Math wars

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 and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM) and subsequent development and widespread adoption of a new generation of mathematics curricula inspired by these standards.

While the discussion about math skills has persisted for many decades, the term "math wars" was coined by commentators such as John A. Van de Walle and David Klein. The debate is over traditional mathematics and reform mathematics philosophy and curricula, which differ significantly in approach and content.

Advocates of reform

The largest supporter of reform in the US has been the National Council of Teachers of Mathematics.

One aspect of the debate is over how explicitly children must be taught skills based on formulas or algorithms (fixed, step-by-step procedures for solving math problems) versus a more inquiry-based approach in which students are exposed to real-world problems that help them develop fluency in number sense, reasoning, and problem-solving skills. In this latter approach, conceptual understanding is a primary goal and algorithmic fluency is expected to follow secondarily. Later research showed that conceptual understanding is usually not retained and algorithmic fluency often doesn't follow. Advocates blame educators saying that failures occur not because the method is at fault, but because these educational methods require a great deal of expertise and have not always been implemented well in actual classrooms.

War

War is a state of armed conflict between societies. It is generally characterized by extreme collective aggression, destruction, and usually high mortality. The set of techniques and actions used to conduct war is known as warfare. An absence of war is usually called "peace". Total war is warfare that is not restricted to purely legitimate military targets, and can result in massive civilian or other non-combatant casualties.

While some scholars see war as a universal and ancestral aspect of human nature, others argue that it is only a result of specific socio-cultural or ecological circumstances.

In 2013 war resulted in 31,000 deaths down from 72,000 deaths in 1990. The deadliest war in history, in terms of the cumulative number of deaths since its start, is the Second World War, from 1939 to 1945, with 60–85 million deaths, followed by the Mongol conquests which was greater than 41 million. Proportionally speaking, the most destructive war in modern history is the War of the Triple Alliance, which took the lives of over 60% of Paraguay's population, according to Steven Pinker. In 2003, Richard Smalley identified war as the sixth (of ten) biggest problem facing humanity for the next fifty years. War usually results in significant deterioration of infrastructure and the ecosystem, a decrease in social spending, famine, large-scale emigration from the war zone, and often the mistreatment of prisoners of war or civilians. Another byproduct of some wars is the prevalence of propaganda by some or all parties in the conflict, and increased revenues by weapons manufacturers.

Wars (series)

The Wars series, also known as Famicom Wars (ファミコンウォーズ, Famikon Wōzu) in Japan, Advance Wars in the West, and occasionally Nintendo Wars as a whole, is a series of military turn-based tactics video games, usually developed by Intelligent Systems and published by Nintendo. The series debuted in Japan on August 12, 1988. Like another Intelligent Systems series, Fire Emblem, earlier installments of the series were released only in Japan; Advance Wars (2001) was the first to reach the North American and European markets. Advance Wars was released in the USA on September 10, 2001, but put on hold in Japan and Europe due to the subsequent terrorist attacks in the USA. Although released in Europe in January 2002, neither GBA game was released in Japan until the Game Boy Wars Advance 1+2 compilation which released for the Game Boy Advance on November 25, 2004 and for the Wii U Virtual Console on April 3, 2014.

In 2005, Advance Wars: Dual Strike was released on the Nintendo DS platform, which follows the basic form of its predecessors. That same year Battalion Wars, developed by Kuju Entertainment, was released for the Nintendo GameCube in Japan under the title "Totsugeki!! Famicom Wars", where it is considered a spin-off from the main series. Battalion Wars is a 3D action real-time strategy game, as opposed to the turn-based strategy of the main series.

Wars (album)

Wars is the third album from American hardcore group XBXRX, released in April 2007 on Polyvinyl Records.

Track listing

All songs by XBXRX

References

Factorial

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example,

The value of 0! is 1, according to the convention for an empty product.

The factorial operation is encountered in many areas of mathematics, notably in combinatorics, algebra, and mathematical analysis. Its most basic occurrence is the fact that there are n! ways to arrange n distinct objects into a sequence (i.e., permutations of the set of objects). This fact was known at least as early as the 12th century, to Indian scholars.Fabian Stedman in 1677 described factorials as applied to change ringing. After describing a recursive approach, Stedman gives a statement of a factorial (using the language of the original):

Now the nature of these methods is such, that the changes on one number comprehends [includes] the changes on all lesser numbers, ... insomuch that a compleat Peal of changes on one number seemeth to be formed by uniting of the compleat Peals on all lesser numbers into one entire body;

Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers),structure,space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.

Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.

Math (disambiguation)

Math (or Maths in most English-speaking countries) is used colloquially to refer to mathematics.

Math may also refer to:

See also