The Inland Publishing Company EACH TEACHER... Can supply you with such primary helps as you need We give below a short list with prices. Drawing Stencils,- Each box contains twenty different stencils, with stock of drawing paper. Price, No. 1, 2, 3, or 4, per box, 25 cents. Postage 8 cents. Combination Drawing Stencils, Each perforated card contains a number of objects with no pictorial relation to each other. The child selects several cards and composes an original picture, the merits of which depend upon the feeling of the little artist. Each box contains eighteen cards with instructions, and sample of possible drawing. Price, per box, 25 cents. Postage 8 cents. Sewing Cards, A complete outfit. The box contains cards of red, yellow, orange, green and blue thread, perforating needle, and a pad on which to place the pictures of animals, children flowers, etc., before picking the holes for sewing. Price, per box, 25 cents. Postage 8 cents. Primary Peg Boards, Price, 1 dozen Boards, $1.75, by express. Price, single Board, 15 cents. Postage 5 cents. Pegs for Peg Board, six colors, 1,000 in box, 20 cents. Colored Pegs, 3,000 square pegs, assorted colors, for number work designs, etc. Price, 15 cents. Postage 11 cents. 1,000 square pegs, assorted colors, very large. Price, 15 cents. Postage 13 cents. Wooden Beads, Consisting of cubes, spheres, and cylinders, in six colors, each form perforated. 1,000 wooden forms, as above, assorted, $2.00. Postage 20 cents. Per dozen, 4 cents. Postage 2 cents. Sticks for Stick Laying, For teaching fractions, etc. 1,000 sticks, from 1 to 5 in. length, in paper box, six colors, Price 25 cents. Postage 8 cents. Educational Toy Money, Put up in boxes having movable trays, one for each denomination. Price, per box, 25 cents. Postage 4 cents. THE INLAND PUBLISHING COMPANY, TERRE HAUTE, IND. In Indiana Should consult the "State Manual and Uniform Course of Study" for books which are recommended as helpful, and write THE INLAND PUBLISHING COMPANY for whatever is needed. We guarantee you correct prices. Prices include postage. Page 41-Wisely's Language for the Grades Page 72-Carpenter's Geographical Reader (Asia) Page 76-Ten Boys . . . . Page 96, 97, and 98-Prince's Arithmetic by Grades. Parts Page 100-House I Live In . . Page 102-Alcohol: Its Effect on Body and Mind Page 81-Guerber's Myths of Greece and Rome Page 72-American Neighbors Page 72-Modern Europe When writing to advertisers please mention THE INLAND EDUCATOR. VOL. VI. THE INLAND EDUCATOR. A JOURNAL FOR THE PROGRESSIVE TEACHER. MARCH, 1898. No. 2. THE RATIO FAD. By M. A. BAILEY, Department of Mathematics, Kansas State Normal. I. A number is ' a collection of units' or 'a ratio, according as the whole is regarded as N units one time or as one unit N times. Both conceptions follow logically from the "Educational Summary," p. 38, Psychology of Number. "Number is the product of the way in which the mind deals with objects in the operation of making a vague whole definite. This operation involves (a) discrimination, or the recognition of the objects as distinct individuals (units); (b) generalization, this latter activity involving two subprocesses; (1) abstraction, the neglecting of all characteristic qualities save just enough to limit each object as one; and (2) grouping, the gathering together the like objects (units) into a whole or class, the sum.” Illustration.-If we wish to make a vague whole of cents definite, we recognize the whole as made up of objects or distinct individuals (units), one cent, one cent, one cent; we neglect all characteristic qualities save just enough to limit each object as one (abstraction); we gather together the like objects (units) into a whole or class, and obtain '3 cents' (grouping). The vague whole has now become the definite whole 3 cents.' The original whole is physical, the parts are physical, the new whole is physical and the same physically as before. And yet there is a difference between the new whole and the old. Is this difference anything physical? It is not; it is something psychical; it is found entirely in the attitude of the mind. This intangible something, this difference, we call number. Hence, 'Number is that psychical product which expresses how many distinct individuals there are in a group of objects.' By analyzing more care fully, we may obtain one cent one time, one cent one time, one cent one time. Then, by synthesis, we may group together the times instead of the cents, and obtain 'one cent 3 times.' The difference between the new and old is something psychical; it is number. Hence, 'Number is that psychical product which expresses how many times a distinct individual is contained in a group has been embodied in the definition, 'Numof objects. The first of these conceptions ber is a collection of units;' the second, in the definition, Number is a ratio.' Both phases of number are illustrated on p. 71 of the Psychology of Number, but the conception 'how many parts' is not recog nized as 'a collection of units.' It is there stated, "Number always expresses ratio." Number "always answers the question 'How many. This 'how many may assume two related aspects; either how many times one part as unit has to be taken or repeated to make up the whole quantity; or how many parts as units, each taken once, compose the whole. In the first case, the times of repetition of the measuring unit is mentally the more prominent; in the second, the actual number of measuring parts; e. g.. in thinking of forty yards, we may at one time dwell on the forty times the unit is repeated; at another time, on the actual forty parts making the unified whole." "Number always expresses ratio" is a partial truth. When the mind dwells upon how many parts, as 'forty yards,' the 'forty' expresses a collection of the parts; when the mind dwells upon how many times, as one yard forty times,' the forty expresses a collection of times that one unit is taken,' or a ratio. The Psychology of Number is sadly |