Arithmetic exhibits some marked contrasts when compared with some of the other content areas of education. Unlike chemistry, physics; and the social sciences, its content is not subject to radical changes due to discoveries such as those involving new elements, forms of energy, or ideas of social organization.

The present chapter is directed to teachers and supervisors rather than to psychologists. The aim of the writer will be to make a sensible interpretation of psychological theory and experiments as they affect the arithmetic program. Illustrations will be drawn from the teaching of arithmetic to make the interpretations as clear as possible.

This chapter consists of two parts. First, there is a brief consideration of some problems of research as they relate to arithmetic; and, second, there is a group of specific proposals for research submitted by some twenty members of the profession who have an active interest in the teaching of arithmetic.

One of the principal ways in which a school attempts to direct the learning of its pupils is by controlling the situations which make up its curriculum. The child's responses to these situations are determined not only by the nature of the content of the curriculum, but also by its organization and sequence. The selection of content is a problem which concerns others as well as psychologists, but the organization and sequence of whatever content is selected involve decisions which are primarily within the province of psychology. It is the function of this chapter to examine the contributions that psychology can offer to the curriculum maker.

Researches dealing with arithmetic were few prior to 1900. While this section is concerned only with the influences of research, a brief consideration of the status of arithmetic at that time will serve as a useful basis of comparison.

As used in education, the laboratory method is similar in general characteristics to laboratory methods in other sciences. Its success often depends upon the degree to which nonessential concomitant factors can be eliminated and an artificial situation set up in which the phenomena under investigation may be thoroughly analyzed. The commonly heard criticism that laboratory situations are artificial betrays a complete misunderstanding of the very nature of laboratory methods. The laboratory is intentionally and purposely artificial, but artificial only in respect to the nonessential in a situation.

Some time ago the writer was attempting to discover why a certain elementary-school boy was experiencing so many difficulties in column addition. The boy had better than average intelligence and, on the whole, was succeeding quite well in his school work. However, in column addition he had no end of trouble, being both slow and in- accurate. Casual observation of the boy's work indicated nothing except that it took him an exceptionally long time to secure an answer and that quite often the answer was wrong when he got it.

In selecting the material for this bibliography, the compiler examined approximately five hundred references. Since it was not the purpose of the Committee to provide a complete bibliography, only those references have been included which are quantitative or critical in character.

Part One of this volume consists in a systematic treatment of the general field of arithmetic. Part Two is devoted to research relating to this subject. In this part of the Yearbook the Committee is presenting two types of material. The first of these, contained in Chapters II and III, is a classification of the entire body of published research in arithmetic arranged under the nineteen techniques which have been employed in such investigations. The second type of material consists in a series of new research studies relating to several aspects of arithmetic.

No attempt will be made in this chapter to present a detailed summary of the research studies in arithmetic which are now in print. Such detailed summaries have already been published and may be procured easily. The chapter will deal with the nature and findings of investigations in arithmetic without attempting to mention all the persons who have made contributions.

Standardized tests in arthmetic have been in general use in the public schools of the United States for the past fifteen years. Most of these tests have been of the survey type. Survey tests in arithmetic are still widely used; in fact, they probably constitute the chief measuring instruments now employed in arithmetic in public schools. The principle involved in survey testing is that of securing a sampling of pupil achievement in a wide range of subject matter on an objective basis.