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WORTH THINKING ABOUT: LEARNING THINGS BACKWARDS AND FORWARDS
"School curricula reinforce the impression that logical subjects like
math and science require starting with basics and progressively adding more
sophisticated conclusions and applications. But the very nature of logical
laws make it equally feasible to work backward from conclusions, or
observations, to hypotheses. Deduction and induction are entirely
complementary.
"In reality, scientists and mathematicians do not do their crafts in
the linear, progressive way their subjects are usually taught. Practitioners
commonly start with a flash of insight (the stereotypical light bulb
lighting), a hunch, a dream, a guess, an elaborate hypothesis or postulate,
and then work backward, forward, and around it to try to make it fit with
established knowledge. Physicists or engineers commonly try using complex
mathematical gadgets to solve the problems that interest them without
knowing or caring how the math was logically derived. Experimenters tinker
in laboratories and make surprising discoveries that theoreticians then
labor to try to explain logically. Alternatively, theorists like Einstein
come up with wild new theories like relativity that experiments may have to
struggle for decades to find a way to test and prove. Scientific knowledge
does not grow incrementally down a predictable track. Rather it grows
volcanolike, sometimes oozing in patient rivulets, sometimes erupting in
fiery ferment, and occasionally exploding, blowing away the rock of
established truth.
"Pedantic, linear teaching rarely conveys the true drama and mystery of
the human quest for knowledge. School plods where human imagination
naturally leaps."

From "School's Out," by Lewis J. Perelman
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Source: NewsScan

"Experience is a hard teacher because she gives the test
first, the lesson afterwards." - Vernon Sanders Law