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Encyclopedia > Mathematics education

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. Researchers in maths 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. This article describes some of the history, influences and recent controversies concerning maths education as a practice. In education, teachers are those who teach students or pupils, often a course of study or a practical skill. ... Learning is the acquisition and development of memories and behaviors, including skills, knowledge, understanding, values, and wisdom. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... This article is about the concept. ...

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

Contents

Image File history File links Download high resolution version (1200x900, 147 KB) A mathematics lecture, apparently about linear algebra, at Helsinki Univeristy of Technology - TKK. File links The following pages link to this file: Mathematics University Student Lecture ... Image File history File links Download high resolution version (1200x900, 147 KB) A mathematics lecture, apparently about linear algebra, at Helsinki Univeristy of Technology - TKK. File links The following pages link to this file: Mathematics University Student Lecture ...

History

Illustration at the beginning of 14th century translation of Euclid's Elements.
Illustration at the beginning of 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. In most cases, a formal education was only available to male children with a sufficiently high status, wealth or caste. Image File history File links Download high-resolution version (1039x1148, 757 KB) [edit] Summary Detail of a scene in the bowl of the letter P with a woman with a set-square and dividers; using a compass to measure distances on a diagram. ... Image File history File links Download high-resolution version (1039x1148, 757 KB) [edit] Summary Detail of a scene in the bowl of the letter P with a woman with a set-square and dividers; using a compass to measure distances on a diagram. ... This article is about institutionalized education. ... The term ancient Greece refers to the periods of Greek history in Classical Antiquity, lasting ca. ... For other uses, see Roman Empire (disambiguation). ... This article or section does not cite its references or sources. ... Khafres Pyramid and the Great Sphinx of Giza, built about 2550 BC during the Fourth Dynasty of the Old Kingdom,[1] are enduring symbols of the civilization of ancient Egypt Ancient Egypt was a civilization in Northeastern Africa concentrated along the middle to lower reaches of the Nile River... This article is about the Male sex. ... Caste systems are traditional, hereditary systems of social classification, that evolved due to the enormous diversity in India (where all three primary races met, not by forced slavery but by immigration). ...


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 was developed in medieval Europe. Teaching of geometry was almost universally based on Euclid's Elements. Apprentices to trades such as masons, merchants and money-lenders could expect to learn such practical mathematics as was relevant to their profession. PLATO was one of the first generalized Computer assisted instruction systems, originally built by the University of Illinois (U of I) and later taken over by Control Data Corporation (CDC), who provided the machines it ran on. ... In the history of education, the seven liberal arts comprise two groups of studies, the trivium and the quadrivium. ... For any other uses see, see Trivium (disambiguation). ... The quadrivium comprised the four subjects taught in medieval universities after the trivium. ... Arithmetic tables for children, Lausanne, 1835 Arithmetic or arithmetics (from the Greek word αριθμός = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. ... For other uses, see Geometry (disambiguation). ... Classical education as understood and taught in the Middle Ages of Western culture is roughly based on the ancient Greek concept of Paideia. ... For other uses, see Euclid (disambiguation). ...


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. ... Year 1540 was a leap year starting on Thursday (link will display the full calendar) of the Julian calendar. ...


In the Renaissance the academic status of mathematics declined, because it was strongly associated with trade and commerce. Although it continued to be taught in European universities, it was seen as subservient to the study of Natural, Metaphysical and Moral Philosophy. This article is about the European Renaissance of the 14th-17th centuries. ...


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. 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. (16th century - 17th century - 18th century - more centuries) As a means of recording the passage of time, the 17th century was that century which lasted from 1601-1700. ... The University of Aberdeen was founded in 1495, in Aberdeen, Scotland. ... Events January - Galileo observes Neptune, but mistakes it for a star and so is not credited with its discovery. ... The University of Oxford (usually abbreviated as Oxon. ... Events May 13 - Dutch statesman Johan van Oldenbarnevelt is executed in The Hague after having been accused of treason. ... The incumbent of the Lucasian Chair of Mathematics, the Lucasian Professor is the holder of a mathematical professorship at Cambridge University. ... The University of Cambridge (often Cambridge University), located in Cambridge, England, is the second-oldest university in the English-speaking world and has a reputation as one of the worlds most prestigious universities. ... Events February 1 - The Chinese pirate Koxinga seizes the island of Taiwan after a nine-month siege. ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Full name The College of the Holy and Undivided Trinity Motto Virtus vera nobilitas Virtue is true Nobility Named after The Holy Trinity Previous names King’s Hall and Michaelhouse (until merged in 1546) Established 1546 Sister College(s) Christ Church Master The Lord Rees of Ludlow Location Trinity Street... 1661 (MDCLXI) was a common year starting on Saturday of the Gregorian calendar (or a common year starting on Tuesday of the 10-day slower Julian calendar). ...


In the eighteenth and nineteenth 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. (17th century - 18th century - 19th century - more centuries) As a means of recording the passage of time, the 18th century refers to the century that lasted from 1701 through 1800. ... Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... A Watt steam engine, the steam engine that propelled the Industrial Revolution in Britain and the world. ... Cities with at least a million inhabitants in 2006 An urban area is an area with an increased density of human-created structures in comparison to the areas surrounding it. ... Arithmetic tables for children, Lausanne, 1835 Arithmetic or arithmetics (from the Greek word αριθμός = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. ... // Public education is education mandated for the children of the general public by the government, whether national, regional, or local, provided by an institution of civil government, and paid for, in whole or in part, by taxes. ...


By the twentieth century mathematics was part of the core curriculum in all developed countries. (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s The 20th century lasted from 1901 to 2000 in the Gregorian calendar (often from (1900 to 1999 in common usage). ... World map indicating Human Development Index (as of 2004). ...


During the twentieth century mathematics education was established as an independent field of research. Here are some of the main events in this development: (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s The 20th century lasted from 1901 to 2000 in the Gregorian calendar (often from (1900 to 1999 in common usage). ...

  • In 1893 a Chair in mathematics education was created at the University of Göttingen, under the administration of Felix Klein
  • The International Commission on Mathematical Instruction (ICMI) was founded in 1908, and Felix Klein became the first president of the organization
  • A new interest in mathematics education emerged in the 1960s, and the commission was revitalized
  • In 1968, the Shell Centre for Mathematical Education was established in Nottingham
  • The first International Congress on Mathematical Education (ICME) was held in Lyon in 1969. The second congress was in Exeter in 1972, and after that it has been held every four years

In the 20th century, the cultural impact of electric age also invested educational theory and 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."[1] Year 1893 (MDCCCXCIII) was a common year starting on Sunday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Tuesday of the 12-day slower Julian calendar). ... Felix Christian Klein (April 25, 1849, Düsseldorf, Germany – June 22, 1925, Göttingen) was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory. ... ICMI (The International Commission on Mathematical Instruction) is an international organisation with a focus on mathematics education. ... 1908 (MCMVIII) was a leap year starting on Wednesday (link will display the full calendar). ... The 1960s decade refers to the years from 1960 to 1969. ... Year 1968 (MCMLXVIII) was a leap year starting on Monday (link will display full calendar) of the Gregorian calendar. ... For other uses, see Nottingham (disambiguation). ... This article is about the French city. ... Also: 1969 (Stargate SG-1) episode. ... The city of Exeter is the county town of Devon, in the southwest of England, also known as the West Country. ... Year 1972 (MCMLXXII) was a leap year starting on Saturday (link will display full calendar) of the Gregorian calendar. ... Education theory is the theory or the philosophy of the purpose, application and interpretation of education and learning. ... Arithmetic tables for children, Lausanne, 1835 Arithmetic or arithmetics (from the Greek word αριθμός = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. ... 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 of problems that arise from their study. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ...


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:

  • The teaching of basic numeracy skills to all pupils
  • The teaching of practical mathematics (arithmetic, elementary algebra, plane and solid geometry, trigonometry) to most pupils, to equip them to follow a trade or craft
  • The teaching of abstract mathematical concepts (such as set and function) at an early age
  • The teaching of selected areas of mathematics (such as Euclidean geometry) as an example of an axiomatic system and a model of deductive reasoning
  • The teaching of selected areas of mathematics (such as calculus) as an example of the intellectual achievements of the modern world
  • The teaching of advanced mathematics to those pupils who wish to follow a career in science
  • The teaching of heuristics and other problem-solving strategies to solve non routine problems.

Methods of teaching mathematics have varied in line with changing objectives. Numeracy is a term that emerged in the United Kingdom as a contraction of numerical literacy. In the United States, it is familiar to math educators and intellectuals but not in the common usage. ... Arithmetic tables for children, Lausanne, 1835 Arithmetic or arithmetics (from the Greek word αριθμός = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. ... Elementary algebra is a fundamental and relatively basic form of algebra taught to students who are presumed to have little or no formal knowledge of mathematics beyond arithmetic. ... For other uses, see Geometry (disambiguation). ... Wikibooks has a book on the topic of Trigonometry All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Trigonometry (from Greek trigōnon triangle + metron measure[1]), informally called trig, is a branch of mathematics that deals with... In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. ... Graph of example function, The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary (the independent variable, argument of the function, or its input) and the other as secondary (the value of the function, or output). A... Euclid Euclidean geometry is a mathematical system attributed to the Greek mathematician [[Euclid]] of Alexandria. ... In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. ... Deductive reasoning is the kind of reasoning where the conclusion is necessitated or implied by previously known premises. ... For other uses, see Calculus (disambiguation). ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Part of a scientific laboratory at the University of Cologne. ... For heuristics in computer science, see heuristic (computer science) Heuristic is the art and science of discovery and invention. ...


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. For other uses, see England (disambiguation). ...


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. 3 + 2 = 5 with apples, a popular choice in textbooks[1] This article is about addition in mathematics. ... 5 - 2 = 3 (verbally, five minus two equals three) An example problem Subtraction is one of the four basic arithmetic operations; it is the inverse of addition. ... In mathematics, multiplication is an elementary arithmetic operation. ... 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. ... In the United States Algebra I is a common title for the first course in elementary algebra. ... For other uses, see Geometry (disambiguation). ... Alegebra II is a continuation of algebra I. The course teaches more fundamentals of algebra and includes logarithms, parabolas, other conic sections, Trigonometry and exponentiation. ... Wikibooks has a book on the topic of Trigonometry All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Trigonometry (from Greek trigōnon triangle + metron measure[1]), informally called trig, is a branch of mathematics that deals with... For other uses, see Calculus (disambiguation). ... This article does not cite any references or sources. ...


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:

Classical education as understood and taught in the Middle Ages of Western culture is roughly based on the ancient Greek concept of Paideia. ... The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times, beginning with the Renaissance. ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... For other uses, see Paradigm (disambiguation). ... Deductive reasoning is the kind of reasoning where the conclusion is necessitated or implied by previously known premises. ... It has been suggested that Rote memory be merged into this article or section. ... In mathematics, a multiplication table is a mathematical table used to define a multiplication operation for an algebraic system. ... In arithmetic, a vulgar fraction (or common fraction) consists of one integer divided by a non-zero integer. ... In mathematics, a quadratic equation is a polynomial equation of the second degree. ... Cuisenaire rods are rods used in elementary school as well as other levels of learning and even with adults. ... Problem solving forms part of thinking. ... Look up Heuristic in Wiktionary, the free dictionary. ... In mathematics education, a word problem is a mathematical question written without relying heavily on mathematics notation. ... Wikipedia does not yet have an article with this exact name. ... The International Mathematical Olympiad (IMO) is an annual mathematical olympiad for high school students. ... New math is a term referring to a brief dramatic change in the way mathematics was taught in American grade schools during the 1960s. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... Thomas Andrew Tom Lehrer (born April 9, 1928) is an American singer-songwriter, satirist, pianist, and mathematician. ... Human interest news articles are about particular individuals or groups of people. ... Principles and Standards for School Mathematics is a document produced in 1989 by the National Council of Teachers of Mathematics [5] (NCTM) to set forth a national vision for precollege mathematics education in the US and Canada. ... Motto: (Out Of Many, One) (traditional) In God We Trust (1956 to date) Anthem: The Star-Spangled Banner Capital Washington D.C. Largest city New York City None at federal level (English de facto) Government Federal constitutional republic  - President George Walker Bush (R)  - Vice President Dick Cheney (R) Independence from... For other uses, see Constructivism. ... The National Council of Teachers of Mathematics (NCTM) was founded in 1920. ... Principles and Standards for School Mathematics was a document produced by the National Council of Teachers of Mathematics [1] to set forth a national vision for precollege mathematics education in the US and Canada. ...

Recent controversy over U.S. mathematics education

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. 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. Student-centered learning is an approach to education focusing on the needs of the students, rather than those of others involved in the educational process, such as teachers and administrators. ... Outcomes Based Education, also known as OBE, is a form of educational reform which is currently being introduced in Western Australia and South Africa. ...


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. 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. 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. New math is a term referring to a brief dramatic change in the way mathematics was taught in American grade schools during the 1960s. ... Outcomes Based Education, also known as OBE, is a form of educational reform which is currently being introduced in Western Australia and South Africa. ...


By the late 1980s, a movement for systemic education reform took hold based on contructivist practices and the belief in success for all groups including minorities and women. Among the development of a number of controversial standards across reading, science and history, the National Council of Teachers of Mathematics [10] of the United States produced the Curriculum and Evaluation Standards for School Mathematics in 1989. Principles and Standards for School Mathematics [11] included new goals such as equity and de-emphasized the traditional idea of relying solely on standard algorithms to get solutions. It has been suggested that this article or section be merged with Standards-based education reform. ... Whole language describes a literacy instructional philosophy which emphasizes that children should focus on meaning and moderates skill instruction. ... It has been suggested that this article or section be merged into inquiry-based learning. ... The National Council of Teachers of Mathematics (NCTM) was founded in 1920. ... Principles and Standards for School Mathematics was a document produced by the National Council of Teachers of Mathematics [1] to set forth a national vision for precollege mathematics education in the US and Canada. ...


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. In standards based education reform, all students, not only the college bound must take advanced mathematics. 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. Principles and Standards for School Mathematics is a document produced in 1989 by the National Council of Teachers of Mathematics [5] (NCTM) to set forth a national vision for precollege mathematics education in the US and Canada. ... Outcomes Based Education, also known as OBE, is a form of educational reform which is currently being introduced in Western Australia and South Africa. ...


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. 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". Some students complained that their new math courses placed them into remedial math in college. The Core-Plus Mathematics Project is an NCTM-standards-based high school mathematics curriculum development project funded by the National Science Foundation. ... 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 student should know and be able to do. ... This article does not cite any references or sources. ... MathLand is a mathematics curriculum that was designed around the 1989 NCTM standards. ...


The standards set forth a democratic vision that for the first time set out to promote equity and mathematical power as a goal for all students, including women and underrepresented minorities. The use of calculator and manipulatives are encouraged, but algebra skills and rote memorization are deemphasized, and there is writing about mathematics as well as computation. Some controversial math curricula such as Investigations in Numbers, Data, and Space were based on research papers such as those by Constance Kamii which assert that teaching of traditional arithmetic methods such as borrowing "not only are not helpful in learning arithmetic, but also hinder children’s development of numerical reasoning".[2] All students are expected to master enough mathematics to succeed in college, and rather than defining success by rank order, uniform, high standards are set for all students. Explicit goals of standards based education reform are to require all students to pass high standards of performance, to improve international competitiveness, eliminate the achievement gap and produce a productive labor force. Such beliefs, which are congruent with the democratic vision of outcome-based education and standards based education reform that all students will meet standards, refute past research which shows an achievement gap in scores between groups of different education development on every test and assessment, even those aligned with reformed mathematics standards and instruction. The U.S. Department of Education would name several standards based curricula as "exemplary", though academics would respond in protest with an ad taken out the in the Washington Post, and they would note selection was made largely on which curricula implemented the standards most extensively rather than on demonstrated improvements in test scores. The reform standards, while widely accepted as a consensus by education agencies from local to federal levels, were met with intense criticism from groups such as Mathematically Correct; the controversy was widely characterized by newspapers such as the Wall Street Journal as "math wars". Investigations in Number, Data, and Space is a complete K-5 mathematics curriculum, developed at TERC in Cambridge, Massachusetts. ... A professor of early childhood education at the University of Alabama at Birmingham. ... Outcomes Based Education, also known as OBE, is a form of educational reform which is currently being introduced in Western Australia and South Africa. ... An achievement gap refers to the observed disparity on a number of educational measures between the performance of groups of students, especially groups defined by gender, race/ethnicity, and socioeconomic status. ... It has been suggested that this article or section be merged with Standards-based education reform. ... Outcomes Based Education, also known as OBE, is a form of educational reform which is currently being introduced in Western Australia and South Africa. ... An achievement gap refers to the observed disparity on a number of educational measures between the performance of groups of students, especially groups defined by gender, race/ethnicity, and socioeconomic status. ... Mathematically Correct is a website created by educators, parents, citizens and mathematicians / scientists who are concerned about the direction of standards-based mathematics and education reform. ... The Wall Street Journal is an influential international daily newspaper published in New York City, New York with an average daily circulation of 1,800,607 (2002). ...


In the era of standards based education reform, a curriculum framework is often set at a state level. For example, the California State Board of Education [12] was one of the first to embrace the 1989 standards, and also among the first to move back towards traditional standards[3]. In a standards based system, the curriculum is aligned with the standards. The final step in the system is that by 2006, nearly two-thirds of students in the USA would have to pass high school graduation examination set to World class standards of what every student must know and be able to do to succeed in the 21st century. However in states such as Washington, the success of mathematics reform was in question as half of sophomores and four-fifths of minorities were still struggling to pass the math standard needed to make the promise made in the 1993 education reform bill a reality that most or all would graduate two years later with a diploma. While some officials blamed this on incomplete adoption of the 1989 standards, other districts which had already embraced the 1989 standards were deciding instead to replace or supplement standards-based curricula with more traditional instruction such as Saxon math or Singapore Math in face of poor standardized test results. Outcomes Based Education, also known as OBE, is a form of educational reform which is currently being introduced in Western Australia and South Africa. ... 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 student should know and be able to do. ... Traditional mathematics is the term used for the style of mathematics instruction used for a period in the 20th century before the appearance of reform mathematics based on NCTM standards, so it is best defined by contrast with the alternatives. ... Outcomes Based Education, also known as OBE, is a form of educational reform which is currently being introduced in Western Australia and South Africa. ... According to a 2006 study by the Center on Education Policy, two-thirds of the 15 million public high school students in the United States of America were required to pass a graduation examination to get a diploma of completion of studies. ... World class standards refers to the level of achievement, mainly in math and science, attained by students in the four countries that make up the East Asian Tigers; South Korea, Singapore, Japan, and Taiwan, as well as in Europe. ... Saxon, also known as Saxon math, developed by John Saxon, is a teaching method for incremental learning of mathematics. ... The Singapore Math Method is based on textbooks from the national curriculum of Singapore. ...


The style of instruction can also vary from traditional direct instruction of multi-digit multiplication in books such as Singapore Math to standards-based instruction such as Investigations in Numbers, Time, and Space which may omit instruction or even discourage use of any standard calculation algorithm or method in favor of guiding students to invent their own mathematical power by using 100 charts, colored pencils, glue, writing, and singing songs in different languages. Some education officials have stated that achieving a numerically correct result is secondary to the higher order thinking process. [4] The Singapore Math Method is based on textbooks from the national curriculum of Singapore. ... Investigations in Number, Data, and Space is a complete K-5 mathematics curriculum, developed at TERC in Cambridge, Massachusetts. ... In traditional mathematics instruction, the goal is to have the student produce a correct numerical answer. ...


In standards-based curriculum frameworks, math topics and goals may include the history and legacy of diverse multicultural groups in mathematics, mathematical communication, number sense, mathematical power, and equity. Real life examples integrate contemporary issues such as the rain forests, environment, careers, and other topics which integrate other fields of knowledge. Critics including US senators would dub one such text as "rainforest algebra" with 812 pages of seemingly anything but algebra content.[5] 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 student should know and be able to do. ...


Related to issues of equity in mathematics, where some groups are under-represented in math and science fields, and others tend to dominate mathematics research, the field of Mathematical Relationships concerns how persons form relationships with mathematics, how they identify with the subject and how they disidentify with it, around social class, gender, race/ethnicity, dis/ability, nationality, and sexuality.[6] Some critics such as David Klein of California State University Northridge believe such issues belong in social studies, not mathematics, and that mathematics should be taught in a classical method to all students without regard to a student's group affinities. Professor David Klein teaches at the California State University Northridge Department of Mathematics. ...


In a February 9, 1994 article in Education Week on the Web, Steven Leinwand wrote: "It's time to recognize that, for many students, real mathematical power, on the one hand, and facility with multidigit, pencil-and-paper computational algorithms, on the other, are mutually exclusive. In fact, it's time to acknowledge that continuing to teach these skills to our students is not only unnecessary, but counterproductive and downright dangerous." Leinwand was part of the expert panel that in early October of 1999 directed the United States Department of Education to endorse ten K-12 mathematics as"exemplary" or "promising." The "exemplary" programs announced by the Department of Education were:

  • Cognitive Tutor Algebra
  • College Preparatory Mathematics (CPM)
  • Connected Mathematics Program (CMP)
  • Core-Plus Mathematics Project
  • Interactive Mathematics Program (IMP)

The "promising" programs were: The Core-Plus Mathematics Project is an NCTM-standards-based high school mathematics curriculum development project funded by the National Science Foundation. ...

  • Everyday Mathematics
  • MathLand
  • Middle-school Mathematics through Applications Project (MMAP)
  • Number Power
  • The University of Chicago School Mathematics Project (UCSMP)

The American Institutes for Research lauded the new U.S. standards for giving greater than nations like Singapore to developing important 21st century mathematical skills that go beyond the skill sets used to develop 20th century technologies such as computers and space flight:[7]

  • Representation
  • Reasoning
  • Making connections
  • Communication
  • Statistics, powerpoint-style charts and probability

Some mathematicians such as David Klein of California State University Northridge challenged the emphasis given to gender and race "equity" in the mathematics reform movement. [8] One of the themes of the mathematics reform movement is that traditional mathematics fails because women and members of ethnic minority groups are treated differently than white males. Objections to mathematics curricula which introduced multicultural writing while often omitting traditional arithmetic methods recognizable to parents came largely from mathematicians rather than educators whose "real life" applications might be to use linear algebra to compute bake sale proceeds [9]. Professor David Klein teaches at the California State University Northridge Department of Mathematics. ...


A few states such as California which were early adopters of the 1989 standards would later revise their math standards and assesements, leading a new movement to reject the assumptions of the original 1989 standards as fatally flawed in favor of traditional skills and memorization of math facts.[10] Some public schools in the mid 2000s started to supplement or replace their standards-based mathematics curricula with texts which emphasized direct instruction of traditional mathematics such as Saxon math, popularized by homeschoolers who often rejected standards-based curricula, and Singapore Math because of poor performance on standardized tests compared to other nations and frustration over standards-based approaches which de-emphasized rather than taught arithmetic as it had been known for generations. [11]. Saxon, also known as Saxon math, developed by John Saxon, is a teaching method for incremental learning of mathematics. ... A young girl studying at home in a 1896 painting by William-Adolphe Bouguereau. ... The Singapore Math Method is based on textbooks from the national curriculum of Singapore. ... A standardized test is a test administered and scored in a standard manner. ...


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 that [12] 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. 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. [13] The National Council of Teachers of Mathematics (NCTM) was founded in 1920. ... The Singapore Math Method is based on textbooks from the national curriculum of Singapore. ...


Mathematics teachers

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

Charles Lutwidge Dodgson (Lewis Carroll) Charles Lutwidge Dodgson (IPA: ) (January 27, 1832 – January 14, 1898), better known by the pen name Lewis Carroll, was an English author, mathematician, logician, Anglican clergyman and photographer. ... and of the Christ Church College name Christ Church Latin name Ædes Christi Named after Jesus Christ Established 1546 Sister college Trinity College, Cambridge Dean The Very Revd Christopher Andrew Lewis JCR president Laura Ellis Undergraduates 426 GCR president Tim Benjamin Graduates 154 Location of Christ Church within central Oxford... John Dalton John Dalton (September 6, 1766 – July 27, 1844) was an English chemist and physicist, born at Eaglesfield, near Cockermouth in Cumberland. ... This article is about the City of Manchester in England. ... This article is about the city of Oxford in England. ... York shown within England Coordinates: , Sovereign state Constituent country Region Yorkshire and the Humber Ceremonial county North Yorkshire Admin HQ York City Centre Founded 71 City Status 71 Government  - Type Unitary Authority, City  - Governing body City of York Council  - Leadership: Leader & Executive  - Executive: Liberal Democrat  - MPs: Hugh Bayley (L) John... Thomas Andrew Tom Lehrer (born April 9, 1928) is an American singer-songwriter, satirist, pianist, and mathematician. ... Harvard University is a private university in Cambridge, Massachusetts, USA, and a member of the Ivy League. ... Mapúa Institute of Technology (MIT, MapúaTech or simply Mapúa) is a private, non-sectarian, Filipino tertiary institute located in Intramuros, Manila. ... “UCSC” redirects here. ... For the Australian film composer, see Brian May (composer). ... Queen are an English rock band formed in 1970 in London by guitarist Brian May, singer Freddie Mercury and drummer Roger Taylor, with bassist John Deacon joining the following year. ... Georg Joachim von Lauchen, also known as Rheticus (February 16, 1514 – December 4, 1574), was a mathematician, cartographer, navigational and other instrument maker, medical practitioner, and teacher. ... Nicolaus Copernicus (in Latin; Polish Mikołaj Kopernik, German Nikolaus Kopernikus - February 19, 1473 – May 24, 1543) was a Polish astronomer, mathematician and economist who developed a heliocentric (Sun-centered) theory of the solar system in a form detailed enough to make it scientifically useful. ... The Martin-Luther-University of Halle-Wittenberg is located in the German cities of Halle, Saxony-Anhalt and Wittenberg. ... Edmund Rich, also known as Saint Edmund or Eadmund of Canterbury, was Archbishop of Canterbury in 1234. ... The Archbishop of Canterbury is the spiritual leader and senior clergyman of the Church of England, recognized by convention as the head of the worldwide Anglican Communion. ... This article is about the city of Oxford in England. ... This article is about the capital of France. ... Archibald Franklin Archie Williams (May 1, 1915 – June 24, 1993) was an American athlete and teacher, winner of 400 m run at the 1936 Summer Olympics. ... Official language(s) English Capital Sacramento Largest city Los Angeles Largest metro area Greater Los Angeles Area  Ranked 3rd  - Total 158,302 sq mi (410,000 km²)  - Width 250 miles (400 km)  - Length 770 miles (1,240 km)  - % water 4. ...

Mathematics educators

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

Tatyana Afanasyeva Tatyana Alexeyevna Afanasyeva (Russian: ) (Kiev, November 19, 1876 – Leiden, April 14, 1964) was a Russian /Dutch mathematician. ... Cuisenaire rods are rods used in elementary school as well as other levels of learning and even with adults. ... For other uses, see Euclid (disambiguation). ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... Leonhard Paul Euler (pronounced Oiler; IPA ) (April 15, 1707 – September 18 [O.S. September 7] 1783) was a pioneering Swiss mathematician and physicist, who spent most of his life in Russia and Germany. ... Robert Lee Moore (14 November 1882, Dallas Texas – 4 October 1974 Austin, Texas) was an American mathematician, known for his work in general topology and the Moore method of teaching university mathematics. ... The Moore method is a manner of instruction used to conduct a number of special sections of mathematics courses at the University of Texas at Austin. ... This is about the educator and civil rights activist; for other uses, see Robert Moses (disambiguation). ... Motto: (Out Of Many, One) (traditional) In God We Trust (1956 to date) Anthem: The Star-Spangled Banner Capital Washington D.C. Largest city New York City None at federal level (English de facto) Government Federal constitutional republic  - President George Walker Bush (R)  - Vice President Dick Cheney (R) Independence from... The Algebra Project is a national U.S. mathematics literacy effort aimed at helping low-income students and students of color successfully achieve mathematical skills that are a prerequisite for a college preparatory mathematics sequence in high school. ... George Pólya (December 13, 1887 – September 7, 1985, in Hungarian Pólya György) was a Hungarian mathematician. ... George Pólyas 1945 book How to Solve It (ISBN 0-691-08097-6) is a small volume describing methods of problem solving. ... Toru Kumon , March 26, 1914 – July 25, 1995) was a Japanese mathematics educator, born in Kochi Prefecture, Korea. ... The Kumon Method, created by Japanese educator Toru Kumon, is one of the largest math and language educational systems in the world. ...

See also

The National Council of Teachers of Mathematics (NCTM) was founded in 1920. ... Principles and Standards for School Mathematics was a document produced by the National Council of Teachers of Mathematics [1] to set forth a national vision for precollege mathematics education in the US and Canada. ... Principles and Standards for School Mathematics is a document produced in 1989 by the National Council of Teachers of Mathematics [5] (NCTM) to set forth a national vision for precollege mathematics education in the US and Canada. ... Mathematically Correct is a website created by educators, parents, citizens and mathematicians / scientists who are concerned about the direction of standards-based mathematics and education reform. ... Principles and Standards for School Mathematics is a document produced in 1989 by the National Council of Teachers of Mathematics [5] (NCTM) to set forth a national vision for precollege mathematics education in the US and Canada. ... It has been suggested that this article or section be merged into anti-bias mathematics practice. ... This box:      Racism has many definitions, the most common and widely accepted is that members of one race are intrinsically superior or inferior to members of other races. ... Traditional mathematics is the term used for the style of mathematics instruction used for a period in the 20th century before the appearance of reform mathematics based on NCTM standards, so it is best defined by contrast with the alternatives. ... Traditional education is usually the absence or target of destruction by Education reform. ... For other uses, see Constructivism. ... Sets of Mathematics, Education, and Computers Computer Based Mathematics Education (CBME) refers to a mathematics education method that is enriched by using computers. ... This article or section is in need of attention from an expert on the subject. ... Wikibooks has more about this subject: Learning Theories The philosophy of education is the study of the purpose, process, nature and ideals of education. ...

References

  1. ^ Marshall McLuhan (1964) Understanding Media, p.13 [1]
  2. ^ [2] “The Harmful Effects of Algorithms in Grades 1-4, NCTM Yearbook by Constance and Ann Dominick
  3. ^ http://www.air.org/news/documents/Singapore%20Report%20(Bookmark%20Version).pdf AIR report in pdf "The California mathematics framework is modeled on Singaporean and Japanese frameworks"
  4. ^ [3] February 9, 2006 "Alpine trio defend approach to math" By Laura Hancock Deseret Morning News (Utah) "while a right answer was important, it is not our belief (it's) as important to get the right answer than to get the process."
  5. ^ [4] "Addison--Wesley's Secondary Math: An Integrated Approach. Following reviews of the book from numerous mathematics professors and reading the text herself, Jennings unofficially dubbed the textbook, Rain Forest Algebra."
  6. ^ [http://ioewebserver.ioe.ac.uk/ioe/cms/get.asp?cid=4381&4381_0=12442 Mathematical Relationships seminars
  7. ^ AMERICAN INSTITUTES FOR RESEARCH. What the United States Can Learn From Singapore’s World-Class Mathematics System [5] February 7, 2005
  8. ^ [6] Published in: How To Teach Mathematics,by Steven Krantz, American Mathematical Society, January 1999. "Big Business, Race, and Gender in Mathematics Reform" by David Klein
  9. ^ McDougal Littell Integrated Mathematics textbook
  10. ^ [7] "A quarter century of US 'maths wars' and political partisanship" David Klein California State University, Northridge, USA. Accepted for publication in the BSHM Bulletin, the journal of the British Society for the History of Mathematics
  11. ^ [8] "Back to basics on kids’ math" Alarmed by low scores, Tacoma school officials OK added Saxon textbook. by Debby Abe; The News Tribune (Tacoma WA) August 25th, 2006
  12. ^ Wall Street Journal, New York Times, Chicago Sun Times
  13. ^ [9] Report Urges Changes in the Teaching of Math in U.S. Schools by TAMAR LEWIN New York Times September 13, 2006
  14. ^ Freddie Mercury Interview, Melody Maker, May 2, 1981

“McLuhan” redirects here. ... Understanding Media is a book by Marshall McLuhan. ...

External links

Teacher organizations and others associated with mathematics education

  • National Council of Teachers of Mathematics (NCTM (USA)
  • [15] The National Centre for Excellence in Teaching Mathematics (NCETM) (England)
  • [16] The Association of Teachers of Mathematics (UK)
  • [17] The Mathematical Association (UK)
  • [18] MatheMagic
  • [19] SNM (Poland)
  • [20]] APM (Portugal)
  • [21] Homi Bhabha Centre for Science Education (India)

The National Council of Teachers of Mathematics (NCTM) was founded in 1920. ... The National Centre for Excellence in Teaching Mathematics (NCETM) [1] is the new institution set up in the wake of the Smith Report to improve mathematics teaching in England. ... The subject of this article may not satisfy the notability guideline or one of the following guidelines for inclusion on Wikipedia: Biographies, Books, Companies, Fiction, Music, Neologisms, Numbers, Web content, or several proposals for new guidelines. ... SNM is a three-character combination that may refer to: Sacred Name Movement SNM Chat Society of Nuclear Medicine Somali National Movement Special nuclear material Sant Nirankari Mission Categories: | ... APM, apm, or Apm may refer to one of the following. ... Homi Bhabha Centre for Science Education (HBCSE) is a National Centre of the Tata Institute of Fundamental Research (TIFR), Mumbai, India. ...

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