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In philosophy and the arts, a fundamental distinction is between things that are abstract and things that are concrete. While there is no general consensus as to how to precisely define the two, examples include that things like numbers , sets , and ideas are abstract objects, while plants , dogs , and planets are concrete objects. [ 1 ]
Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.
The term "concrete mathematics" also denotes a complement to "abstract mathematics". The book is based on a course begun in 1970 by Knuth at Stanford University. The book expands on the material (approximately 100 pages) [1] in the "Mathematical Preliminaries" [2] section of Knuth's The Art of Computer Programming. Consequently, some readers ...
Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept or object, removing any dependence on real-world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of ...
Mathematical manipulatives are frequently used in the first step of teaching mathematical concepts, that of concrete representation. The second and third steps are representational and abstract, respectively. Mathematical manipulatives can be purchased or constructed by the teacher.
A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling .
A mathematical object is an abstract concept arising in mathematics. [1] ... Objects can range from the concrete: ... and all mathematical concepts, ...
Singapore math teaches students mathematical concepts in a three-step learning process: concrete, pictorial, and abstract. [3] This learning process was based on the work of an American psychologist, Jerome Bruner .