PREFACE

The recent movement in testing results in education by means of standard scales and tests has revolutionized methods of instruction in many of the subjects. One of its results in the field of arithmetic has been to emphasize the necessity of wellplanned drill work to secure speed and accuracy in the fundamental processes.

The authors, realizing that these drills should be based upon more accurate experimental data than those which had been previously obtained, formulated and carried out an experiment to determine the degrees of difficulty presented by the various facts in each of the processes of addition, subtraction, multiplication and division. The facts in each of these processes were then arranged into three groups: An easy group, a middle group and a difficult group.

When the Exercises for Speed and Accuracy were formulated, each fact was recorded as it was put into a problem, and the most difficult facts were made to occur most frequently. This plan was also followed in preparing the lists of abstract problems in addition, subtraction, multiplication and division. The emphasis is thus placed where it is needed.

The ability to select the proper process to solve a problem which is met in a social situation is just as important as the ability to compute correctly. This ability is developed by coming, in contact with a wide variety of concrete problems.

The first difficulty that confronts a pupil in the second grade, when he attempts to solve a concrete problem, is the language difficulty. Attention is called to the method used in this text to minimize this difficulty. The concrete problem is stated in

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full for the teacher to read so that the pupil gets the concrete background. Each problem is followed by a condensed statement of the problem, which the pupil is to read and answer. After hearing a large number of concrete problems read and abbreviated in this way, the pupils learn how to select the process and condense the problem into the brief form.

The illustrations used in this book give the child a concrete background for the various activities and situations presented in many of the problems and take only a minimum amount of space. The authors believe they justify much more space than they actually take by helping the child over another difficulty -picturing the social situation involved in the problem.

Attention is also called to the care with which each of the fundamental processes is developed and to the explanations of the various steps from the easy to the difficult. This careful organization eliminates any necessity for a reorganization of the subject matter on the part of the teacher who uses this text.

The authors wish to express their indebtedness to Miss Katherine L. McLaughlin, Supervisor of City Grades, Department of Public Instruction, State of Wisconsin, and to Miss Myra Banks, Instructor in Arithmetic, Northrop Collegiate School, Minneapolis, Minnesota, for helpful material supplied.