s job at the coffee and coffee machine company: if they are working as an active listener as well as communicator, they will then be able to make creative decisions based on a framework of team thinking. The basic argument of the current thinking, regarding foundational vision and mission, is for the establishment of new marketing principles that are not based on rigid rule structures, but are instead more able to dynamically respond to an ever-evolving present where the customer is the one who has the power. An overall conclusion that can be drawn from the Keur ig case

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. 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