Howard Whitley Eves Famous Quotes
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A good problem should be more than a mere exercise; it should be challenging and not too easily solved by the student, and it should require some "dreaming" time.
There is a distinction between what may be called a problem and what may be considered an exercise. The latter serves to drill a student in some technique or procedure, and requires little if any, original thought ... No exercise, then, can always be done with reasonbable dispatch and with a miniumum of creative thinking. In contrast to an exercise, a problem, if it is a good one for its level, should require though on the part of the student.
How are you going to teach logic in a world where everybody talks about the sun setting, when it's really the horizon rising?
[Cal Craig]
Mathematics may be likened to a large rock whose interior composition we wish to examine. The older mathematicians appear as persevering stone cutters slowly attempting to demolish the rock from the outside with hammer and chisel. The later mathematicians resemble expert miners who seek vulnerable veins, drill into these strategic places, and then blast the rock apart with well placed internal charges.
