CHAPTER XIII APPLICATION OF PRINCIPLES TO PRIMARY ARITHMETIC, WRITING, AND SPELLING Origin of Methods in Arithmetic. - Many of our socalled methods in arithmetic are but partial truths elaborated out of all proportion. The result is that much of our primary arithmetic has been one-sided, unnatural, and uninteresting. For example, Pestalozzi's notion that number concepts should be built up from sense contact with objects our practice a theory that has materially influenced though true, by no means represents all the truth. It does not take into consideration the native interest of the child, which is indeed an important consideration. As Dewey has pointed out, the application of the unit in measurement, because it affords opportunity for movement and because it relates more directly to the child's natural experiences, is vastly more interesting to children than the observation of cubes, rectangles, pyramids, and the like, advocated so strenuously by the Swiss reformer. - Notable Features in Textbooks. The most notable features of primary books in arithmetic, excluding the absence of obsolete subjects, are the attempts, first, to present subject-matter in such a way as to develop mathematical concepts inductively; and secondly, to present opics in the cyclic, or psychological, way. Both of these methods employed in primary arithmetics are a decided concession to the rights of the child in the learning process. Mathematical concepts through the measuring process are gradually developed without the child being conscious of the fact that the teacher has purposely, though pleasantly, helped him to acquire new and useful concepts. Ideas of the perimeter and area of rectangles are developed as a by-product through the solving of practical problems in which the child measures walls, yards, and gardens for the purpose of estimating the amount of paper, sod, and seeds needed respectively to meet the demands of the problem. These problems appeal to his experience and thus stimulate effective effort. Such problems are but means to an end in the acquisition of mathematical concepts. MOTIVATING FACTORS IN PRIMARY ARITHMETIC An Initial Device for Creating Motive. - "Keeping score" in the little games initiated by the teacher beautifully stresses the intrinsic function of arithmetic. Here for the first time the child feels a real need for written arithmetic. He wants his side to win and for that reason he has an impelling desire to master the tools which control the situation. Bean bags or walnuts, and a waste-basket are all the materials required to initiate this game. The teacher appoints two captains who choose sides. Each member of a team when his turn comes pitches four bags at the basket. Each captain keeps score for his team. pitched the teacher asks for the results. computation in earnest. At first only a few will fully comprehend what is being done. Some bright pupil will add the two columns of scores, compare the sums, and if his side has won will probably begin to clap his hands; if he When all have loses, he will look abashed. After the result is comprehended the game is continued as before. Keeping Store. - Keeping store makes a strong appeal to the interests of pupils. It relates to their home experiences and makes a keen appeal to their curiosity. The financial factor has made store articles forbidden fruit. Freed from this economic restraint by the use of paper money, the child's desire for investment runs rampant. The necessity of accounting for his investment develops a sense of the intrinsic function of arithmetic and lays the foundation for habits of the fundamentals. The greatest weakness in this phase of primary method in arithmetic lies in the lack of a graded series of projects capable of being extended over a long period. Use of the Cycle. — The psychological, or cyclic, method of presenting arithmetical topics rather than the logical method has made for greater interest in arithmetic. The topical method ignores the fact that the various arithmetical topics depend more or less upon each other and consequently an attempt to master one topic thoroughly, before considering others, deprives the child of knowledge that is needed in the mastery of the first topic considered. Then, again, such a procedure ignores the fact that ability to understand depends upon maturity, both in the sense of experience and in the sense of natural development. While the native ability and natural experiences of a child of ten or eleven enable him to understand some of the elements of percentage or of mensuration, they by no means qualify him to understand these subjects sufficiently to meet the demands that will later be made upon him. Persons who object to the cyclic method do so on the ground that it is difficult for the teacher to follow con sistently. For example, the teacher of the seventh grade when considering percentage is not quite sure what experiences the child has had in this subject in previous grades. The course of study should reveal this, but better still the child should reveal it. If he does not it is evident that a review, at least upon the fundamentals of the subject, is essential to further work. Progressive ideas in arithmetic method have suffered more perhaps than in any other subject with the exception of grammar. This is probably due to the tradition that has been persistent here. The exactness of these subjects has made them less adaptable to the needs of the child and has made it more difficult for the teacher to lay aside the method of her own school days and adopt one different in form and structure. Problems Should Precede Drill. Excesses in primary arithmetic usually result in one of the following practices: Either too much consideration is given to drill exercises upon the four fundamentals at the expense of problemsolving, or problem-solving is given major consideration with the thought that skill in the fundamentals will come as a by-product. A "middle of the road" policy is better suited to the needs of the pupils. A strong lead with problems which grow out of the child's needs, followed by supplementary drill exercises properly stimulated by instinctive appeals, brings the best results. These processes are complemental, not supplemental, to each other. The one tends to strengthen the other. Accuracy and Speed. Accuracy and speed are assured only by reducing these processes to automatic reaction. Recent tests given in the Training School at Normal, Illinois, show conclusively that there is a close correlation between accuracy and speed. These tests indicate that a number combination that is habitual is worth more to the possessor than one which must have conscious direction. To the extent that fundamentals are habituated in the early grades one can feel assured that energy will be conserved in the higher processes of the upper grades. Free the child from the drudgery that results from inefficient preparation in the fundamentals and you have added materially to his power and interests. Again, accuracy in the fundamental processes insures success, and success is in itself a strong stimulating factor. of Since the child is largely a creature of impulse instinct his native reactions must be drawn upon to intensify the personal experiences that the school sees fit to create. As these personal experiences increase and thus form the basis for other experiences, they should be appealed to. The problem, often in the form of the indirect question, is an effective device for stimulating thought. It is so because it is a natural one. From the time the child began to creep until he arrived at the school he had been solving problems because he found gratification in so doing. This gratification arose partly from the desire to know and partly because of the social approval it afforded. Success. We must not retard this problem-solving tendency by withholding social approval in the schoolroom. It is a positive motivating force. Strong students usually receive sufficient approval. The teacher who understands the importance of social approval as a motivating factor in the solving of the problems of the school will avail himself of every opportunity to encourage the children by manifesting appreciation of every worthy effort, especially of those who are less fortunate than their fellows. |