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WORTH THINKING ABOUT: LEARNING THINGS BACKWARDS AND FORWARDSlike
"School curricula reinforce the impression that logical subjects
math and science require starting with basics and progressively addingmore
sophisticated conclusions and applications. But the very nature oflogical
laws make it equally feasible to work backward from conclusions, orin
observations, to hypotheses. Deduction and induction are entirely
complementary.
"In reality, scientists and mathematicians do not do their crafts
the linear, progressive way their subjects are usually taught.Practitioners
commonly start with a flash of insight (the stereotypical light bulbpostulate,
lighting), a hunch, a dream, a guess, an elaborate hypothesis or
and then work backward, forward, and around it to try to make it fitwith
established knowledge. Physicists or engineers commonly try usingcomplex
mathematical gadgets to solve the problems that interest them withouttinker
knowing or caring how the math was logically derived. Experimenters
in laboratories and make surprising discoveries that theoreticians thenEinstein
labor to try to explain logically. Alternatively, theorists like
come up with wild new theories like relativity that experiments may haveto
struggle for decades to find a way to test and prove. Scientificknowledge
does not grow incrementally down a predictable track. Rather it growsmystery of
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
the human quest for knowledge. School plods where human imagination
naturally leaps."
From "School's Out," by Lewis J. Perelman---------------------------------------------
Source: NewsScan
"Experience is a hard teacher because she gives the test
first, the lesson afterwards." - Vernon Sanders Law