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• W883122256 abstract "ion has been an object of discussion across several disciplines. Particularly in philosophy and the philosophy of mathematics, it has been the central topic of intense inquiry as far back as the days of Plato and Aristotle. As Hershkowitz, Schwarz and Dreyfus (2001) put it, “not only did Plato and his followers see in abstraction a way to reach 'eternal truths', but modern philosophers such as Russell (1926) characterized abstraction as one of the highest human achievements” (p. 196). In this chapter, rather than providing a detailed review of research on abstraction in philosophy and other disciplines, I will focus on the notion of abstraction as used in mathematics and mathematics education. 2.1. Abstraction in Mathematics: Historical Roots Abstraction is often seen as the fundamental characteristic of mathematics. For Aristotle, “mathematical objects are the result of abstraction” (Lear, 1982, p.161). Similarly, for Davis and Hersh (1983), abstraction is “the life’s blood of mathematics” (p. 113). But, what constitutes a mathematical object, and how do (or can) we know them? These have been the central questions in the philosophy of mathematics from time immemorial. Plato’s answer for this question is the following: mathematical objects, like circles and triangles, are forms, which can be accessed only by intellect. What we experience through our senses is merely the imperfect reflection of these perfect forms. Hence, in Platonic view, “there are two separate realms accessible to human cognition: A transient, changing realm perceptible to the senses, and a timeless, eternal realm thation is often seen as the fundamental characteristic of mathematics. For Aristotle, “mathematical objects are the result of abstraction” (Lear, 1982, p.161). Similarly, for Davis and Hersh (1983), abstraction is “the life’s blood of mathematics” (p. 113). But, what constitutes a mathematical object, and how do (or can) we know them? These have been the central questions in the philosophy of mathematics from time immemorial. Plato’s answer for this question is the following: mathematical objects, like circles and triangles, are forms, which can be accessed only by intellect. What we experience through our senses is merely the imperfect reflection of these perfect forms. Hence, in Platonic view, “there are two separate realms accessible to human cognition: A transient, changing realm perceptible to the senses, and a timeless, eternal realm that is conceivable to the intellect”(Campbell, 2004, p. 12). In the theory of recollection, Plato maintained that before we are born, our soul has knowledge of the form, but somehow we forgot this knowledge during the traumatic experience of our own birth. Therefore, gaining knowledge means remembering the knowledge that we already" @default.
• W883122256 created "2016-06-24" @default.
• W883122256 creator A5007999997 @default.
• W883122256 date "2014-08-08" @default.
• W883122256 modified "2023-09-26" @default.
• W883122256 title "Dealing With Abstraction: Reducing Abstraction in Teaching (RAiT)" @default.
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