The Nature of Understanding
by William A. Brownell & Verner M. Sims — 1946
When a geometry student sees the usefulness of the Pythagorean theorem for laying off the comers of a tennis court, we may be sure that he has some understanding of that theorem. When a fifth-grade pupil by means of his maps discovers for himself a probable connection between the physical features of a region and the manner of life of its inhabitants, we may be sure that he too has some understanding, in this case of the geographic principles involved. And when a primary-grade pupil translates the statement 5 + 2 = 7 into a concrete representation, by setting up one group of five objects and another of two objects and then' combining them into a new ,group of seven, we may be sure once again that he also has some understanding, this time of the abstract relationships in the statement.
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