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100-437: Although research into mathematics education is primarily concerned with the tools, methods, and approaches that facilitate practice or the study of practice, it also covers an extensive field of study encompassing a variety of different concepts, theories and methods. National and international organisations regularly hold conferences and publish literature in order to improve mathematics education. Elementary mathematics were

200-535: A major subject in its own right, such as partial differential equations , optimization , and numerical analysis . Specific topics are taught within other courses: for example, civil engineers may be required to study fluid mechanics , and "math for computer science" might include graph theory , permutation , probability, and formal mathematical proofs . Pure and applied math degrees often include modules in probability theory or mathematical statistics , as well as stochastic processes . ( Theoretical ) physics

300-481: A quadrangle with an interior court, two sides of which have been rebuilt and expanded with a library wing in the 19th century. The Crown Tower and the chapel, the oldest parts, date from around 1500. The original foundation contained the chapel, the Great Hall and living accommodation, with its own kitchen and brewery, a well in the quadrangle, and a college garden to provide herbs and vegetables. The Grammar School

400-476: A core part of education in many ancient civilisations, including ancient Egypt , ancient Babylonia , ancient Greece , ancient Rome , and Vedic India . In most cases, formal education was only available to male children with sufficiently high status, wealth, or caste . The oldest known mathematics textbook is the Rhind papyrus , dated from circa 1650 BCE. Historians of Mesopotamia have confirmed that use of

500-525: A financial settlement agreement with the former Principal Sir Ian Diamond , the university failed to make best use of public funds or exercise good governance. As a result of the investigation, the university was ordered to repay £119,000 of grant finance to the SFC and undertake an externally-facilitated examination of its governance and culture. On 5 December 2023 it was announced that a working group, chaired by Professor Karl Leydecker, had been set up to look at

600-588: A given method gives the results it does. Such studies cannot conclusively establish that one method is better than another, as randomized trials can, but unless it is understood why treatment X is better than treatment Y, application of results of quantitative studies will often lead to "lethal mutations" of the finding in actual classrooms. Exploratory qualitative research is also useful for suggesting new hypotheses , which can eventually be tested by randomized experiments. Both qualitative and quantitative studies, therefore, are considered essential in education—just as in

700-531: A graduate of the University of Glasgow drafting a request on behalf of King James IV to Pope Alexander VI resulting in a papal bull being issued. It seems that James was keen to ensure that Scotland had as many universities as England at the time, and it was to possess all the privileges enjoyed by those of Paris and Bologna , two of the most highly favoured in Europe. The university, modelled on that of

800-616: A graduation hall and the Marischal Museum ( Marischal College has now been restored as the headquarters of Aberdeen City Council, which is leasing a portion of the complex from the university). Following extensive fundraising, a £57 million new university library (the Sir Duncan Rice Library ) opened in autumn 2011 at the King's College campus to replace the outgrown Queen Mother Library and was officially opened by

900-538: A key role in the Scottish Enlightenment , and it was the most important forum for the promotion of enlightened thought and values in Aberdeen. The Philosophical Society was revived in 1840, with the object of receiving and debating original scientific, literary and philosophical papers from its members; however, the decision was taken on 13 September 1939 to discontinue its meetings, chiefly in view of

1000-604: A large number of modern ones housing most facilities and academic departments. Most date from the second half of the 20th century. Some of these echo the existing architecture of Old Aberdeen , such as the Fraser Noble Building with its distinctive concrete crown designed to resemble the one adorning King's College. Other buildings were constructed of stone in the 1950s (e.g. the Taylor Building and Meston Building). A number of other buildings are designed in

1100-407: A poem for a special number of the student publication, Alma Mater , in celebration of the quatercentenary of the university. 'I looked and thought, "All is too gray and cold To wake my place-enthusiasms of old!" Till a voice passed: "Behind that granite mien Lurks the imposing beauty of a Queen." I looked anew; and saw the radiant form Of Her who soothes in stress, who steers in storm, On

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1200-655: A projected deficit for Modern Languages of £1.64m in 2023/24." The financial statements were contested by staff and UCU. At an online meeting of the University Senate on 6 December, senators voted 78–15 in favour of a motion which "called for an immediate halt in the consultation process until an overall plan is presented in detail to Senate for appropriate scrutiny." Five senators abstained. On 8 December The Gaudie reported that staff had been sent 'Risk of Redundancy' letters which stated that staff who are made redundant would receive four months pay. This contrasts with

1300-569: A university in Old Aberdeen, mentions as the chief motive for the undertaking, the profound ignorance of the inhabitants of the north of Scotland, and the great deficiency of properly educated men to fill the clerical office in that part of his kingdom. The first university in Aberdeen, King's College , formally The university and King's College of Aberdeen (Collegium Regium Aberdonense) , was founded on 10 February 1494 by William Elphinstone , Bishop of Aberdeen , Chancellor of Scotland, and

1400-535: A very early period, a studium generate, or university, attached to the episcopal chapter of the See of Aberdeen. It is said to have been founded in 1157 by Edward, Bishop of Aberdeen, and although, according to Hector Boece , it still existed at the period when King's College was founded, it is probable that it had in some way ceased to answer the purposes which it must have been designed to serve, since King James IV, in his letter to Pope Alexander VI, requesting him to found

1500-501: Is Brian Buckley. Marischal College is a neo-Gothic building, having been rebuilt in 1836–41, and greatly extended several years later. Formerly an open three-sided court, the college now forms a quadrangle as additions to the buildings were opened by Edward VII in 1906 and form the current facade from Broad Street. The building is widely considered to be one of the best examples of neo-Gothic architecture in Great Britain;

1600-572: Is given if not specified in name. University of Aberdeen The University of Aberdeen (abbreviated Aberd. in post-nominals ; Scottish Gaelic : Oilthigh Obar Dheathain ) is a public research university in Aberdeen , Scotland. It was founded in 1495 when William Elphinstone , Bishop of Aberdeen and Chancellor of Scotland , petitioned Pope Alexander VI on behalf of James IV, King of Scots to establish King's College , making it one of Scotland's four ancient universities and

1700-466: Is mathematics-intensive, often overlapping substantively with the pure or applied math degree. Business mathematics is usually limited to introductory calculus and (sometimes) matrix calculations; economics programs additionally cover optimization , often differential equations and linear algebra , and sometimes analysis. Throughout most of history, standards for mathematics education were set locally, by individual schools or teachers, depending on

1800-485: Is the Science Teaching Hub . Completed in 2021, the building contains laboratories for subjects including biological sciences, chemistry, geosciences and medical sciences. The Aberdeen Sports Village , located across King Street from the Old Aberdeen campus, houses sports facilities and the aquatics centre. The university's Foresterhill Campus is located approximately 1.75 kilometres (1.09 mi) to

1900-587: Is thought to be a copy of an even older scroll. This papyrus was essentially an early textbook for Egyptian students. The social status of mathematical study was improving by the seventeenth century, with the University of Aberdeen creating a Mathematics Chair in 1613, followed by the Chair in Geometry being set up in University of Oxford in 1619 and the Lucasian Chair of Mathematics being established by

2000-716: The National Council of Teachers of Mathematics (NCTM) published the Principles and Standards for School Mathematics in 2000 for the United States and Canada, which boosted the trend towards reform mathematics . In 2006, the NCTM released Curriculum Focal Points , which recommend the most important mathematical topics for each grade level through grade 8. However, these standards were guidelines to implement as American states and Canadian provinces chose. In 2010,

2100-569: The Pythagorean rule dates back to the Old Babylonian Empire (20th–16th centuries BC) and that it was being taught in scribal schools over one thousand years before the birth of Pythagoras . In Plato 's division of the liberal arts into the trivium and the quadrivium , the quadrivium included the mathematical fields of arithmetic and geometry . This structure was continued in the structure of classical education that

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2200-838: The School of Medicine, Medical Science and Nutrition . In addition, there are smaller facilities at other sites such as the Royal Cornhill Hospital to the west of the city centre, and the Rowett Institute in Bucksburn . The King's College campus covers an area of some 35 hectares around the ancient King's College buildings and the High Street. It hosts around two-thirds of the university's built estate and most student facilities, and lies 2 miles north of Aberdeen city centre. The university does not own all

2300-546: The Scottish Enlightenment . Both colleges supported the Jacobite rebellion and following the defeat of the 1715 rising were largely purged by the authorities of their academics and officials. The nearest the two colleges had come to full union was as the Caroline University of Aberdeen , a merger initiated by Charles I in 1641, which united the two colleges for twenty years. Following the civil conflicts of

2400-481: The Scottish Reformation in 1560, King's College was purged of its Roman Catholic staff but in other respects was largely resistant to change. George Keith , the fifth Earl Marischal , was a moderniser within the college and supportive of the reforming ideas of Peter Ramus and Andrew Melville . In April 1593 he founded a second university in the ' New Town ', Marischal College . It is also possible

2500-640: The Universities (Scotland) Act 1858 , which also created a new medical school at Marischal College. The 1858 Act of Parliament stated the " united University shall take rank among the Universities of Scotland as from the date of erection of King's College and University. " The university is thus Scotland's third oldest and the United Kingdom's fifth oldest university. The transference of the arts classes from Marischal to King's College required

2600-607: The University Court responsible for finances and administration, and the Academic Senate ( Senatus Academicus )—the university's supreme academic body. There are correspondingly three main officers of the university. It is nominally headed by the chancellor , a largely ceremonial position traditionally held by the Bishop of Aberdeen , but as a result of the Scottish Reformation holders are now elected for life by

2700-500: The University of Cambridge in 1662. In the 18th and 19th centuries, the Industrial Revolution led to an enormous increase in urban populations. Basic numeracy skills, such as the ability to tell the time, count money, and carry out simple arithmetic , became essential in this new urban lifestyle. Within the new public education systems, mathematics became a central part of the curriculum from an early age. By

2800-451: The University of Paris and intended principally as a law school , soon became the most famous and popular of the Scots seats of learning, largely due to the prestige of Elphinstone and his friend, Hector Boece, the first principal appointed in 1500. Its aim was to train doctors, teachers and clergy who would serve the communities of northern Scotland, as well as lawyers and administrators for

2900-621: The Wars of the Three Kingdoms , a more complete unification was attempted following the ratification of Parliament by Oliver Cromwell during the interregnum in 1654. This united university survived until the Restoration whereby all laws made during this period were rescinded by Charles II and the two colleges reverted to independent status. Charles I is still recognised as one of the university's founders, due to his part in creating

3000-572: The What Works Clearinghouse (essentially the research arm for the Department of Education ) responded to ongoing controversy by extending its research base to include non-experimental studies, including regression discontinuity designs and single-case studies . List of mathematical societies This article provides a list of mathematical societies . This list is sorted by continent. Country and/or subregion/city

3100-635: The brutalist style , such as the Arts Lecture Theatre and adjoining William Guild Building, opened in 1969 to house the School of Psychology. Also on the site is the Cruickshank Botanic Garden which was presented to the university in 1899 and is open to the public. The Powis Gateway forms the east gate and archway from College Bounds, Old Aberdeen. These oriental style towers with minarets have provoked much interest over

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3200-480: The fifth-oldest university in the English-speaking world . Along with the universities of St Andrews , Glasgow , and Edinburgh , the university was part of the Scottish Enlightenment during the 18th century. The university as it is currently constituted was formed in 1860 by a merger between King's College and Marischal College , a second university founded in 1593 as a Protestant alternative to

3300-403: The minor or AS in mathematics substantively comprises these courses. Mathematics majors study additional other areas within pure mathematics —and often in applied mathematics—with the requirement of specified advanced courses in analysis and modern algebra . Other topics in pure mathematics include differential geometry , set theory , and topology . Applied mathematics may be taken as

3400-525: The 18th and early 19th centuries. William Ogilvie , known as the Rebel Professor, proposed a paper on the union and reform of the two colleges in 1787, but the proposals were rejected by seven (known as the 'seven wise Masters') out of ten professors at King's. The evolving examination system and university research now required much higher academic standards from the students. The two colleges in Aberdeen merged on 15 September 1860 in accordance with

3500-540: The 1960s onward were constructed in brutalist style. Meanwhile, the Foresterhill campus began to train medical students in the 1930s next to Aberdeen Royal Infirmary. During the mid-20th century departments which had been at Marischal College moved into one of these new buildings (most at King's College) and by the late 20th-century Marischal College had been abandoned by all but the Anatomy Department,

3600-588: The British Academy, and a champion Charles Darwin's work, made one of the first announcements that Darwin had undertaken a body of work on evolution and was about to release his findings. The organisers felt that they might be risking something in holding the meeting much further north than they had done before but in the event the Aberdeen meeting was the most well attended the BA had ever had. Further unsuccessful suggestions for union were brought about throughout

3700-623: The Caroline University and his benevolence towards King's College. The Aberdeen Philosophical Society (known locally as the Wise Club) was created by Thomas Reid , George Campbell , David Skene, John Gregory , John Stewart , and Robert Traill , and held its first meeting in the Old Red Lion Inn on 12 January 1758. From its inception, the society was an intimate, private body whose members were drawn exclusively from

3800-566: The General Council. There is also a rector of the university , who chairs the University Court and is elected by the students for a three-year term to represent their interests. There are also four assessors, ten masters, including the principal and vice principal, and the factor or procurator. The administrative head and chief executive of the university is its principal and vice-chancellor . The principal acts as chair of

3900-756: The National Governors Association Center for Best Practices and the Council of Chief State School Officers published the Common Core State Standards for US states, which were subsequently adopted by most states. Adoption of the Common Core State Standards in mathematics is at the discretion of each state, and is not mandated by the federal government. "States routinely review their academic standards and may choose to change or add onto

4000-549: The Prince Consort, took on the role of president for the year. The young Maxwell himself, still only 28, spoke on three different subjects, one being a presentation of his newly discovered law of molecular velocities in a gas. The ' Maxwell distribution law ', as it is now known, is the law of physics with the strongest Aberdeen connection. In addition, Sir Charles Lyell , president of the Geological Section of

4100-601: The Queen in September 2012. Today, most students spend most of their time in modern buildings which provide up-to-date facilities for teaching, research and other activities such as dining. However, the old buildings at King's College are still in use as lecture and tutorial rooms and accommodation for various academic departments. In February 2020, the Scottish Funding Council (SFC) found that in approving

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4200-469: The School of Biological Sciences. It also includes the Rowett Institute of Nutrition and Health , the Institute of Medical Sciences, Institute of Applied Health Sciences, Institute of Dentistry, and Institute of Education for Medical & Dental Sciences. The Foresterhill site is managed jointly with NHS Grampian. The university has had a presence at Foresterhill since around 1938, and the management of

4300-753: The Scottish Crown. It was a collegiate foundation with 36 full-time staff and students and walls protecting it from the outside world. In 1497 the college established the first chair of medicine in the English-speaking world. The first book (there was no printing press in Scotland at the time) to be printed in Edinburgh and in Scotland was the Aberdeen Breviary , which was written by both Elphinstone and Boece in 1509. Following

4400-649: The Sumerians were practicing multiplication and division. There are also artifacts demonstrating their methodology for solving equations like the quadratic equation . After the Sumerians, some of the most famous ancient works on mathematics came from Egypt in the form of the Rhind Mathematical Papyrus and the Moscow Mathematical Papyrus . The more famous Rhind Papyrus has been dated back to approximately 1650 BCE, but it

4500-552: The United States. During the primary school years, children learn about whole numbers and arithmetic, including addition, subtraction, multiplication, and division. Comparisons and measurement are taught, in both numeric and pictorial form, as well as fractions and proportionality , patterns, and various topics related to geometry. At high school level in most of the US, algebra , geometry , and analysis ( pre-calculus and calculus ) are taught as separate courses in different years. On

4600-477: The University's severance policy which states that "the maximum redundancy package available to staff is 12 months of pay or £100,000; whatever is lower." A group of academics from the department released a statement which described the proposed changes as "institutional vandalism". They continued "The management's self-destructive plan would see the University of Aberdeen become the first ancient university in

4700-488: The University, in support of Modern Languages degrees. Staff-led business proposals were positively received and the consultation on Modern Languages was ended in March 2024 with the removal of risk of compulsory redundancies. The university's main campus is at King's College in Old Aberdeen, where the original buildings are still in use in addition to many 20th century buildings. A second campus at Foresterhill accommodates

4800-553: The architect, Alexander Marshall Mackenzie was a native of Aberdeen as well as an alumnus of the university. The Mitchell Tower at the rear is named for the benefactor (Dr Charles Mitchell ) who paid for the graduation hall. The opening of this tower in 1895 was part of celebrations of the 400th anniversary of the university. Until 1996, Marischal College housed the Departments of Molecular & Cell Biology and Biomedical Sciences, which had been there for many decades. From 1996,

4900-502: The buildings on the "campus" which also include private houses, shops and businesses (although many of these rely heavily on custom from the university community) and it is best thought of as a district of the city dominated by the university. It can be reached from the city centre by bus routes 1, 2, 13, 19 and 20 operated by First Aberdeen and from northern Aberdeenshire or Aberdeen bus station by various routes operated by Stagecoach Bluebird . The historic King's College buildings form

5000-714: The changes in math educational standards. The Programme for International Student Assessment (PISA), created by the Organisation for the Economic Co-operation and Development (OECD), is a global program studying the reading, science, and mathematics abilities of 15-year-old students. The first assessment was conducted in the year 2000 with 43 countries participating. PISA has repeated this assessment every three years to provide comparable data, helping to guide global education to better prepare youth for future economies. There have been many ramifications following

5100-592: The chapel contains original oak-canopied stalls, miserere seats, and lofty open screens in the French flamboyant style. They were preserved by the college's Principal during the Reformation , who fought off local barons who had attacked the nearby St Machar's Cathedral . The Cromwell Tower, created between 1658 and 1662 opposite the Crown Tower, was originally built as residential accommodation, but an observatory

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5200-538: The church reunion of 1929, Christ's College became a Church of Scotland college and was integrated into the University of Aberdeen. The college building is no longer used by either the church or the university, and the college is contained completely within the buildings of King's College, maintaining its own divinity library. The university hosted its first meeting of the British Science Association in 1859. Having no suitable meeting place to host

5300-601: The city and coastline are available from the upper floors. In addition to expanded facilities it also houses public exhibition space and the university's historic collections, comprising more than a quarter of a million ancient and priceless books and manuscripts collected over five centuries since the university's foundations. Other libraries are in the Taylor Building on the same campus (for law books and materials) and at Foresterhill (for medicine and medical sciences). The university's library service (i.e. including all libraries) holds over one million books. The most recent building

5400-400: The city, which included church services, banquets, torchlight processions, and fireworks displays. In all, the cost of the four days of festivities was the modern equivalent of £1.34 million. The ceremony saw the granting of honorary degrees to over a hundred public and academic figures from across the academic world. In an extravagant display of luxury, Lord Strathcona , the then chancellor of

5500-477: The college. The two rival colleges often clashed, sometimes in court, but also in brawls between students on the streets of Aberdeen. Duncan Liddell endowed the first chair in mathematics at Marischal College in 1613, but the first professor was not appointed until 1626. As the institutions put aside their differences, a process of attempted (but unsuccessful) mergers began in the 17th century. During this time, both colleges made notable intellectual contributions to

5600-433: The continuous and discrete sides of the subject: Similar efforts are also underway to shift more focus to mathematical modeling as well as its relationship to discrete math. At different times and in different cultures and countries, mathematics education has attempted to achieve a variety of different objectives. These objectives have included: The method or methods used in any particular context are largely determined by

5700-410: The current findings in the field of mathematics education. As with other educational research (and the social sciences in general), mathematics education research depends on both quantitative and qualitative studies. Quantitative research includes studies that use inferential statistics to answer specific questions, such as whether a certain teaching method gives significantly better results than

5800-409: The departments moved to Kings College campus and Foresterhill campus. Teaching no longer takes place at Marischal College, with many of the departments formerly based there having moved to King's College some decades previously. While graduations and other events (e.g. concerts) took place in the cathedral-like Mitchell Hall in the north wing, for many years much of the building (including the frontage to

5900-441: The difficulties posed by the war, although it does not appear to have been ever formally wound up. The Free Church of Scotland founded Christ's College in Aberdeen in 1843 for the training of ministers. An extravagant Gothic building, with a commanding oriel window and tower, was erected for the college at the western end of Union Street in 1850. Linked to the college was a museum and library (containing 17,000 volumes). Following

6000-414: The east of the Old Aberdeen campus and is home to the university's Life Sciences and Medicine facilities. It is co-located with Aberdeen Royal Infirmary , Royal Aberdeen Children's Hospital and Aberdeen Maternity Hospital , all teaching hospitals operated by regional health board NHS Grampian . The campus accommodates the School of Medicine, Medical Science and Nutrition ; the School of Psychology; and

6100-594: The effects of such treatments are not yet known to be effective, or the difficulty of assuring rigid control of the independent variable in fluid, real school settings. In the United States, the National Mathematics Advisory Panel (NMAP) published a report in 2008 based on studies, some of which used randomized assignment of treatments to experimental units , such as classrooms or students. The NMAP report's preference for randomized experiments received criticism from some scholars. In 2010,

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6200-439: The extension of King's at the cost of £20,000. This included the rebuilding of two sides of the quadrangle for the class-rooms (1862) and the erection of the library (1870), which for many years had occupied the nave of the chapel. In 1873, university students voted against university degrees being open to women. However, all faculties were open to women in 1892, and in 1894 the first 20 matriculated females began their studies at

6300-471: The former. The university's iconic buildings act as symbols of wider Aberdeen, particularly Marischal College in the city centre and the crown steeple of King's College in Old Aberdeen . There are two campuses; the predominantly utilised King's College campus dominates the section of the city known as Old Aberdeen , which is approximately two miles north of the city centre. Although the original site of

6400-579: The founding of the Fraserburgh University in nearby Fraserburgh by Sir Alexander Fraser , a business rival of Keith, was instrumental in its creation. Aberdeen was highly unusual at this time for having two universities in one city: as 20th-century university prospectuses observed, Aberdeen had the same number as existed in England at the time (the University of Oxford and University of Cambridge ). Initially, Marischal College offered

6500-404: The future of teaching of modern languages at the University. It was looking at three options, "all of which involve the end of single honours French, Gaelic, German and Spanish", and was engaging in consultation with student and faculty. It was stated that departmental "income does not cover even the direct costs of staff delivering Modern Languages provision before any central costs ... leading to

6600-459: The grave influence of whose eyes sublime Men count for the stability of the time' In the 20th century, the university expanded greatly, particularly at King's College. New buildings were constructed on the land around King's College throughout the 20th century. Initially, these were built to match the ancient buildings (e.g. the New King's lecture rooms and Elphinstone Hall), but later ones from

6700-850: The institution for 2022–23 was £268.6 million of which £56.3 million was from research grants and contracts, with an expenditure of £259.3 million. Aberdeen has educated a wide range of notable alumni, and the university played key roles in the Scottish Reformation , Scottish Enlightenment , and the Scottish Renaissance . Five Nobel laureates have since been associated with the university: two in Chemistry , one in Physiology or Medicine , one in Physics , and one in Peace . There appears to have existed in Old Aberdeen, from

6800-515: The lawn opposite King's College was removed before the First World War. New King's groups to form a yet larger quadrangle-like green for the campus also bordered by the High Street, King's and Elphinstone Hall , a traditional 1930 replacement for the Great Hall. The Elphinstone Hall was subsequently used as a dining facility but is now used for graduations, examinations, fairs, and other large university events. However, most students and staff spend relatively little time in these historic buildings, with

6900-408: The learned professions, and this feature differentiated it from the more open and socially inclusive societies like the Glasgow Literary Society or the Select Society of Edinburgh . Over 133 papers were given and discussed at the meeting, and many of these formed the basis of books subsequently published. The society was eventually disbanded in March 1773. The society and its individual members played

7000-583: The levels of achievement that were relevant to, realistic for, and considered socially appropriate for their pupils. In modern times, there has been a move towards regional or national standards, usually under the umbrella of a wider standard school curriculum. In England , for example, standards for mathematics education are set as part of the National Curriculum for England, while Scotland maintains its own educational system. Many other countries have centralized ministries which set national standards or curricula, and sometimes even textbooks. Ma (2000) summarized

7100-435: The meeting, the town raised the money themselves by personal subscription and built the Music Hall . It was capable of holding about 2,500 people and so successful was the meeting that associate membership, necessary to gain access to the proceedings, had to be capped. Prominent among the local organisers were Professors James Clerk Maxwell (Natural Philosophy) and James Nicol (Geology) of Marischal College. Prince Albert ,

7200-507: The objectives that the relevant educational system is trying to achieve. Methods of teaching mathematics include the following: Different levels of mathematics are taught at different ages and in somewhat different sequences in different countries. Sometimes a class may be taught at an earlier age than typical as a special or honors class . Elementary mathematics in most countries is taught similarly, though there are differences. Most countries tend to cover fewer topics in greater depth than in

7300-415: The other hand, in most other countries (and in a few US states), mathematics is taught as an integrated subject, with topics from all branches of mathematics studied every year; students thus undertake a pre-defined course - entailing several topics - rather than choosing courses à la carte as in the United States. Even in these cases, however, several "mathematics" options may be offered, selected based on

7400-649: The other social sciences. Many studies are “mixed”, simultaneously combining aspects of both quantitative and qualitative research, as appropriate. There has been some controversy over the relative strengths of different types of research. Because of an opinion that randomized trials provide clear, objective evidence on “what works”, policymakers often consider only those studies. Some scholars have pushed for more random experiments in which teaching methods are randomly assigned to classes. In other disciplines concerned with human subjects—like biomedicine , psychology , and policy evaluation—controlled, randomized experiments remain

7500-454: The preferred method of evaluating treatments. Educational statisticians and some mathematics educators have been working to increase the use of randomized experiments to evaluate teaching methods. On the other hand, many scholars in educational schools have argued against increasing the number of randomized experiments, often because of philosophical objections, such as the ethical difficulty of randomly assigning students to various treatments when

7600-411: The principal of King's College a role in selecting its academics, but this was refused – the first blow in a developing rivalry. Marischal College, in the commercial heart of the city (rather than the ancient but much smaller collegiate enclave of Old Aberdeen), was quite different in nature and outlook. For example, it was more integrated into the life of the city, such as allowing students to live outwith

7700-442: The research of others who found, based on nationwide data, that students with higher scores on standardized mathematics tests had taken more mathematics courses in high school. This led some states to require three years of mathematics instead of two. But because this requirement was often met by taking another lower-level mathematics course, the additional courses had a “diluted” effect in raising achievement levels. In North America,

7800-481: The results of triennial PISA assessments due to implicit and explicit responses of stakeholders, which have led to education reform and policy change. According to Hiebert and Grouws, "Robust, useful theories of classroom teaching do not yet exist." However, there are useful theories on how children learn mathematics, and much research has been conducted in recent decades to explore how these theories can be applied to teaching. The following results are examples of some of

7900-502: The site was formalised in 1997 by the completion of an operational agreement between the two parties. A new campus in Doha , Qatar was established in May 2017. Known as AFG College with the University of Aberdeen, it is a partnership with Al Faleh Group for Educational and Academic Services (AFG). The courses currently offered are accounting, finance and business management. The campus Principal

8000-482: The standards to best meet the needs of their students." The NCTM has state affiliates that have different education standards at the state level. For example, Missouri has the Missouri Council of Teachers of Mathematics (MCTM) which has its pillars and standards of education listed on its website. The MCTM also offers membership opportunities to teachers and future teachers so that they can stay up to date on

8100-460: The status quo. The best quantitative studies involve randomized trials where students or classes are randomly assigned different methods to test their effects. They depend on large samples to obtain statistically significant results. Qualitative research , such as case studies , action research , discourse analysis , and clinical interviews , depend on small but focused samples in an attempt to understand student learning and to look at how and why

8200-526: The street) was derelict. The majority of the building was leased to Aberdeen City Council in 2008, with significant re-development taking place to allow the council to occupy it as its new administrative headquarters. Occupation of the rear portion of the building is retained by the university including the former Marischal Museum and Mitchell Hall, which was used previously for graduation and other academic ceremonies before moving to Elphinstone Hall at King's College. A small campus at Hilton became part of

8300-751: The student's intended studies post high school. (In South Africa, for example, the options are Mathematics, Mathematical Literacy and Technical Mathematics.) Thus, a science-oriented curriculum typically overlaps the first year of university mathematics, and includes differential calculus and trigonometry at age 16–17 and integral calculus , complex numbers , analytic geometry , exponential and logarithmic functions , and infinite series in their final year of secondary school; Probability and statistics are similarly often taught. At college and university level, science and engineering students will be required to take multivariable calculus , differential equations , and linear algebra ; at several US colleges,

8400-474: The submission of two motions calling to protect languages degrees at the University of Aberdeen, a debate took place in Scottish Parliament, where the University was urged to explore alternative options. EU consulates also spoke out in favour of the languages programmes. , as well as scome of Scotland's best-known folk music starts. The local UCU branch successfully balloted for strike action at

8500-460: The teaching of mathematics. While previous approach focused on "working with specialized 'problems' in arithmetic ", the emerging structural approach to knowledge had "small children meditating about number theory and ' sets '." Since the 1980s, there have been a number of efforts to reform the traditional curriculum, which focuses on continuous mathematics and relegates even some basic discrete concepts to advanced study, to better balance coverage of

8600-400: The twentieth century, mathematics was part of the core curriculum in all developed countries . During the twentieth century, mathematics education was established as an independent field of research. Main events in this development include the following: Midway through the twentieth century, the cultural impact of the " electronic age " (McLuhan) was also taken up by educational theory and

8700-594: The university estate following a merger in 2001 between the university and the Aberdeen campus of the Northern College of Education, and temporarily became home to the university's Faculty of Education. It was less than a mile southwest of King's College campus. Following the renovation of the MacRobert Building at King's College to house the School of Education (completed in 2005), the Hilton campus

8800-446: The university's foundation, most academic buildings apart from the King's College Chapel and Quadrangle were constructed in the 20th century during a period of significant expansion. The university's Foresterhill campus is next to Aberdeen Royal Infirmary and houses the School of Medicine and Dentistry as well as the School of Medical Sciences. Together these buildings form one of Europe's largest health campuses. The annual income of

8900-399: The university, spent £8518 in entertaining around 2500 invited guests in a tent specially designed for the occasion. After having received an honorary degree (LLD) in 1905, Thomas Hardy celebrated Aberdeen as 'a University which can claim in my opinion to an exceptional degree that breadth of view & openness of mind that all Universities profess to cultivate, but many stifle'. Hardy wrote

9000-461: The university. Four women graduated in arts by 1898, and by the following year, women made up a quarter of the faculty. The closing of the quadrangle of Marischal College was completed during the university's quatercentenary in 1906, which was officially opened by Edward VII and Alexandra , and which saw some of the most extravagant celebrations and expressions of civic pride ever demonstrated in Aberdeen. Four days of festivities took place across

9100-496: The world not to offer language degrees in one of the most monolingual countries" A University statement said: "Our difficulty is that this academic year, following longer term declining demand in the UK for traditional specialist language study, a total of just five students began Single Honours across our four Modern Language programmes including Gaelic." A public petition to save Modern Languages gained over 18,600 signatures. After

9200-642: The years. At one time there was a portrait of John Leslie dressed in Turkish costume, on the walls of Powis House, but there is no obvious connection between the estate and the Middle East. The gateway is also adorned with panels bearing the coats of arms of the Lairds of Powis. The Estate of Powis was owned by the Frasers—their crest is shown on the towers—until the marriage of an heiress to a Leslie. Powis House

9300-464: Was built by Hugh Leslie. The house was the home of John Leslie, Professor of Greek at Kings College. It was subsequently owned by the Burnett family. In 1936, J.G. Burnett sold most of the estate to Aberdeen Town Council who built a housing estate in the area comprising over 300 residences. The Sir Duncan Rice Library was designed by Danish architects Schmidt Hammer Lassen and completed in 2011. It

9400-470: Was built on top in 1826. The library wing was converted into an exhibition and conference venue in the 1990s and today also houses the university's Business School. The first of the modern age of construction in the King's campus began with the construction in 1913 of the New Building (now known as "New King's" ), largely in a similar architectural style to the old buildings. A large manse located on

9500-496: Was closed and sold to developers. The campus was demolished and the land is now occupied by a residential development called "The Campus". In common with the other ancient universities in Scotland, the university's structure of governance is largely regulated by the Universities (Scotland) Acts of 1858. This gives the university a tripartite constitution comprising the General Council of senior academics and graduates,

9600-614: Was developed in medieval Europe. The teaching of geometry was almost universally based on Euclid's Elements . Apprentices to trades such as masons, merchants, and moneylenders could expect to learn such practical mathematics as was relevant to their profession. In the Middle Ages , the academic status of mathematics declined, because it was strongly associated with trade and commerce, and considered somewhat un-Christian. Although it continued to be taught in European universities , it

9700-426: Was just outside the walls, in front of the college. The Crown Tower is surmounted by a structure about 40 ft (12 m) high, consisting of a six-sided lantern and Imperial crown, both sculptured, and resting on the intersections of two arched ornamental slips rising from the four corners of the top of the tower. This crown, also known as the "Crown of Kings", frequently acts as a symbol of the university. The choir of

9800-825: Was more philosophical and concerned numbers as concepts rather than calculating methods. They also contrasted with mathematical methods learned by artisan apprentices, which were specific to the tasks and tools at hand. For example, the division of a board into thirds can be accomplished with a piece of string, instead of measuring the length and using the arithmetic operation of division. The first mathematics textbooks to be written in English and French were published by Robert Recorde , beginning with The Grounde of Artes in 1543. However, there are many different writings on mathematics and mathematics methodology that date back to 1800 BCE. These were mostly located in Mesopotamia, where

9900-418: Was officially opened by Queen Elizabeth II in September 2012 and named after Duncan Rice , a previous Principal of the university. This seven-storey tower, clad in zebra-like jagged stripes of white and clear glass, replaced the smaller Queen Mother Library as the university's main library and can be seen prominently from the entire campus and much of the city. It is open to the public and outstanding views of

10000-461: Was seen as subservient to the study of natural , metaphysical , and moral philosophy . The first modern arithmetic curriculum (starting with addition , then subtraction , multiplication , and division ) arose at reckoning schools in Italy in the 1300s. Spreading along trade routes, these methods were designed to be used in commerce. They contrasted with Platonic math taught at universities, which

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