Definition
An abstraction, to most mathematicians, is an object, such as a vector space, which incorporates a structure – elements and relationships between them – common to many instances appearing in diverse contexts. Mathematics educators, on the other hand, are more interested in the processes that lead learners to grasp a structure than in the structure itself. Hence, for mathematics educators, abstraction is a process rather than an object, and they tend to identify abstraction with construction of knowledge.
Elaboration
The example of vector space illustrates the above. Instances of vector spaces appearing in different contexts include Euclidean 3-space, the complex plane, the set of solutions to a system of linear equations with real coefficients, and the space of states of a quantum mechanical system. The nature of the elements that serve as vectors in different contexts may be different: An element of Euclidean 3-space is a point; an element of the complex plane is a complex...
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Dreyfus, T. (2018). Abstraction in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-77487-9_2-5
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