NCREASINGLY, during the last twenty years, the literature relating to arithmetic instruction has carried the words meaning, meaningful, and meaningfully. For some persons, these terms seem to be no more than words-mere items in the vocabulary of modern elementary education, adopted because, for the moment, they are fashionable. For others, these words serve as symbols of a vague protest against what they call the traditional arithmetic, though they have little except pious wishes to offer as a substitute. For still others, the terms are appropriate for use in connection with arithmetic experiences which arise out of felt needs on the part of children. This third usage, unlike the first two, has in its favor a certain definiteness. It implies particular conditions of learning and motivation. Children see the chance to use their arithmetical ideas and skills to further some end, and they use the ideas and skills for this purpose. We should, however, at this point, distinguish between what I shall designate the meaning of a thing and the meaning of a thing for something else; for the sake of brevity, between meaning of and meaning for. I know little about the meaning of the atomic bomb, because I lack the knowledge of chemistry and physics which are requisite to accurate understanding, but I think I know a good deal about the meaning of the atomic bomb for other things-for peace or for the destruction of our culture, for example. The distinction I am suggesting is no verbal quibble, no bit of theoretical hairsplitting. Failure to recognize the difference between meanings of and meanings for makes it difficult for those of us who are interested in the