History of Mathematics - Report Example

History of Mathematics Introduction The mathematics has undergone various transformations and growth in the United States in an effort to enhance it efficiency. In all the discussion of mathematics, the century that began in 1861 has been one of assurance and fulfillment. In the American society, higher education and secondary education are two institutions that are given permission to rule their territory as long as they are within the confines of the law and stick to the set budget. Mathematics in not an institution in itself but it has a central place in both higher education and secondary education. Most of the problems, especially in mathematics, have been brought about by the detached and almost autonomous governance of these institutions. However, the histories of these two institutions are well documented and they offer the best accessible structure that can help in the social history of American mathematics. To a commendable extent they fill in the spaces in the social history of mathematics, which is only scantily documented. This research tries to trace the history of mathematics in secondary schools in the period spanning 1861-2001 to establish why mathematics seems to be a hard subject for students as well as the importance of this subject in our lives (Wu 947). Mathematics in the Curriculum In 1860, mathematics had a solid place in American history, and this was founded on its long-established place, together with Latin and Greek classics, as one of the mandatory studies that formed the curriculum from the initial medieval universities. Mathematics was one of the important humanities and its development and growth was a major area of focus. For the next twenty years, many people academicians openly promoted the learning of mathematics in their institutions. In 1868, the administrator of John Hopkins University claimed that the only way to effectively start a university was to look for a great mathematician then everything else would fall into place. Historians have consistently claimed that this belief in mathematics explains the continuous success of John Hopkins University (Jones and Arthur 70) The place of mathematics was further augmented by the insistence that it be included in the secondary school curriculum. Starting from 1861-1865, there were several public academies that were tasked with preparing students for entry into college but this role was preserved for autonomous private academies. Although it cannot be said that there was an absence of any reliable standard, their curricula were fashioned in such a way as to prepare for the general studies syllabus of the colleges by a mandated universal studies syllabus of their own, which was subject to the entry requirements of the colleges. Mathematics was necessary for a student to graduate from these academies even though the essence of this stipulation was somewhat out of place (Klein 57). The duration of the American Civil War up to 1893 experienced an outburst of higher education in the country’s history, and new state universities sprang up in every location in the country. These were inclusive of new land grant colleges such as MIT and Purdue, which were inclusive of engineering colleges as well as those teaching applied science. New colleges that catered for the needs of blacks and women were also set up. By the commencement of the Cold War, Yale was in the helm by being the first university to offer a Ph.D. program and this was followed by many more graduate degree programs. Science had finally found its way into the university syllabus over the resistance of the well-established humanities. However, this was done in a separate B.S. degree program that was separated from the conventional liberal arts. The position of mathematics was further augmented by its requirements in the syllabus of the new B.S. degree programs and those of the new schools of engineering and those of applied science (Klein 57). Despite this development, American mathematics still relied heavily on European and English mathematics. Young Americans who had desires for researching mathematics went to Germany and especially Gottingen to pursue their Ph.D. degrees. In 1888, applied mathematics appeared to be taking shape while it growth became apparent within the society. Ideally, the conventional applied mathematics comprising of the application of trigonometry to survey, diagrams and military science had come to its conclusion and was being overridden by civil engineering. But mathematics then incorporated balanced mechanics and positional astronomy. This was the applied mathematics that took shape in 1888. Only a couple of American mathematicians were undertaking serious research in celestial mechanics but they taught the classical works used in London (Cremin 123). The Problem with American Mathematics The current challenges in American mathematics can be traced back to 1893. In essence, this period was marked by acute countrywide economic panic at the time when the presidency was under Cleveland. Historians categorize this as having been the end of an era and the beginning of another. The years starting 1893-1940 experienced a slow but significant development in American mathematical research. In this sense, it was a period of great accomplishment. However, if it were not for the position of mathematics in the society, the earlier prospect could not have been met. Immediately after the robust growth experienced before, there were a series of disasters that befell the mathematical learning, applied mathematics and on the application of mathematics in the American society (Osborne and Joe 70). In the examination of mathematics history, one thing that historians agree on is that the factors that make mathematics hard have their roots in the 1893-1840 factors. The conventional syllabus of necessary general studies had been carried over into the expanded colleges from the earlier form of schooling that prepared students for teaching jobs. This hard course of studies included Greek and Latin for their traditional values as well as for interpreting scriptures from their original text. It was inclusive of mathematics partly due to the absolute weight of tradition, and partly for exercising the mind. By 1888, it had become clear that there would never be sufficient jobs as ministers of the gospel or teachers to take in the large number of B.A. students who were graduating from universities. There were also no enough jobs to employ the ever rising number of graduates in the newly inducted science and engineering programs. In addition to this, students in the conventional degree program were striving for a German-model free elective system to take the place of the complex and old fashioned general studies syllabus (Osborne and Joe 70). Charles W. Eliot, who was the Harvard President and perhaps the most influential educator of the 19th century, had begun his career as a mathematics teacher before altering to chemistry before he became the president of Harvard. He was in the frontline in according students what they were seeking for, a liberal elective model. Other universities quickly followed the example that had been set by Harvard. This led to the ruination of the classics and the replacement by a new subject called English. This led mathematics to lose a big portion of its enrollment and could have been completely obliterated had it not been for it being a requirement in the entrance to physical sciences and engineering. In addition to this, there was no any ideal substitute for mathematics since in that period people did not study computer science. In the following years, mathematics was widely viewed in government circles as a supplementary of the physical sciences and engineering. The widespread assimilation of the free elective system created so much pandemonium in the college syllabus that some boundaries had to be put in place to restore order. One of the main issues to be implemented included the provision of a main subject as introduced by Woodrow Wilson who was then the head of Princeton University. This was closely followed by Yale and Harvard who introduced models of group necessities and scholarly counseling that together with the major make up the system that is used in American universities today. Despite these efforts, the old position of mathematics was not restored (Wu 947). Mathematics in Secondary Schools The major problem with the growth of higher education that was experienced in the latter part of the 19th century was that it was founded on shaky foundation. There was no nationalized model of secondary schools to organize students for the newly set communal universities. A committee headed by Eliot was set up in 1891 to review the model that schools would adopt. In the report that they produced in 1893, the committee opposed the existing English, French and German systems that had taken root. In its place, the committee proposed the formation of a novel American high school that would fall under the same local school boards that guided the general public elementary education. The extra four years would be provided but would not be mandatory. The colleges which had overshadowed the conventional institutions that prepared students to join college were to have no mandate over the newly established secondary schools. At that time, the committee believed that the bulk of the new students would not join colleges but would not join colleges but would only end up with four extra years to their overall education. Majority of these students would be better off by getting vocational training instead of scholastic education (Wu 947). While the newly established high schools were supposed to offer college foundational mathematics courses, these courses were not incorporated into the graduation necessities as they had been in the traditional academies. The new provisions only needed about 10-15 percent of the public high school students to enroll into the college-bound syllabus. These plans threw the school college interface in to some sort of confusion so a new Commission on College Entrance Requirements was set up just before the turn of the century to address this issue. However, the proposals made by this new commission did very little to cement the position of mathematics in the country. However, the new admissions maintained the control of registrations in the major universities just as they had done before the 1893 changes. In the following years, these universities were only successful in ensuring that the quality of performance in their schools was maintained. In the private universities whose admission was dependent on high school diploma, there was minimal control of admission standards. Without a doubt, this had a great effect on mathematics above all the other subjects. Although the mathematicians hated this arrangement, there was very little that they could do to change the situation. In addition to this, the newly created secondary schools were only contributing a small fraction of students joining colleges and so the problem was not easily recognized. In the following years, there were various committees that were set up to come up with ways to better education standards but sadly mathematics was not feature anywhere among these subjects. This apparent neglect of mathematics created a scenario where students and academicians feel out of favor with the mathematics subject and this led to negativism as far as the subject was concerned. This explains perfectly why most students even today find the mathematics subject unattractive. Another challenge experienced in mathematics and which has affected the learning of mathematics today was its isolation from European mathematics. The challenge with the American model of high school was that it was different from the rest of the European model and this meant that the college system was affected too. Unlike in the past, it was now impossible to transfer European teachers to America and vice versa. The implication for this was that American mathematicians were forced to draft new textbooks that were aligned to this new curriculum, and beginning 1900, there were no outside textbooks used for study in American schools. According to historians, the first textbook written for mathematics study in America was that of calculus in 1904. Since college algebra was non-existent before, new textbooks had to be drafted to cater for the new lessons. Although the new books written for this field were in essence ideal for teaching the subject, the problem was that there was no emphasis that was placed in the teaching of this almost new subject. While mathematics had been a compulsory subject before, the new learning scheme only allowed students to select mathematics as an option. Ideally, not many students chose to pursue mathematics in universities and as such the subject was highly neglected. Even when the learning of mathematics was made compulsory in later years, there was an absence of zeal among students. For a long time, this negative perception was not corrected and as a result it led to majority of them viewing mathematics as a hard subject. This problem persisted to nearly the time World War I was starting (Loveless 116). Before America went into World War 1, a national accord was reached mandating the increase of public education from 8-12 years. Before this, the secondary component was provided for but it was not mandatory. With the passage of this new law, there was an influx of students into secondary schools something which brought about the need for more teachers. This new influx of students brought a new challenge since there were not many trained teachers to teach this subject. Even with the increase in the number of students joining colleges, there was no any special emphasis placed on the learning of mathematics. If anything, the attacks on mathematics intensified with the whole debate gaining a political angle. The result of this debate was that mathematics became even more hated and in the following years it was only the students intending to study engineering only studied. Due to mathematics not being appreciated, those teaching it got even lesser salaries and as such there was a scarcity of teachers. This diminished the status of mathematics further and those studying it were believed to be the very bright students (Loveless 116). Renaissance: The New Math Period The new math period came into being in the second half of the 20th century and went on to nearly 1970. Ideally, this was not a monolithic period. According to historians, this period was born by the adoption of new teaching skills and comprehension. This period was characterized by various meeting between mathematicians and psychologists but the two soon found out that there was nothing to discuss about. Unlike in the last century, the new 1950’s brought about a period where mathematicians were actively involved in the formation of the secondary school syllabus. Within 1950 and 1960, there were numerous committees that were tasked with ensuring that mathematics was acceptable in schools. This led to the formation of numerous groups that were meant to promote the study of mathematics something that led to a wide acceptance of this subject. The recommendations given by the various committees helped in restoring the place of mathematics in the American society. However, this did not achieve much in eradicating the negative perception of this subject among students. Perhaps the only problem with the new math period was that much emphasis was placed on calculus but very little was accomplished in the application of this subject. This formal nature of mathematics led to much critic from mathematicians who felt that enough was not being done to promote mathematics in the society. This period went on till the late 1980’s (Loveless 116). 1980’s-2001: Introduction to National Standards In the early years of the 1980’s, it was becoming apparent that the standards of mathematics were fast diminishing. This led to the formation of various committees that were supposed to examine the rather low entry requirements among individuals. In the run up to the 1990’s, there were numerous committees that called for the examination in the national standards of this subject. As a result of this, academicians began calling for the examination of mathematics as a problem solving issue and this led to a change in the manner that the subject was taught. Due to the advancement of technology, academicians pointed out that problem solving would now be available without the acquisition of basic skills. Despite these observations, the traditional paper and pencil were soon replaced by calculators and even computers. The result was that students abandoned the use of their brains and instead relied on the emerging technology to solve mathematics problems. The biggest problem with mathematics that has continued to plaque students over the years is that it provides learners with no room for application. In the run to the new century, there were numerous calls for mathematics teachers to go back to teaching the basics. However, despite these calls, there have been very minimal efforts towards going back the basics of teaching the subject. There has also been very little motivation and very few individuals are willing to take on mathematics as a professional subject. This has led to a chronic shortage of teaching staff especially in public institutions where the pay is still minimal (Klein 178). Mathematical Education in Life In evaluating the history of mathematics in the society, it becomes clear that the value of this subject in daily life issues is mainly ignored. In most cases, those who insist on the learning of mathematics do so to acquire better grades in the class. However, very little of this acquired knowledge is applied anywhere in life. However, mathematics is an integral part of the American society and its service has led to the betterment of the American society. Most of this contribution has been in the area of education then going on into life (Wu 947).Actually, the importance of mathematics is believed to go beyond just the acquisition of degrees or even credits. While many students would prefer to take evening lessons in areas of their interest, very few of them are keen on joining evening classes just to study algebra. Although the advantages of studying mathematics may not be quickly visible, a closer examination shows the important role that mathematics has to play in life. In essence, at the present, there is an acute shortage of mathematicians in the society. The biggest problem with this is that mathematics is only left to those pursuing careers in engineering and the few other courses that demand the study of mathematics. However, there is need for the society to begin seeing mathematics as a subject that can bring about a revolution in the society. Today, medicine together with its changing technologies demands that there be mathematicians to come up with ground breaking researches that will help the society. However, there is very little efforts directed towards mathematics research and this has perhaps been the genesis of all the problems bedeviling the industry as well as the low inspiration to study the subject among students (Klein 178). Works Cited Cremin, Lawrence Arthur. The transformation of the school: Progressivism in American education, 1876-1957. Vol. 519. New York: Knopf, 1961. Print. Jones, Phillip S., and Arthur F. Coxford Jr. "Mathematics in the Evolving Schools." Nat Counc Teachers Math Yearbook 32nd 9.90 (1970): 70. Klein, David. "A brief history of American K-12 mathematics education in the 20th century." Mathematical cognition (2003): 175-225. Klein, David. "Math Problems: Why the Department of Educations Recommended Math Programs Dont Add Up." American School Board Journal 187.4 (2000): 52-57. Loveless, Tom, ed. The great curriculum debate: How should we teach reading and math?. Washington, DC: Brookings Institution Press, 2001. Print. Osborne, Alan R., and F. Joe Crosswhite. "Forces and Issues Related to Curriculum and Instruction, 7-12." Nat Counc Teachers Math Yearbook 32nd 153.297 (1970): 70. Wu, Hung-Hsi. "The mathematics education reform: Why you should be concerned and what you can do." American Mathematical Monthly (1997): 946-954. Read More