But we should never crowd this
abstract work on the memory unassisted by the suggestive concrete, when
the concrete aid is possible.
7. All that is taught should be true. It is not necessary to attempt to
exhaust a subject, nor to attempt to teach minute details regarding it
to the pupils in our schools, but it is necessary that every statement
given to the pupil to be learned and remembered should contain no
element of falsehood.
The student in mathematics experiences a feeling of growing strength and
power when he finds, in algebra, that the formula he used in arithmetic
in extracting a square root has grown in importance by leading
indirectly to a theorem of which it is only one particular case--a
theorem with a more definite proof, and a larger capability for use than
he had thought possible. When he finds a still simpler proof for the
binomial theorem in his study of the calculus, his feeling of increasing
power and the desire for still greater results deepens and intensifies.
Were he to find, on the contrary, that from a false notion of the means
to be used in making a thing simple, his teacher in arithmetic had
taught him what is false, we should approve his feeling of disgust and
disappointment. Early impressions are the most lasting, and the hardest
part of school work for the teacher is the unteaching of false ideas,
and the correcting of imperfectly formed and partially understood ideas.
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