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In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system.
The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with our base-ten numbers. It is necessary to memorize the table up to 9 × 9, and often helpful up to 12 × 12 to be proficient in traditional mathematics. As noted below many schools in the United States adopted standards-based mathematics texts which completely omitted use or presentation of the multiplication table, though this practice is being increasingly abandoned in the face of protests that proficiency in elementary arithmetic is still important.
The times tables were invented by the Chinese.
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Multiplication tables can also define binary operations on groups, fields, rings, and other algebraic systems. In such contexts they can be called Cayley tables. For an example, see octonion.
In 1989, the National Council of Teachers of Mathematics (NCTM) developed new standards which were based on the belief that all students should learn higher-order thinking skills, and which played down the teaching of traditional methods that relied on rote memorization, such as multiplication tables. Widely adopted texts such as Investigations in Numbers, Data, and Space (widely known as TERC after its producer, Technical Education Research Centers) omit aids such as multiplication tables, instead guiding students to invent their own methods, including skip counting and coloring in multiples on 100s charts. It is thought by many that electronic calculators have made it unnecessary or counter-productive to invest time in memorizing the multiplication table. Standards organizations such as the NCTM had originally called for "de-emphasis" on basic skills in the late 1980s, but they have since refined their statements to explicitly include learning mathematics facts. Though later versions of texts such as TERC have been rewritten, the use of earlier versions of such texts has been heavily criticized by groups such as Where's the Math and Mathematically Correct as being inadequate for producing students proficient in elementary arithmetic.
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