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184 geometry, a pupil must learn both to narrow and to extend the meanings of such familiar words as line, surface, angle, square, circle; to narrow them to the precise meanings involved in demonstrations; to extend them to cover generic relations not expressed in ordinary usage. Qualities of color and size must be excluded; relations of direction, of variation in direction, of limit, must be definitely seized. A like transformation occurs, of course, in every subject of study. Just at this point lies the danger, alluded to above, of simply overlaying common meanings with new and isolated meanings instead of effecting a genuine working-over of popular and practical meanings into adequate logical tools.

Terms used with intentional exactness so as to express a meaning, the whole meaning, and only the meaning, are called technical. For educational purposes, a technical term indicates something relative, not absolute; for a term is technical not because of its verbal form or its unusualness, but because it is employed to fix a meaning precisely. Ordinary words get a technical quality when used intentionally for this end. Whenever thought becomes more accurate, a (relatively) technical vocabulary grows up. Teachers are apt to oscillate between extremes in regard to technical terms. On the one hand, these are multiplied in every direction, seemingly on the assumption that learning a new piece of terminology, accompanied by verbal description or definition, is equivalent to grasping a new idea. When it is seen how largely the net outcome is the accumulation of an isolated set of words, a jargon or scholastic cant, and to what extent the natural power of judgment is clogged by this accumulation, there is a reaction to the opposite extreme. Technical terms are banished;