As opposed to the most harmful heuristics, what are the most useful heuristics which
are hand-waving,
are conducive to proper mathematical education, and
you have seen taught or taught yourself?
In this context:
Hand-waving means imprecise, intuitive, ambiguous, with a purpose of impressing or convincing.
Proper mathematical education means that a person can understand, use, discuss, and derive the learnt mathematical claims after finishing the education process to the levels (a) advertised by goals of the education process and at the same time (b) having, up to some allowed degree of ambiguity, the same, widely accepted meaning in the community. Example: "Real Calculus" could mean "basics of differentiation and integration over the functions $\mathbb{R}\to\mathbb{R}$".
Seen taught means you closely observed or participated as a learner in the educational process.
Taught yourself means you were a lecturer or an author of used educational material.
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