Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms.
In mathematics, a multiplication table is a mathematical table used to define a multiplication operation for an algebraic system.
Subtraction is one of the four arithmetic operations along with addition, multiplication and division. Subtraction is an operation that represents removal of objects from a collection. For example, in the adjacent picture, there are 5 − 2 peaches—meaning 5 peaches with 2 taken away, resulting in a total of 3 peaches. Therefore, the difference of 5 and 2 is 3; that is, 5 − 2 = 3. While primarily associated with natural numbers in arithmetic, subtraction can also represent removing or decreasing physical and abstract quantities using different kinds of objects including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices.
In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge.
New Mathematics or New Math was a dramatic but temporary change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries and elsewhere, during the 1950s–1970s.
A classroom, schoolroom or lecture room is a learning space in which both children and adults learn. Classrooms are found in educational institutions of all kinds, ranging from preschools to universities, and may also be found in other places where education or training is provided, such as corporations and religious and humanitarian organizations. The classroom provides a space where learning can take place uninterrupted by outside distractions.
Elementary arithmetic is a branch of mathematics involving addition, subtraction, multiplication, and division. Due to its low level of abstraction, broad range of application, and position as the foundation of all mathematics, elementary arithmetic is generally the first branch of mathematics taught in schools.
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction consists of an integer numerator, displayed above a line, and a non-zero integer denominator, displayed below that line. If these integers are positive, then the numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. For example, in the fraction 3/4, the numerator 3 indicates that the fraction represents 3 equal parts, and the denominator 4 indicates that 4 parts make up a whole. The picture to the right illustrates 3/4 of a cake.
Caleb Gattegno (1911–1988) was an educator, psychologist, and mathematician. He is considered one of the most influential and prolific mathematics educators of the twentieth century. He is best known for introducing new approaches to teaching and learning mathematics, foreign languages and reading. Gattegno also developed pedagogical materials for each of these approaches, and was the author of more than 120 books and hundreds of articles largely on the topics of education and human development.
In mathematics education, a manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name. The use of manipulatives provides a way for children to learn concepts through developmentally appropriate hands-on experience.
Investigations in Numbers, Data, and Space is a K–5 mathematics curriculum, developed at TERC in Cambridge, Massachusetts, United States. The curriculum is often referred to as Investigations or simply TERC. Patterned after the NCTM standards for mathematics, it is among the most widely used of the new reform mathematics curricula. As opposed to referring to textbooks and having teachers impose methods for solving arithmetic problems, the TERC program uses a constructivist approach that encourages students to develop their own understanding of mathematics. The curriculum underwent a major revision in 2005–2007.
Pattern Blocks are a set of mathematical manipulatives developed in the 1960s. The six shapes are both a play resource and a tool for learning in mathematics, which serve to develop spatial reasoning skills that are fundamental to the learning of mathematics. Among other things, they allow children to see how shapes can be composed and decomposed into other shapes, and introduce children to ideas of tilings. Pattern blocks sets are multiple copies of just six shapes:
Early Algebra is an approach to early mathematics teaching and learning. It is about teaching traditional topics in more profound ways. It is also an area of research in mathematics education.
Base ten blocks, also known as Dienes blocks after popularizer Zoltán Dienes, are a mathematical manipulative used by students to practice counting and elementary arithmetic and develop number sense in the context of the decimal place-value system as a more concrete and direct representation than written Hindu–Arabic numerals. The three-dimensional blocks are made of a solid material such as plastic or wood and generally come in four sizes, each representing a power of ten used as a place in the decimal system: units, longs, flats and blocks. There are also computer programs available that simulate base ten blocks.
The Silent Way is a language-teaching approach created by Caleb Gattegno that makes extensive use of silence as a teaching method. Gattegno first described the method in 1963, in his book Teaching Foreign Languages in Schools: The Silent Way. Gattegno was critical of mainstream language education at the time, and he based the method on his general theories of education rather than on existing language pedagogy. It is usually regarded as an "alternative" language-teaching method; Cook groups it under "other styles", Richards groups it under "alternative approaches and methods" and Jin & Cortazzi group it under "Humanistic or Alternative Approaches". Gattegno continued to develop and describe the Silent Way until his death in 1988.
A mathematical exercise is a routine application of algebra or other mathematics to a stated challenge. Mathematics teachers assign mathematical exercises to develop the skills of their students. Early exercises deal with addition, subtraction, multiplication, and division of integers. Extensive courses of exercises in school extend such arithmetic to rational numbers. Various approaches to geometry have based exercises on relations of angles, segments, and triangles. The topic of trigonometry gains many of its exercises from the trigonometric identities. In college mathematics exercises often depend on functions of a real variable or application of theorems. The standard exercises of calculus involve finding derivatives and integrals of specified functions.
Georges Cuisenaire (1891–1975), also known as Emile-Georges Cuisenaire, was a Belgian teacher who invented Cuisenaire rods, a mathematics teaching aid.
Catherine Brieger Stern (1894–1973) was a German psychologist and educator. Born under the name Käthe Brieger, she developed sets of mathematical manipulatives similar to Cuisenaire rods for children to use in building up their number sense and knowledge of arithmetic. Her book, Children Discover Arithmetic (1949) was used by others to work on the problems that children face when learning arithmetic.
Eclectic approach is a method of language education that combines various approaches and methodologies to teach language depending on the aims of the lesson and the abilities of the learners. Different teaching methods are borrowed and adapted to suit the requirement of the learners. It breaks the monotony of the class.
Words in Colour is an approach to literacy invented by Caleb Gattegno. Words in Colour first appeared in 1962, published simultaneously in the UK and US. Later versions were published in French and Spanish.
