These historical changes assist the educator to appreciate the changes that occur with individuals together with advance in intellectual resources. In studying 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. [Sidenote: The value of technical terms] 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: "name words" exist but not nouns; "action words" but not verbs; pupils may "take away," but not subtract; they may tell what four fives are, but not what four times five are, and so on. A sound instinct underlies this reaction--aversion to words that give the pretense, but not the reality, of meaning. Yet the fundamental difficulty is not with the word, but with the idea. If the idea is not grasped, nothing is gained by using a more familiar word; if the idea is perceived, the use of the term that exactly names it may assist in fixing the idea. Terms denoting highly exact meanings should be introduced only sparingly, that is, a few at a time; they should be led up to gradually, and great pains should be taken to secure the circumstances that render precision of meaning significant. [Sidenote: Importance of consecutive discourse]