Symbols in Mathematics


The other Misconception:
"Precision demands symbols: writing promotes 'fuzzy thinking' "

. Symbols are indeed often indispensable for expressing answers and statements (theorems) precisely; however:

(a) mastering new material,
(b) gaining intuition, and
(c) communicating with others
(d) and answering "how" and "why " questions

...can often be enhanced by (and sometimes require) writing, speaking, pictures/illustrations, and other non-symbolic representations.

. These other representations are useful, sometimes necessary, for communication not only with others -- but also for our own, internal understanding

Ways of Learning/Knowing, pt I:

. "You Learn by (from) Teaching"

-- Giving driving directions (requires remembering, thinking)

-- Writing a recipe for a friend (requires mental organization)

-- Preparing for a class/ Teaching a course (above & much more!)


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