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Teaching: In the PSSM, the NCTM promotes sound teaching methods, without prescribing a one-size-fits-all approach. [7] The NCTM wants teachers to be able to use their professional judgment in choosing teaching techniques. They favor professional development opportunities in both mathematics (content) and in effective teaching techniques (methods).
If a positional numeral system is used, a natural way of multiplying numbers is taught in schools as long multiplication, sometimes called grade-school multiplication, sometimes called the Standard Algorithm: multiply the multiplicand by each digit of the multiplier and then add up all the properly shifted results.
Rote learning: the teaching of mathematical results, definitions and concepts by repetition and memorisation typically without meaning or supported by mathematical reasoning. A derisory term is drill and kill. In traditional education, rote learning is used to teach multiplication tables, definitions, formulas, and other aspects of mathematics.
The grid method (also known as the box method) of multiplication is an introductory approach to multi-digit multiplication calculations that involve numbers larger than ten. Because it is often taught in mathematics education at the level of primary school or elementary school , this algorithm is sometimes called the grammar school method.
In mathematics education, there was a debate on the issue of whether the operation of multiplication should be taught as being a form of repeated addition.Participants in the debate brought up multiple perspectives, including axioms of arithmetic, pedagogy, learning and instructional design, history of mathematics, philosophy of mathematics, and computer-based mathematics.
Criticism of traditional mathematics instruction originates with advocates of alternative methods of instruction, such as Reform mathematics.These critics cite studies, such as The Harmful Effects of Algorithms in Grades 1–4, which found specific instances where traditional math instruction was less effective than alternative methods.
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