This series of books aims to give the child the ability to compute easily and accurately, and to enable him to interpret and solve the quantitative situations which he will meet in everyday life. In the achievement of this aim, these books incorporate the most valuable findings of modern experimentation in the teaching of arithmetic, including the results of important researches conducted by the authors themselves. These books present only those methods and materials which have been thoroughly tested in the classroom by many experienced teachers.
It is an established principle of teaching that nothing stimulates a pupil's interest so much as the satisfaction he gets from his ability to do things successfully. If he finds himself steadily perfecting new skills in arithmetic, he will look forward to his arithmetic period and will approach each new problem with intelligent interest. In accordance with this principle, these texts require the pupil to take only one new step at a time and supply him with enough exercises to assure mastery of that step before proceeding to the next one. Thus the constant stimulus of success is made possible for the pupil.
In this book the following features are worthy of note:
1. This book is written for children, in language with which they are familiar. The greatest care has been taken in the selection of the vocabulary.
2. The problems relate to the life and interests of the pupils. They are real problems in every sense of the word.
3. Motivation is the keynote of successful work in arithmetic. When a new topic is being presented, the pupils should know why the topic is important and how it is used in life. This fundamental principle of teaching is applied throughout this series of books by presenting every new operation or detail of a process in connection with an interesting motivating problem that treats of some situation with which the child is familiar.
4. The explanations of new principles and processes have been made as simple and clear as possible.
5. All the abstract exercises have been scientifically constructed so as to provide drill on all the fundamental number combinations, with ample repetition of those recognized as most difficult. The pupil thereby acquires that automatic mastery of the basic combinations which is so essential to rapid and accurate computation.
6. The total number of abstract exercises in this book is far greater than that usually found in elementary school texts. All these exercises have been graded with extreme care with reference to the difficulty of the steps involved.
7. The checking of computations is one of the most important habits that a child can form. Throughout this book checking is taught early in the presentation of each new operation and is required in all exercises.
8. Long division is presented in this text in an unusually simple and clear manner. In learning long division the pupil has to become acquainted with many new steps, the most difficult of which is the finding of the correct quotient figures. In this book the several steps in long division are presented one at a time, with many exercises upon each step before the next one is introduced. Further, the pupil is systematically trained in the method of estimating the quotient figures so that he soon becomes able to find the correct quotient figure on first trial in 75% of all cases. The procedure so often found in schoolrooms, by which the pupil tries first one quotient figure and then another until he finds the correct one, is thus avoided. This improved method of long division, which is the result of many years of research and experimentation on the part of one of the authors, has been enthusiastically indorsed by many teachers who have already used it.
9. This book provides more fully and generously for diagnostic and remedial work than any other text in arithmetic. Frequent diagnostic tests are given throughout the book, with keyed references to remedial work.
10. Another feature of this book is its carefully planned instruction in problem solving. In developing the ability to solve one-step problems, the pupil is taught the more important language expressions of arithmetic that often suggest the operation that is to be performed. In teaching two-step problems emphasis is placed upon those types of two-step problems that occur most frequently in everyday life. Throughout the book there are very few pages upon which all the problems require the same operation. There are, however, many pages containing problems of several kinds, where the pupil must decide whether to add, subtract, multiply, or divide to get the answer. Thus the pupil's ability in problem solving is developed us systematically as his skill in computation.
11. A series of tests on problem solving is also provided throughout the book. These tests cover types of problem situations with which every pupil should be familiar. An important feature of these tests is that they not only measure the pupil's mastery of types of thinking frequently employed in problem solving, but they also check his ability to interpret important language expressions and technical phrases peculiar to arithmetic. These tests are arranged in groups known as Groups A, B, and C. Each group consists of three tests; thus, Group A consists of Tests Al, A2, and A3. The problems on Test Al cover the same variety and types of problem situations and the same range of difficulty as those found on Tests A2 and A3. A pupil, therefore, should do better on the second and third tests of any group than on the first test. Thus the pupil has the satisfaction of seeing himself grow in problem-solving ability. The problems on the tests of Groups B and C cover, in similar manner, other sets of type problems.
12. Full provision has been made for pupils of varying levels of ability. For those of superior ability more difficult exercises, marked with a star (*), are provided. For pupils of average and below-average ability additional exercises may be prescribed if needed; the diagnostic tests indicate whether extra work is necessary and also give references to suitable materials.
GEORGE DRAYTON STRAYER
CLIFFORD BREWSTER UPTON