The basis of an instructional program in language and composition should be a well-established body of information about the uses of oral and written speech at various stages of development. At the present time there is no general agreement as to what should be taught at the different grade levels, because there is a lack of dependable objective data about the ways in which children at each stage use composition. There is also no agreement about the items they should learn, the grade placement of these items, and the standards of composition children should be expected to achieve at the various levels.

In the modern curriculum, arithmetic has much broader functions than were commonly recognized in the traditional school. Present thinking emphasizes four major functions of arithmetic: (a) the computational function, which deals with the development of essential computational skills; (b) the informational function, which deals with the development of an understanding of the history, evolution, and present status of institutions, such as banks, insurance, and taxation, that have been created by society to deal with social uses of number; (c) the sociological function, which deals with the development of an awareness of the problems faced by these institutions and of the means, current and proposed, for solving those problems; and (d) the psychological function, which deals with the development of the power to do quantitative thinking and of an appreciation of the value and significance of quantitative data and methods in dealing with the affairs of life

The most direct way in which to evaluate the effectiveness of any educational program is to observe the behavior of its product in the affairs of daily life. When this behavior is inefficient, unwholesome, or not in accord with accepted social standards, the school must examine its own program, the personality of the learner, and elements in the environment both in and out of school, to locate the causes of the unfavorable condition.

The factors associated with learning difficulty are to be found not only in the physical and mental equipment of the learner but also in the instructional situation itself.

The two expressions, preventive teaching and remedial teaching, may be applied to two different aspects of a program of instruction concerned with the improvement of the conditions under which learning takes place.

The principles of developmental and remedial teaching here presented are generalizations that have grown out of the consideration of many case studies. To give clarity to these generalizations, two typical cases have been selected. One of them presented a relatively simple difficulty, easily corrected; the other was a more complicated case, presenting a wide variety of problems less easily solved.

Investigations of causes of pupil failure and retardation in the elementary school show that arithmetic is a subject that is extremely difficult for many children. Above the second grade inferior work in arithmetic has caused more non-promotions than any other subject in the curriculum.

Recent developments in the techniques for analyzing and constructing instructional materials in arithmetic include two methods related to procedures for studying the content of drill in fractions. These methods make it possible to construct practice exercises in fractions according to specifications that can be set in advance, as can now be done in the work with whole numbers. It is the purpose of this paper to point out the fundamental difference between the two methods that have been proposed by Knight and his co-workers and by Brueckner for analyzing the content of drill materials in fractions. The discussion will be limited to a consideration of the procedures as applied to the subtraction of fractions.

An experimental study was recently performed by the authors in the public schools of St. Paul to determine to what extent the teaching of a fundamental number combination in the direct order transfers to the reverse order of that combination; thus, if the combination 7 + 5 = 12 has been learned, to what degree has the combination 5 + 7 = 12 been established?