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Mathematical objects include concepts, relationships, structures, and processes. In mathematics learning, the term abstraction is used in two senses: An abstraction is a mental representation of a mathematical object. Abstraction, without an article, is the mental process by which an individual constructs such an abstraction. The term derives from the Latin abstractum, literally “drawn out.”
Abstraction in mathematics learning takes many forms. At the most elementary level, called empirical abstraction, learners recognize that some objects, situations, or experiences are similar in a particular way that distinguishes them from others. The essence of this similarity is then drawn out to form a mental object in its own right. In horizontal mathematization, symbols are used to create a mathematical object that expresses the underlying structure of a given situation. In vertical mathematization, a new object...
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Mitchelmore, M.C., White, P. (2012). Abstraction in Mathematics Learning. In: Seel, N.M. (eds) Encyclopedia of the Sciences of Learning. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1428-6_516
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