Mathematical Abstraction as the Result of a Delicate Shift of Attention – John Mason (1989)

Source:

For the Learning of Mathematics,

Vol. 9, No. 2 (Jun., 1989), pp. 2-8

Published by: FLM Publishing Association

Stable URL: http://www.jstor.org/stable/40247947

Accessed: 04-03-2015 23:49 UTC

The author discusses abstraction as experienced by expert and by student.

Perhaps all the students are aware of is the having been drawn away rather than the drawing itself.

…an extremely brief moment which happens in the twinkling of an eye; a delicate shift of attention from seeing an expression as an expression of generality, to seeing the expression as an object or property.

Algebraic expressions provide a generic example of how meaning can remain connected to symbols: it is important, for algebraic thinking to develop effectively, to maintain a dual awareness of expressions, as entities or objects, and as statements about how a calculation is to be performed [Mason, 1982].

The paper offers as an example a sequence to be defined using an expression and discusses the processes involved in drawing ideas out from it.

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