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Mathematics education is a term that refers both to the practice of teaching and learning mathematics, as well as to a field of scholarly research on this practice. In Education, a teacher is one who helps Students or pupils often in a School, as well as in a Family, religious or In the fields of Neuropsychology, Personal development and Education, Learning is one of the most important Mental function of humans Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Research is defined as Human activity based on Intellectual application in the investigation of Matter. Researchers in math education are in the first instance concerned with the tools, methods and approaches that facilitate practice and/or the study of practice. However mathematics education research, known on the continent of Europe as the didactics of mathematics has developed into a fully fledged field of study, with its own characteristic concepts, theories, methods, national and international organizations, conferences and literature. A didactic method ( Greek: didáskein = to teach lore of teaching is a Teaching method that follows a consistent scientific approach or educational style to engage This article describes some of the history, influences and recent controversies concerning math education as a practice.

A mathematics lecture at Helsinki University of Technology.
A mathematics lecture at Helsinki University of Technology.

Contents

History

Illustration at the beginning of a 14th century translation of Euclid's Elements.
Illustration at the beginning of a 14th century translation of Euclid's Elements.

Elementary mathematics was part of the education system in most ancient civilizations, including Ancient Greece, the Roman empire, Vedic society and ancient Egypt. Education encompasses both the Teaching and Learning of Knowledge, proper conduct, and technical competency The term ancient Greece refers to the period of Greek history lasting from the Greek Dark Ages ca The Roman Empire was the post-Republican phase of the ancient Roman civilization, characterised by an autocratic form of government and large territorial The Vedic Period (or Vedic Age) is the period in the History of India during which the Vedas, the oldest sacred texts of Hinduism, were being Ancient Egypt was an Ancient Civilization in eastern North Africa, concentrated along the lower reaches of the Nile River in what is now In most cases, a formal education was only available to male children with a sufficiently high status, wealth or caste. Male (♂ refers to the sex of an organism or part of an organism which produces small mobile Gametes called spermatozoa. Castes are Hereditary systems of occupation, Endogamy, social culture, Social class, and Political power.

In Plato's division of the liberal arts into the trivium and the quadrivium, the quadrivium included the mathematical fields of arithmetic and geometry. Biography Early life Birth and family Plato was born in Athens Greece The term liberal arts refers to a particular type of educational Curriculum broadly defined as a Classical education. In medieval universities, the trivium comprised the three subjects taught first Grammar, Logic, and Rhetoric. The quadrivium comprised the four subjects or arts taught in Medieval universities after the trivium. Arithmetic or arithmetics (from the Greek word αριθμός = number is the oldest and most elementary branch of mathematics used by almost everyone Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position This structure was continued in the structure of classical education that was developed in medieval Europe. Teaching of geometry was almost universally based on Euclid's Elements. Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry Apprentices to trades such as masons, merchants and money-lenders could expect to learn such practical mathematics as was relevant to their profession.

The first mathematics textbooks to be written in English and French were published by Robert Recorde, beginning with The Grounde of Artes in 1540. Robert Recorde (c 1510 &ndash 1558 was a Welsh Physician and Mathematician.

In the Renaissance the academic status of mathematics declined, because it was strongly associated with trade and commerce. The Renaissance (from French Renaissance, meaning "rebirth" Italian: Rinascimento, from re- "again" and nascere Although it continued to be taught in European universities, it was seen as subservient to the study of Natural, Metaphysical and Moral Philosophy.

This trend was somewhat reversed in the seventeenth century, with the University of Aberdeen creating a Mathematics Chair in 1613, followed by the Chair in Geometry set up in University of Oxford in 1619 and the Lucasian Chair of Mathematics, established by the University of Cambridge in 1662. As a means of recording the passage of Time, the 17th Century was that Century which lasted from 1601 - 1700 in the Gregorian calendar The University of Aberdeen is an Ancient university founded in 1495, in Old Aberdeen, Scotland. The University of Oxford (informally "Oxford University" or simply "Oxford" located in the city of Oxford, Oxfordshire, England is the The incumbent of the Lucasian Chair of Mathematics, the Lucasian Professor is the holder of a mathematical Professorship at the University of Cambridge The University of Cambridge (often Cambridge University) located in Cambridge, England, is the second-oldest university in the However, it was uncommon for mathematics to be taught outside of the universities. Isaac Newton, for example, received no formal mathematics teaching until he joined Trinity College, Cambridge in 1661. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Trinity College is a constituent college of the University of Cambridge in Cambridge, England.

In the eighteenth and nineteenth centuries the industrial revolution led to an enormous increase in urban populations. The 18th century lasted from 1701 to 1800 in the Gregorian calendar, in accordance with the Anno Domini / Common Era numbering system The 19th century of the Common Era began on January 1, 1801 and ended on December 31, 1900, according to the Gregorian calendar The Industrial Revolution was a period in the late 18th and early 19th centuries when major changes in agriculture manufacturing and transportation had a profound effect on the 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. Arithmetic or arithmetics (from the Greek word αριθμός = number is the oldest and most elementary branch of mathematics used by almost everyone Within the new public education systems, mathematics became a central part of the curriculum from an early age. Public education is education mandated for or offered to the children of the general public by the Government, whether national regional or local provided by an institution

By the twentieth century mathematics was part of the core curriculum in all developed countries. The twentieth century of the Common Era began on The term developed country, or advanced country, is used to categorize countries with developed Economies in which the tertiary and quaternary sectors

During the twentieth century mathematics education was established as an independent field of research. The twentieth century of the Common Era began on Here are some of the main events in this development:

In the 20th century, the cultural impact of the "electric age" (McLuhan) was also taken up by educational theory and the teaching of mathematics. Exeter ( (IPA ˈeksɪtər is a city, district and County town of Devon, England. Education theory is the Theory or the Philosophy of the purpose application and interpretation of Education and Learning. 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'. Arithmetic or arithmetics (from the Greek word αριθμός = number is the oldest and most elementary branch of mathematics used by almost everyone Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes "[1]

Objectives

At different times and in different cultures and countries, mathematics education has attempted to achieve a variety of different objectives. These objectives have included:

Methods of teaching mathematics have varied in line with changing objectives.

Standards

Throughout most of history, standards for mathematics education were set locally, by individual schools or teachers, depending on the levels of achievement that were relevant to and realistic 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. England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland

Ma (2000) summarized the research of others who found, based on nationwide data, that students with higher scores on standardized math tests had taken more mathematics courses in high school. This led some states to require three years of math instead of two. But because this requirement was often met by taking another lower level math course, the additional courses had a “diluted” effect in raising achievement levels.

In North America, the National Council of Teachers of Mathematics (NCTM) has published the Principles and Standards for School Mathematics. In 2006, they released the Curriculum Focal Points, which recommend the most important mathematical topics for each grade level.

Ma, X. (2000). A longitudinal assessment of antecedent course work in mathematics and subsequent mathematical attainment. Journal of Educational Research, 94, 16-29.

Content and age levels

Different levels of mathematics are taught at different ages. Sometimes a class may be taught at an earlier age as a special or "honors" class. A rough guide to the ages at which the sub-topics of arithmetics and algebra are taught in the United States is as follows:

For comparison to American grade levels, most Americans begin kindergarten, the year before first grade in the American schooling system, between the ages of 4 and 6. The United States of America —commonly referred to as the Addition is the mathematical process of putting things together Subtraction is one of the four basic Arithmetic operations it is the inverse of Addition, meaning that if we start with any number and add any number and then subtract In Mathematics, especially in elementary Arithmetic, division is an arithmetic operation which is the inverse of Multiplication. Pre-algebra is a common name for a course in Elementary mathematics. Mathematics education is a term that refers both to the practice of Teaching and Learning Mathematics, as well as to a field of scholarly Research Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position Circle-trig6svg|300px|thumb|right|All of the Trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives In American Mathematics education, Precalculus an advanced form of secondary school algebra, is a foundational mathematical discipline ( German, literally means "children's garden" is a form of education for young children which serves as a transition from home to the commencement of more formal schooling

Methods

The method or methods used in any particular context are largely determined by the objectives that the relevant educational system is trying to achieve. Methods of teaching mathematics include the following:

Recent controversy over U. S. mathematics education

Main articles: Math wars and National Council of Teachers of Mathematics

Near the end of the 20th century diverse and changing ideas about the purpose of mathematical education would lead to wide adoption of reform-based standards and curricula funded by the US federal government, and also adopted by other national curriculum standards These were based on student-centered learning methods and equity in mathematics as a centerpiece of the standards based education reform movement. Math wars is the debate over modern Mathematics education, textbooks and curricula in the United States that was triggered by the publication in 1989 of the Curriculum The National Council of Teachers of Mathematics (NCTM was founded in 1920. Student-centred learning (also called child-centred learning) is an approach to Education focusing on the needs of the Students rather than those Education reform in the United States since the late 1980s has been largely driven by the setting of academic standards for what students should know and be able to do This movement in turn was met with opposition which called for a return to traditional direction instruction of time-tested arithmetic methods by the start of the 21st century as some schools and districts supplemented or replaced standards-based curricula.

With the adoption of substantially different teaching reform standards and the development and widespread adoption of federally funded curricula during the 1990s, mathematics education has become the most hotly debated subject since the original 1960s "New Math" in mainstream news journals such as the Wall Street Journal and New York Times. New Math was a brief dramatic change in the way Mathematics was taught in American Grade schools during the 1960s The name is commonly given There is a significant difference in perspective between the relative few who practice mathematics in their careers, and those who have been tasked with teaching mathematics to children. The goals for educators since the 1990s have been expanded in the context of systemic standards based education reform in the United States and other nations to promote increased learning for all students. Education reform in the United States since the late 1980s has been largely driven by the setting of academic standards for what students should know and be able to do It is a goal to achieve equity and success for all groups in society. It is no longer acceptable to many in the education community that some were historically excluded from the full range of opportunities open to those who learned the most advanced mathematics.

By the late 1980s, a movement for systemic education reform took hold based on constructivist practices and the belief in success for all groups including minorities and women. Outcome-based education (OBE is a recurring Education reform model Among the development of a number of controversial standards across reading, science and history, the National Council of Teachers of Mathematics [3] of the United States produced the Curriculum and Evaluation Standards for School Mathematics in 1989. Whole language describes a literacy instructional philosophy which emphasizes that children should focus on meaning and moderates skill instruction Inquiry-based learning or inquiry-based science describes a range of philosophical curricular and pedagogical approaches to teaching The National Council of Teachers of Mathematics (NCTM was founded in 1920. Principles and Standards for School Mathematics [4] included new goals such as equity and de-emphasized the traditional idea of relying solely on standard algorithms to get solutions. Principles and Standards for School Mathematics is a book produced by the National Council of Teachers of Mathematics (NCTM in 2000 to set forth a national vision for precollege

The controversial 1989 NCTM standards recommended teaching elements of algebra as early as grade 5, and elements of calculus as early as grade 9, though this was rarely adopted even as late as the 2000s. Principles and Standards for School Mathematics is a book produced by the National Council of Teachers of Mathematics (NCTM in 2000 to set forth a national vision for precollege In standards based education reform, all students, not only the college bound must take advanced mathematics. Education reform in the United States since the late 1980s has been largely driven by the setting of academic standards for what students should know and be able to do In some large school districts, this means requiring algebra of all students by the end of junior high school, compared to the tradition of tracking only college bound and the most advanced junior high school students to take algebra.

The standards soon became the basis for many new federally funded curricula such as the Core-Plus Mathematics Project and became the foundation of many local and state curriculum frameworks. The Core-Plus Mathematics Project is one of the five NCTM -standards-based High school Mathematics Curriculum development projects funded by the A curriculum framework is an organized plan or set of standards or learning outcomes that defines the content to be learned in terms of clear definable standards of what the Although the standards were the consensus of those teaching mathematics in the context of real life, they also became a lightning rod of criticism as math wars erupted in some communities that were opposed to some of the more radical changes to mathematics instruction such as Mathland's Fantasy Lunch and what some dubbed "rainforest algebra". Consensus has two common meanings One is a general agreement among the members of a given group or Community, each of which exercises some discretion in MathLand was one of many controversial mathematics curricula that were designed around the 1989 NCTM standards. Some students complained that their new math courses placed them into remedial math in college.

In 2000 and 2006 NCTM released another standards document and the Curriculum Focal Points which expanded on the work of the previous standards documents. Refuting reports and editorials [2] that it was largely an admission that the previous standards had mistakenly de-emphasized instruction of basic skills, NCTM spokesmen maintained that it provided more grade by grade specificity on key areas of study for a coherent and consistent development of mathematical understanding and skill.

In 2000 and 2006, the same NCTM issued new studies that criticized American math standards as a "mile wide and an inch deep" in comparison to the math of nations such as Singapore Math. The National Council of Teachers of Mathematics (NCTM was founded in 1920. In the United States the Singapore Math Method of teaching Mathematics is based on textbooks from the national curriculum of Singapore. Rather than backing research which had called them harmful, it called for strong instruction of basic skills. The New York Times and the Wall Street Journal called it a significant retreat back towards traditional mathematics, and some warned it might lead to a generation who could solve equations accurately, but not deeply understand mathematics, or relate it to real life issues such as the environment. [3]

Mathematics teachers

The following people all taught mathematics at some stage in their lives, although they are better known for other things:

Mathematics educators

The following people had a significant influence on the teaching of mathematics at various periods in history:

See also

References

  1. ^ Marshall McLuhan (1964) Understanding Media, p. Principles and Standards for School Mathematics is a book produced by the National Council of Teachers of Mathematics (NCTM in 2000 to set forth a national vision for precollege Mathematically Correct is a website created by educators parents mathematicians and scientists who were concerned about the direction of reform mathematics curricula based Principles and Standards for School Mathematics is a book produced by the National Council of Teachers of Mathematics (NCTM in 2000 to set forth a national vision for precollege Anti-racist mathematics is a branch of Education reform theory that attempts to form an Anti-bias curriculum in Mathematics. List of racism-related topics|Racism by country Racism, by its simplest definition is the belief that race is the primary determinant of human traits and capacities and that Traditional mathematics (sometimes classical math education) is a term used to describe the predominant methods of Mathematics education in the United States Traditional education refers to long-established customs found in schools that society has traditionally deemed appropriate Constructivism is a psychological theory of knowledge ( Epistemology) which argues that humans construct knowledge and meaning from their experiences Computer Based Mathematics Education (CBME refers to a mathematics education method that is enriched by using computers Dyscalculia is a type of specific learning disability (SLD involving innate difficulty in learning or comprehending Mathematics. A math worksheet generator is a Software program that generates Math problems The philosophy of education is the study of the purpose process nature and ideals of Education. 13 [1]
  2. ^ Wall Street Journal, New York Times, Chicago Sun Times
  3. ^ [2] Report Urges Changes in the Teaching of Math in U. S. Schools by TAMAR LEWIN New York Times September 13, 2006
  4. ^ Freddie Mercury Interview, Melody Maker, May 2, 1981

External links

Teacher organizations and others associated with mathematics education

Scholarly journals: print

Scholarly journals: on-line

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The National Council of Teachers of Mathematics (NCTM was founded in 1920. The National Centre for Excellence in Teaching Mathematics ( NCETM) is the new institution set up in the wake of the Smith Report to improve Mathematics teaching Homi Bhabha Centre for Science Education (HBCSE is a National Centre of the Tata Institute of Fundamental Research (TIFR Mumbai India Education encompasses both the Teaching and Learning of Knowledge, proper conduct, and technical competency Agricultural education is instruction about Crop production Livestock management soil and water conservation and various other aspects of agriculture For general education in the broad range of Arts see Arts education, for education in the Performing arts see Performing arts education Bilingual education involves teaching all subjects in school through two different languages - in the United States instruction occurs in English and a minority language such as Chemistry Education (or often “Chemical Education” is a comprehensive term that refers to topics related to the study or description of the Teaching and Learning Language education includes the Teaching and Learning of a Language. Legal education is the education of individuals who intend to become legal professionals or those who simply intend to use their law degree to some end either related to law Medical education is education related to the practice of being a medical practitioner, either the initial training to become a doctor (i Military education and training is a process which intends to establish and improve the capabilities of military personnel in their respective roles Music education is a field of study associated with the teaching and learning of music Peace education is the process of acquiring the values, the knowledge and developing the attitudes skills and behaviors to live in harmony with oneself Education in the performing arts is a key part of many primary and Secondary education curricula and is also available as a specialisation at the tertiary Physics education refers both to the methods currently used to teach Physics and to an area of pedagogical research that seeks to improve those methods Reading education is the process by which individuals are taught to derive meaning from text In Secular usage religious education is the Teaching of a particular Religion (although in England the term religious instruction would refer Science education is the field concerned with sharing Science Content and Process with individuals not traditionally considered part of the scientific community Sex education is a broad term used to describe Education about human sexual anatomy, Sexual reproduction, Sexual intercourse, Reproductive Technology education is a study of technology which provides an opportunity for students to learn about the processes and knowledge related to technology Vocational education or Vocational Education and Training (VET also called Career and Technical Education (CTE prepares learners for jobs that are based
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