CHAPTER II. THE PROCESSES OF LEARNING AND TEACHING........ 26 CHAPTER III. THE LEARNING EXERCISES OF ARITHMETIC......... 33 CHAPTER IV. THE LEARNING EXERCISES PROVIDED BY TEXTS IN PREFACE The research reported in this monograph deals with a very practical problem. Every teacher of arithmetic continually faces the problem, "What learning exercises should I ask my pupils to do?" It is true that few teachers explicitly formulate this question but all must answer it. Incidentally it may be noted that the answer given is a very potent factor in determining the efficacy of the instruction. Attempts to answer questions that ask what should be done may be designated as "complete research" to distinguish such investigations from fact-finding inquiries which may be called "auxiliary research." The work reported in this monograph represents an attempt to carry out a piece of "complete research." In this endeavor the results of a number of "auxiliary" or "fact-finding" studies have been utilized but reference to them has been subordinated to the consideration of the two basic problems. Even the report of the analysis of ten series of arithmetic texts, which represents more than 2500 hours of work, is made incidental to the solution of these problems. A critical reader will probably be impressed by the incompleteness of the data needed for definite answers to the two basic questions. This condition is due in part to the complexity of these apparently simple problems but the available fact-finding studies relating to them furnish only fragments of the data necessary for detailed solutions. Many more auxiliary studies must be made before we can have what is commonly called a scientific answer to the question, "What is the responsibility of a teacher of arithmetic for devising and selecting learning exercises?" It may even occur to the critical reader that an attempt to answer this question is not justified at the present time because the answer must be based upon fragmentary data and consequently judgment must be introduced at many places. In reply to this criticism, one may point out that every teacher is forced to give some answer to the question. Furthermore, if research workers become aware of the inadequacy of data for dealing with such practical questions, it is possible that they may be stimulated to group their fact-finding studies about certain fundamental problems. The justification of auxiliary studies is based upon the contributions they make to the solution of problems that ask "what should be." WALTER S. MONROE, Director Bureau of Educational Research May 14, 1926. |