arV 16134 0|atneU IttituecBitg Hibcacg Jt^Bca. Sltni fork SOUGHT WITH THE INCOME OF THE FISKE ENDOWMENT FUND TMK BEQUEST OF WILLARD FISKE LIBRARIAN OF THE UNIVERSITY 1868-1863 1905 The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031304540 COURTIS STANDARD PRACTICE TESTS IN ARITHMETIC TEACHER'S MANUAL For use with the Card-Cabinet Edition BY S: A. COURTIS '^"^ Supervisor of Educational Research, Detroit Public Schools Contains full instructions for the proper use of the Standard Practice Tests in Arithmetic, together with sample graphs and records and suggestions for the diag- nosis and remedy of the difEculties of in- dividual children, by means of which alone it is possible to effect any radical improvement in the efficiency of teaching. WORLD BOOK COMPANY YONKERS-ON-HUDSON, NEW YORK 1918 STANDARD PRACTICE TESTS Personal Note to Teachers: The Courtis Standard Practice Tests in Arithmetic were designed to decrease the amount of a teacher's routine drudgery and to improve the efficiency of his teaching. Measurement proves that when the tests are rightly used both objects are ac- comphshed. Measurement also proves that the degree of suc- cess attained depends upon how far -the teacher comprehends the purpose of this new tool, and uses the opportunities it pro- vides for adjusting the drill work to the needs of the individual children. Will you not, therefore, study the instructions care- fully until you understand the essential features of the system, then make such adjustment of the general method to your local conditions as will enable you to a. Measure your class to determine the, initial ability of its members. (See pages 6, 7-11) b. Eliminate from the drill class those who have (or reach) standard ability. (See pages 6, 11-13) c. Give to each of the other members drill upon those les- sons where drill is needed. (See pages 6, 13) d. Permit each individual to practice in his own way and to grow at his own rate. (See pages 6, 20-27) e. Give exactly the assistance needed to each child that fails. (See pages 27-44) f . Measure the efficiency of your teaching, (See page 22) If you will do this faithfully and intelligently, the efficiency of your teaching of the four operations with whole numbers will rise from the conventional 5% to 10% to from 60% to 75%. Copyright, 1914, 1915, 1916, by World Book Company, Yonkers-on-Hudson. New York CSPTA-TM-.CC Ed-A TEACHER'S MANUAL Ten Essential Points 1. The purpose of the Practice Tests is to develop ability that will transfer to regular arithmetic work, and to all situa- tions in which computations are used ; not to give a few children a chance to show how rapidly they can finish the series of lessons. 2. Lack of ability to "cipher" will prove a handicap in the life of any man or woman. On the other hand, once standard degrees of ability have been attained, further drill is a waste of time and effort. Children of standard abUity should be set at more profitable work. 3. Ten minutes a day, day after day, spent in intense, purposeful, snappy practice, has proved adequate to develop proper habits of speed and accuracy. Why use more? 4. Skill cannot be developed in growing children by in- struction, or by any other form of personal exertion on the part of the teacher. Consequently the teachers who best inspire their classes to voluntary effort will secure the best returns. 5. Mere repetition does not develop skill; it is repetition accompanied by the conscious desire to improve that brings results. Mark for growth, riot for the ntimber of lessons completed. 6. Remember always that "nothing succeeds like success." It is easy to get a child to try once, but he will not keep on 4 STANDARD PRACTICE TESTS trying unless his efforts bring success. The Practice Tests will automatically set for each child each day a task within his reach. If you reward growth in proportion to effort, the children will do the rest. 7. There has always been some cheating in school work, and some children wiU always cheat. The best safeguard against cheating is not the repressive vigilance of authority, but the development of ideals of honesty and self-mastery. 8. The surest sign of faulty use of the Practice Tests is the speed that is due to excessive effort and nervous strain. The speed that is desired is the perfection of execution pro- duced' by thoroughness of preparation. The speed that is merely hurry makes for exhaustion. Do not force speed. Inspire conscientious practice and the questibn of speed will take care of itself. 9. Under no circumstances forget that when a child fails, there is a reason, and that only as you discover the true reason will you be able to render real assistance. Neither age, experi- ence, training, nor "puU" will make a wrong diagnosis effec- tive. It pays to take the time necessary to determine the causes of the difficulties of individuals, because then, and then only, can you apply the proper remedy. 10. Through appeals to basic instincts, drill work with the Practice Tests becomes so interesting and enjoyable that it takes on the nature of play. This in no way decreases the value of the results secured, however. See that the children look forward to the drill period as to play time, and have a little human interest yourself in the records made. TEACHER'S MANUAL Section I General Description Each child should be supplied with a Student's Record and Practice Pad and the teacher with a cabinet of" lesson cards and a Teacher's Manual. Each lesson card in the cabinet consists of a number of examples of one type, the types being so chosen that the range is from the simplest examples to the most difficult a child in the grades is called upon to solve. Further, the mastery of the examples on each card insures the mastery of some one of the many component elements that enter into skill in the four operations. In addition, for instance, one of the early lessons is designed to [teach the combinations, another the bridging of the tens, another carrying, another control of the attention span. Four of the cards (Lessons 45, 46, 47, and 48) are study cards for the use of children who have trouble in learning the combinations. Four other cards (Lessons 13, 30, 31, and 44) are test cards to be used in determining what practice a child needs, and in measuring the efficiency of the child's efforts. These eight cards, strictly speaking, are not practice lessons, although their use is essen- tial to the success of the plan. The lessons are issued in two editions. Form A and Form B. The examples in these two forms differ, but the two forms are equal in the number and difficulty of the examples in each lesson. In filling an order, equal quantities of Form A and Form B are supphed; the two should be equally distributed in each class. It makes no difference whether a child begins to work on Form A or Form B. The corresponding lessons of either form serve as a test for the study and practice put upon the other. No one lesson in the same grade should take any longer to complete than any other lesson. The remaining forty cards are practice lessons and are used as follows: A lesson card, practice side up, is placed under the topmost tissue-paper sheet of the Student's Practice Pad. The child sees the examples through the paper but does his work directly upon the tissue-paper sheet. The num- ber of examples in each lesson has been so chosen with respect to the diffi- culty of the examples that all the lessons require the same working time. That is, an eighth-grade child of standard ability, for instance, will require three minutes to finish each and every lesson.^ At the end of the practice period, the card is taken out, turned over so that the answer side is uppermost, and again placed under the tissue- paper sheet. It is then easy for the child to compare his answers with the true answers and find his own mistakes. The perforated tissue sheets are now torn out, but only the papers the children judge to he perfect are handed inj, so that the teacher is relieved of much drudgery of correction of papers. The lesson cards are printed on strong cardboard and may be used again and again, and year after year. It is the supply of tissue-paper sheets that is renewed each year. ^Except those marked "Double Time,'' which require six minutes. 6 STANDARD PRACTICE TESTS The scores made each day are recorded by the child in the Student's Record, and graphs drawn that the child may see the effect of his own practice. In other words, the children take care of their own progress in every possible way, that the teacher may be relieved of the mere mechanical details of preparation and marking, in order that he may give his time to the actual teaching of children. Program At the beginning of the term, the first activity is measurement. The teacher gives Lesson 13 (Test A) to determine which children need drill on Lessons 1-12. Those who have perfect scores are excused from drill work until the rest of the class has completed these lessons. Their drill time is spent upon other work. The next day the remaining children take Lesson 1. The third day those who are successful take Lesson 2, and sc on. But those who failed on Lesson 1 spend the third drill period in practicing the examples in the lesson, and the following day try the lesson again, to test the effectiveness of their practice. Only when Lesson 1 has been completed successfully do they go on to Lesson 2. In this way each child masters the simple work before attempting the more complex; each child practices only on the type of example in which he falls below the standard, and each child progresses as fast or as slowly as his native powers and personal efforts allow. At the end of two months each child in a class of 40 may be working on a different lesson. To a teacher reading the foregoing description for the first time, it may seem that it would be very confusing to have children working on different lessons and progressing at different rates. It must be remembered, however, that as far as the teacher is concerned his work is the same whether the child is on Lesson 1 or on Lesson 40, and that at the start Cthe most confusing time) all the children work on the same lesson. By the time the number of lessons in use reaches four or five, the system will be running smoothly and will give no trouble. There are two important reasons' why every teacher should be willing to make whatever effort may be necessary to adopt this new form of class- room procedure. The first one is that experimental psychology has proved that children differ enormously in their natural powers and rates of growth, so that pnly that teacher can be efficient who adapts school work to the needs of each individual child. No teacher, by mere intuition alone, can make such adjustments for fifty children, while the system described above will do it automatically. Once you have made the system your own, you will get better results than ever before and with less effort. The second reason is that the system itself has been a gradual evolu- tion. It is based primarily upon a careful, scientific measurement of the relative effect of the various factors which condition teaching, and the origiiial plan has been modified by the contributions of many successful TEACHER'S MANUAL teachers. Each device has been adopted in response to a real need. The system as a whole has proved practical in the hands of a large number of teachers and is rapidly being extended to other subjects. You cannot afford, professionally, not to master this new and efficient tool. Section II Detailed Instructions for Each Day of the First Two Weeks Do not begin the Practice Test work until the second week of school, or until the organization of your class is completed, so that you have some knowledge of the personal characteristics of the children in it. Monday Give to each child a card of Lesson 1 and a Student's Record and Practice Pad.i Show them how to put it in their practice pads under the topmost tissue sheet, practice side up, so that the ex- amples may be seen through the paper. Explain the necessity for lifting the tissue-paper sheet well up from the rest of the pad, and pushing the card as far up into the stub as possible so that it will be held firmly in place and not slip. Have the children read aloud the instructions for starting and stopping as given in the Student's Record, page 3. Go through the motions once or twice until you are sure every child understands. Then let them work on Lesson 1 for a half-minute interval, and score their papers, following the instructions. This, of course, is mere practice, to make them familiar with the general procedure. Explain that the first real work will be to find out which children need the drill. Collect all the cards of Lesson 1. Distribute the cards of Lesson 13 and have the children put them in position in the practice pads ready for work. Warn the children that to study a card before the proper time is cheating. Then put the Lesson 1 cards back into the cabinet in their proper place. A little care in returning cards to the cabinet will enable you to keep your material in good order. Always put a card after the numbered separator, with the top of the card to the left, the face of the card towards you. You will then be able to select Form A or B as need arises. Assign the task of filing the returned cards each day to the children who are excused from drill. It is ex- cellent practice in an important form of office work. Have all the pads and cards put away ready for the work of the next day. Tuesday For the testing work, the teacher needs a timepiece showing seconds. A dollar watch having a second hand does very nicely. A football timer (price $2.50 at any store that sells sporting goods) is very much better, as ' If the children buy this material themselves, be sure that all are supplied before you begin explanations. 8 STANDARD PRACTICE TESTS 3 minutes Low sixth grade, 4j4 minutes 3J4 minutes High fifth grade, 4J4 minutes 3j4 minutes Low fifth grade, 5j4 minutes 354 minutes High fourth grade. 5^ minutes 4 minutes Low fourth grade. 6>4 minutes it starts from zero, and shows minutes and seconds of elapsed time more clearly than a regular watch. It is of the utmost importance that the teacher use scientific care in keeping exact time. If the time interval varies from day to day, the chil- dren's scores will vary for no apparent reason, and the whole force of the timing be lost. Give the signal to start just as the second hand reaches the sixty mark, and give the signal to stop sharply at the end of the interval. The time to be allowed for the various grades is as follows: High eighth grade, Low eighth grade. High seventh grade. Low seventh grade. High sixth grade. All lessons in any one grade are to have the same time allowance. Those to whom these standards seem high are, of course, at liberty to change these time allowances to suit their own ideas. The standards above, however, have been set after a careful investigation of the actual speed of work of children in the grades, and are believed to represent the speeds at which children can work without strain. Speed is apparently fixed by the maturity of the individual, so that there is an op- timum speed for each age. If a teacher has several grades in one room, he may adopt one of several methods. The best way is probably to start all the children together, and give each grade its own signal to stop. For instance, in a room having both A 6th and B 7th children, the teacher should start all together, and at the end of 3J4 minutes should say "B 7th, stop. Hands up. Score your papers," and at the end of four minutes, "A 6th, stop. Hands up. Score your papers." Other methods are to use the time of the youngest grade, or of the largest grade, but either of these methods means a lack of adjustment for some children. If this is done, however, it is better to have tiie time too long than too short. Still another method is to use the time of the oldest class for all, but require all other classes to do but a part of the test. The following table Shows the per cent of each lesson that should be completed by each grade for each time allowance: TEACHER'S MANUAL , Grades 8 7 6 5 4 L H L H L H L H L 92% 85% 80% 73% 70% 63% 57% 42% 38% 100 92 87 81 76 68 62 56 52 100 93 87 82 73 66 61 56 100 94 88 79 71 65 60 100 94 84 76 69 64 100 89 81 74 68 100 90 100 82 91 100 76 84 92 100 Time Allowance, Minutes H 3 100% 3J4 3^ i m 5J4 6J4 For instance, if a teacher used a time allowance of four minutes with his oldest class (High 6th), for the low sixth he would set 94% of the examples in Lesson 1, or 68 (72 x 94%) examples as the number to be completed. This is a good method, but a little difficult to handle. The teacher should work out and post on the board the number of examples to be completed by eaeh grade for each lesson. Work may be done in either pencil or ink. Probably ink is to be preferred, particularly in the upper grades, as children should learn to write rapidly and neatly with ink. Most commercial work requires a permanent record, and is done in ink. Having decided the plan to be followed, give Lesson 13 to all, following the instructions in the Student's Record. The answers' to the test cards are not given on the back of the cards as in the regular lessons, but are found in the Teacher's Manual on pages 54-57. Note that there are two forms of Lesson 13, A and B. Both sets of answers will, of course, have to be read. Have the children exchange papers, and mark each wrong answer with a cross as you read the correct answers from the manual. In checking similar work in business, it is customary to read the figures in order without giving them their place values. The figures should be read in groups of three, with scarcely perceptible pauses' between the periods. \ Thus 3,456,789 would not be read three million, four hundred fifty-six thou- sand, seven hundred eighty-nine, but three (pause), four five six (pause), seven eight nine. If the answers are read slowly, the scoring of the children may be depended upon in all but the lowest grades. An answer is to be counted wrong if it is illegible because of poor figures, or if it has been written over, or erased, or corrected in any way after the first writing, even if the error was discovered before the answers were read. The reason for this drastic rule is twofold: (1) it prevents cheating, and (2) it emphasizes the need of close attention and absolute accuracy. 10 STANDARD PRACTICE TESTS The purpose of the Practice Tests is to develop habits of accuracy and this cannot be done if any form of correction is tolerated. Experience has shown that absolute accuracy in first-draft, straight-ahead work is easily attainable by from 30% to 50% of the children, and that the accuracy of the remaining children can be brought to very high levels if the ideal is constantly kept in mind.^ Have the children count the number of examples tried, and the number right. These results will be called their scores. The small figures written to the right and above certain examples in the lessons save time in counting. Teach the children to go back to the small figure nearest the point where, they stopped, and count only from that point on.' In this way they will never have to count more than four examples. In getting the number right, it is usually better to count the number wrong and subtract from the number tried. The scores from Test A are to be written in the summary on page 6 of the Student's Record. Have the children point to their open records on their desks, while you go rapidly up and down the aisles making sure each record is in the right place. Take pains with the records for the first week, and you will have no trouble later. The child should understand that the keeping of a neat record book is part of the work, that in business and in life they will often have occasion to make such records, and that the two things demanded are accuracy and neatness. Exhibit sample record books from time to time, of the worst in the. room as well as the best, that the children may have some idea of what is wanted. The record book provides an opportunity for a kind of valuable training which is too often neglected by teachers of arithmetic. Ask the children who completed all the examples in the test to stand, then ask of those standing, that all who had one or more examples wrong sit down. Collect the perfect papers. Then ask those who came within one example, in either speed or accuracy, of having perfect papers, to stand. Collect these papers also. Finally, collect the remaining papers. Then ask how many think they could do better if they took the same test again the following day. Nearly all will respond. Promise to give them another trial and have the pads put away. Reliability of Results Every teacher should understand that measurement of human ability is the measurement of a variab|ie quantity. The amount and character of the work a person can do in a given time varies from hour to hour and from _ * Those who do not accept the opinions given, should make up regulations to fit their own convictions. ' That is, a child who had tried 37 examples, would go back to 35, then count, 36, 37, instead of counting the whole 37 examples. TEACHER'S MANUAL 11 situation to situation. Fortunately, however, if the conditions of testing are kept constant, ajjout half the children will have almost identically the same scores on the second day, and of the remaining children, all but about 10% will make the same score within two examples more or less. There are usually, however, about 10% of the average class whose scores will vary widely from their true abilities. Two tests are, therefore, better than one, particularly at the beginning of the testing work, and it will pay to repeat the test the next day. Teacher's Scoring After school or at some convenient time go over the papers handed in. Place them over the proper page in your Manual and make sure the children have made no mistakes in scoring. Enter the scores in your record on page 45. Then fill out a report similar to that on page 51. Record the number of children who had perfect papers, and the number who missed but one example ; find what per cent each of these numbers is of the total membership of the class. Be sure to date the report and to mark it "First Trial." Such report should be carefully preserved, as comparisons with later tests will show the efficiency of the teaching. Wednesday Begin by having the children who on Tuesday used Form A exchange cards with those who used Form B. This will tend to eliminate the effect of any special "cramming" that may have been done. When all have a different form from the one used Tuesday, give the test as before, scoring the papers and entering the records, col- lecting the papers, and scoring and recording them as before. Comparison of the two results will show how reliable the first test was. Selection of Those Who Do Not Need Drill Test A covers simple work in the four processes. Children who had perfect papers do not need the drill contained in the first twelve lessons. Moreover, experiments have proved that such children not only do not need drill, but are likely to be injured by it, so that they would have lower scores after taking the drill lessons. Therefore, put on the board the names of all who had perfect scores in both tests and make it plain that they are excused from the drill work in Lessons 1-12, and are to spend the drill time in study upon such assignments as the teacher may make. Try to make the other children understand that the practice lessons are to develop in them the abilities which the perfect children already have. It is of vital importance that the children understand that their daily practice and success in the various drills are simply a means to an end, and that the real measure of their success will be their scores when Test A is reached in its regular position as Lesson 13, 12_ STANDARD PRACTICE TESTS Warning. Lessons 13, 31, 32, and 44 are not practice lessons but tests. They should not be studied or practiced except under test conditions. With children who cannot be trusted these lessons should be collected at once and given out only as tests. The teacher who is lax in his care of this point will be deceived by his results and dishonest in any comparisons he may make with the results of other teachers. Alternative Plans The instructions above call for the elimination of those who had perfect papers both days. Some teachers extend this to include those who were perfect either day^ while still others include those who missed but a single example in either speed or accuracy. The author advises the latter for Grades 4, 5, and 6, but absolute perfection both days for Grades 7 and 8. He favors' giving those who missed but a single example on one of the days a third chance, counting the best two out of the three scores. The course to be followed from this point on depends somewhat upon the conditions within the class. If only a few qualify for release from Lessons 1 to 12, it is best to begin the next day with Lesson 1 and follow the series through in regular order according to the instructions given be- low. If, however, half of the class or more than half the class are to be excused, give Tests B (Lessons 30 and 31) to these children on Thursday. If, again, half the class have perfect papers, give Test C (Lesson 44) i. In other words, children who fail on Test A should start on Lesson 1, those who succeed on Lesson 13 but fail on Test B should start on Lesson 14, while those who have perfect papers with the first two tests but fail on Test C should start on Lesson 31. That is, the tests divide the series of lessons into three groups. Lessons 1-12, 14-29, 32-43, each more difficult than the one before it, so that by means of the tests the teacher is able to start each child at the exact point in the series where he needs drill. ' Children who complete all the tests successfully do not need the slightest drill work in the four operations, as they already have more than average adult ability in these skills.^ The author and the publishers hereby give emphatic warning that the drill lessons are designed only for children who need them, and that they should not be held responsible for the bad effects and loss of efficiency sure to follow the use of the drills with children who have already attained the desired goal. Failure to determine the needs of children and to adjust individual work accordingly is one of the greatest factors operating to decrease the effectiveness of almost all the drill work found in common practice. The method of handling the class work also depends somewhat on the conditions within the class, and somewhat upon the individual preference of the teacher. Some like to have the class complete each group of lessons * Note that the time allowance for Test C is six minutes. ° Children who complete all the tests successfully but who are careless and inaccurate in their regular arithmetic work, should be put back into the drill class until they prove that they can transfer their skill to the regular work. TEACHER'S MANUAL. 13 as a unit. That is, no child works on any lesson beyond 13 until 90fo of the class or more have completed Lesson 13. Then Test B is given and the second group of lessons is carried through. This method divides into small groups the free time of the children who are excused from drill because of their ability. One after another escapes from the drill class until all have finished tiie first group of lessons, then all begin on the second group, and so on. Other teachers give Test A, then Test B to those eliminated by Test A, and Test C to those eliminated by Test B. Each child then starts to work directly upon the lesson corresponding to his needs. Under this method, however, when a child finishes the series he has no more work to do, so that if already of standard ability he may have one long unbroken period without drill or test. Under the first method, he would at least be tested once every two months and his free time broken into short periods. The author advises the first plan, and the instructions which follow are based upon it. When, however, most of the class would be excused from drill to wait for one or two children to complete the first group of lessons, it is better at once to adjust the work of the class to the group of lessons needed by the largest number of children. Each teacher must decide for himself the plan that best suits the needs of the class. Thursday Collect and return to the cabinet the cards for Lesson 13, then supply all the children not excused from drill with the card for Lesson 1. Give the test under standard conditions, have the children score their own papers and record their scores in their daily records.^ Note that if a child is absent, when he returns he is to record " ab " (absent) in the place of his scores. Some score is to be recorded by each child every day. This means that the record book of every child in the room should in- dicate at any time during the year just how many days the practice tests have been in use. If a child enters late, his score for his first lesson should be writ- ten opposite the day indicated by the books of the rest of the class. Children who are excused from drill should write "ex" for a score. If the drill period is omitted for any reason, have all the children write "om" for a score. These records are necessary to compare the efficiency of teaching under differ- ent conditions. It is evident that it is not right to compare results in a class having practice every day with one having practice but three times a week. Such records will make possibly comparisons on the basis of loo days' prac- tice, or any other equal interval. They are of the utmost importance in de- termining the character of the changes that need to be made to render the system still more efficient. When the work of scoring and recording has been completed, ask those who had perfect papers to stand. Collect their cards and papers, giving them in exchange cards for Lesson 2, which 14 STANDARD PRACTICE TESTS they should put into their pads in position ready for work the next day. Have them write "2" in the column headed "Lesson" in their Student's Record opposite Day 2, then put everything away ready for the drill the next day. Next have the children who missed on Lesson 1 stand. Tell them that their scores show that they need practice, and that on Friday they are to spend the drill period in study and practice on Lesson 1, and that the test on Monday will show how well they study. Have these children write '« 1 " opposite Day 2 in the col- umn headed "Lesson," and "pr" (practice) for their score, so that they will remember what they are to do. They, of course, retain the cards for Lesson 1. Teacher's Scoring Go over the perfect papers carefully. At first the children will score carelessly, leaving it to you to detect their mistakes. For the first week or so, therefore, rescore the papers carefully, but keep a record in your manual of each child who turns in a paper in which you find mistakes. Such children, of course, should study Lesson 1 instead of trying Lesson 2 on Friday, Put the names of such children on the board and for a day or two refuse to accept perfect papers from them until their scoring has been checked by other children. If you make it a disgrace to hand in an imperfectly scored paper, and if you keep a record of the children from whom such papers come, it will not be long before you will need to examine only the papers from certain children. After two weeks, the daily scoring and recording should not take more than ten minutes of your time. You should always remember that mistakes are likely to happen with any one. Even your own scoring will not be perfect. It is important only that you detect any cheating that may be attempted. It is very foolish painfully and tediously to rescore each day all the papers handed in. Such over-con- scientiousness is just as much to be criticized as a failure to detect dishonesty in the few children who are sure to try to deceive you. Therefore use judg- ment in scoring and do not waste time on such unprofitable work when it is not needed. In the same way, use judgment in the degree of perfection required for perfect papers. Do not have the same standard for all. If an indifferent child is finally induced to make a little effort, and turns in a paper poor in figures and neatness but perfect in results, accept it and give it the praise it deserves, waiting until the habit of effort has been well established before requiring perfection in the minor elements. On the other hand, set before the able children who lead the class the highest standards possible. In the same way, the standards at the end of a term should be higher than those at the beginning. TEACHER'S MANUAL 15 Teacher's Record Record each day in the record provided in this Manual the papers accepted as perfect, by putting the number of the trial in the proper space. This will keep the progress of the children in such form that you can tell instantly the condition of the class and of individual children. A glance at the illustration on this page will show the children who are progress- ing rapidly and those making little progress'. A similar glance at the record of any one child will tell the character of his work. For instance, a record of 15, 8, and 2 trials for Lessons 1, 5, and 8, respectively would mean that a child was making very satisfactory progress as the number of trials needed for each additional lesson was steadily decreasing, but a child whose record was five trials each for these three lessons would be doing little more than memorizing the answers. ^ TEACHER'S RECORD SHEET Name.. (2. 7t :%ytM/.... .School. KsLc-'I.'IjC.^'UH^ Grade ../T. Names of Children Score Number of Trials to complete saccessfalljr Lesson Score test A 1 a 3 4 6 6 7 S 9 10 11 12 test A 1 Q^-crA/yt ^O.'TnCtA 24- 3 2 2 3 3 / 2 / 2 2. / / 29 ^^bn^ /3y,..„w .^^^^^ ^.,^...„w ..^ ^„. j.j.u,,^, cuw 294 ^ child actually write out on paper the whole 46 — — — of the tens in which the divisor falls, as shown 45 i2t *" ^^^ illustration. He can then see that 49 is 44 ^^— nearer to fifty than forty and appreciate that 43 when the second figure of the divisor is larger 42 than five, he must use, not the first figure of 41 the divisor, but the next larger digit as the 40 trial divisor. If much practice in finding the nearest number does not help, have the child multiply 63 by each of the numbers from 40 to 60 and divide each product by the multiplier from which it came. If the child uses the first figure of the divisor as the trial divisor in all these cases, he will make mistakes in four or five cases. That is, his first trial quotient will not be the true quotient. The teacher must remember that the use of a trial divisor was originally the result of much experience, and the child without either experience or imagination will not appreciate readily the value of a device which eliminates many mistakes. The result will be a slow speed and the irritation which comes from making errors. Successful use of the proper trial divisor can easily be shown to "pay." Lesson 23. Subject, Addition Combination of Attention Span and Carrying See Lessons 19 and 20. Lesson 24. Subject, Subtraction See Lesson 2. Lesson 25. Subject, Multiplication . Practice with Longer Examples TEACHER'S MANUAL. 41 Lesson 26. Subject, Division Third Case, Where the First Figure of the Divisor Is the Trial Divisor, but the True Quotient Is One Smaller than the Trial Quotient The teacher's task here is to develop caution and judgment in the child. In this lesson, the method previously followed 89 produces incorrect results. The beginner is apt to feel that 63)5607 the selection of the true quotient is only guesswork, but the 504 teacher must lead him to see that the mere determination of ~S67 a trial quotient is not enough, that he must not proceed with 567 the work of division until he has' estimated at least the probable ^~-" effect of the second figure in the divisor upon the product. Gradually he will come to see that when the dividend is al- most an exact multiple of the first figure of the divisor, the true quotient will probably be one less than the trial quotient. In' a large number of such cases he will get the true quotient on the first trial, and the greater the number of successes the better his judgment. He will also be learning another lesson of great value, that there are situations in life in which it pays not to go ahead until the consequences of an action have been carefully determined. Lesson 27. Subject, Addition Practice with Larger Examples Unfortunately, when the number of examples is so few, the answers are soon learned. Have the child make up his own examples for practice, and alternate Form A and Form B for tests. Lesson 28. Subject, Multiplication Practice with Larger Examples Lesson 29. Subject, Division The Fourth Case, Where the First Figure of the Divisor Must Be Increased by One to Obtain a Trial Divisor, and the Second Trial Quotient Must Be Increased by One to Get the True Quotient 79 This case is, of course, very much like the last (Lesson 36') 2844 26), except that the difficulty comes in the second figure of the 252 quotient instead of the first. Judgment must be built up slowly ~^a in the same way as before. ^oa. 43 STANDARD PRACTICE TESTS Lessons 30, 31. Subject, Test B These two lessons form a single test, and only the children who are perfect in both tests, or have but a single example wrong in the two days' work, should be excused from drill on Lessons 14-29. The score in Test B is the sum of the scores for Lessons 30 and 31, not either score alone. The reason for the two tests is that the examples are so long that only a few can be done in three minutes. In a single test covering the four opera- tions, the result would 'be based upon so few examples of each operation that its reliability would be low. Even under the present arrangement, any child excused from drill because of success in this test, but inaccurate in daily work in arithmetic, should be put back into the drill class. Test B should be given again as a general test 48 days after the first trial. Be sure to compare the results of the second trial of this test with the first, and to record the same in the summary, on page 47 of the Teacher's Manual. Read again page 22. Following the second trial of Test B, give Test C, Lesson 44, Forms A and B, to determine the children who should be excused from drill on Lessons 32 to 43. Note that Test C measures endurance and calls for double the usual time allowance. In Grades 4, 5, and 6 only the exceptional child will reach the last group of lessons. It is expected that about T5% of the children will finish Lesson 31 in a half year. In the sixth, seventh, and eighth grades, therefore, more and more children will be excused from the earlier lessons, so that eventually 75 or 80% will finish all the lessons. However, do not expect this the first year the tests are used. If 30% finish all the lessons in the eightii grade the first year, the class is better than the average. Lesson 32. Subject, Addition Addition of Numbers of DiflFerent Lengths 14896 635 Difficulties in this lesson are likely to be wholly difficulties 74 of attention. Make sure the child understands that he is to add 380 merely the figures that appear in any one column, and show him 7492 how to follow up a column. Practice will do the rest 716 85 294 54957 TEACHER'S MANUAL 43 Lesson 33. Subject, Subtraction Practice with Long Examples Lesson 34. Subject, Multiplication Practice with Long Examples Lesson 35. Subject, Division Practice with Long Examples Lessons 36, 37, 38, 39. Subject, Endurance These examples are taken from the writer's Research Tests, Series B, Forms 1 and 2, and are the smallest examples that will measure all the com- ponent abilities that enter into each operation. They also measure endur- ance. It is not enough that a child be able to figure correctly for a short interval. He must be able to keep at it for some time. The time interval is accordingly doubled, and the confusion of scoring papers, etc., of the children who have not reached these tests is an added factor of difficulty. In business offices computations must be carried on in spite of noise, con- fusion, and interruption. Help the child to get the necessary poise and concentration in the busy classroom. Practice is the only remedy needed for failure. Forms 3 and 4 of the Research Tests Series B* are composed of entirely different examples of equal value, and are available to measure the results of the use of the Practical Tests, or for other research work. Lessons 40, 41, 42, 43. Subject, Copying The examples in these lessons are based upon the writer's Research Tests, Series A, Test 1. Measurement has proved the very great need for training in copying. The difficulties that arise, so far as is known, are due wholly to lack of concentration or attention. Lesson 44. Subject, Test C Allow six minutes for this test. This test measures endurance and copying in the four operations. In almost all commercial work records must be copied from slips to books, and from one book to another. Such copying calls for a peculiar kind of atten- tion, which may or may not be generated by the previous work. Every answer must not only be correct, but written in the correct space in the answer column. ' Yhese may be obtained from S. A. Courtis, 83 Eliot St., Detroit, Mich. 44 STANDARD PRACTICE TESTS The child who completes Test C successfully has no further need of drill work, except the incidental drill of daily use of computation in his arithmetic work. As with previous tests, be sure to keep on page 49 a record of your results on both the first and second trial of this test. Lessons 45, 46, 47, 48. Subject, Combinations in the Four Operations For use, see Lessons 1 to 4. Conclusion The foregoing lessons have been designed to cover every known diffi- culty in the development of ability in the four operations with whole num- bers. Unfortunately, the collection of such difficulties has been a recent activity, and the author will, therefore, welcome letters from teachers giving symptoms and remedies for difficulties that have not fallen within his teach- ing experience, that the series of lessons may be made more complete. For the same reason he will welcome results of tests, and summaries of the time required to complete the different groups of lessons, etc., that the same may be completely standardized. TEACHER'S RECORD SHEET Name... .SchooL Grade... Name of Children Score Number of Trialt to complete saccettfnlly Luson Score Test A 1 2 3 4 5 6 7 8 9 10 11 12 te.t A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 1 16 1 16 1 . 17 1 18 19 20 21 22 23 24 25 1 1 1 ;l 1 1 -- — — 26 1 1 27 28 29 SO 1 Forward 45 TEACHER'S RECORD SHEET (Continued) Name.. .School. Grade.. Name of Children Score Nnmber of Triali to complete laccetsfolly Lesson Score Te»t A 1 2 3 4 C 6 7 8 9 10 11 12 teit A 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 60 1 61 62 63 64 66 66 67 68 69 60 Forward 46 TEACHER'S RECORD SHEET (Continued) Name- ..School.. Grade.. Name of Children Nomber of Triali to complete racceiifally Leiion s Test B 14 15 16 17 18 1920 21 22 23 24 25 26 27 28 29 Test B 1 2 3 4 5 6 7 8 — 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 25 26 — 27 28 29 30 Forward 47 TEACHER'S RECORD SHEET (Continued) Name.. Schools Grade^ Name of Children 1 Number of Triali to complete ncccufnlly Le»on i CO Test B 14 16 16 17 181930 21 2223242626 27 2829 Test B 31 32 S3 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 61 52 53 54 55 56 67 68 1 59 1 60 1 Total 48 TEACHER'S RECORD SHEET (Continued) Name... JSchooL. Grade Name of Children Score Number o{ Trials to complete lacceitliilly Lesion Score Test C 32 33 34 35 36 37 38 3940 41 42 43 test c 1 3 - 3 4 5 6 7 8 9 ■ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Forward 49 TEACHER'S RECORD SHEET (Continued) Name„ JSchooL. Grade... Name of Children Score Number of Trials to complete sneceufnlly Leisoo Score Test C 32 33 34 35 36 37 38 39 40 41 42 43 teat C 31 32 33 34 35 36 37 38 39 40 41 42 - 43 44 45 46 47 48 49 50 61 ' ' 52 53 j 54 55 56 1 1 67 58 69 60 1 Total - Report of Test Teacher. School- Grade- Room- Date_ Form. 1st Trial 2d Trial Total number of children in class Number having perfect papers. Per cent having perfect papers Number missing but one example- Per cent missing but one example Number excused from Lessons Nos.. Per cent excused from Lessons Nos.. Efficiency. Efficiency Previous Trial. Gain, 51 SUMMARY-TIME COST Teacher To be filled out at end of term School Grade Number of Days No. Lessons Finished Names Tests Lnsoni Practice Excused Omitted or Abient Total 1 2 3 4 6 6 7 8 9 10 11 12 13 14 , 15 16 17 18 19 . 20 21 22 23 24 25 26 1 27 28 29 30 Forward 52 SUMMARY-TIME COST (Continued) Teacher... To be filled out at end of term School . Grade.. . Number of Days No. Lessons Finished Names Tests Lessons Practice Excused Omitted or Absent Total 31 32 33 34= ' 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 68 69 60 Totals Per cent of time saved. fDivide the total of the excused column by the sum of the totals of teste, lessons, prac- tice, and excused columns.) 53 54 STANDARD PRACTICE TESTS ANSWERS Lesson No. 13 Test A Lessons 1-12 Form A Add Subtraction 96 50 68 71 23 74 19 28 41 36 37 42 25 35 34 75 68 85 Multiplication 744 966 299 2982 1488 2397 19 21 13 Division 37 82 SMANUAL 55 ANSWERS Lecson No. 13 Test A Lessons 1-12 Form B Add Subtraction 58 61 78 49 16 94 33 84 37 24 40 35 29 37 47 96 50 47 Multiplication 399 672 559 1887 2788 2993 24 23 23 Division 42 62 56 STANDARD PRACTICE TESTS ANSWERS Lesson No. 30 Test B Part 1 Lessons 14-29 Addition Form A 4816 5767 6199 Form B 6119 4866 5797 Subtraction Form A 64879321 88225099 18115955 Form B 76884659 82657718 96538845 TEACHER'S MANUAL 57 ANSWERS Lesson No. 31 Test B Part II Lessons 14-29 Multiply Form A 579014 585354 Form B 741228 416698 Divide Fonii A 861 973 Form B , 971 862 58 STANDARD PRACTICE TESTS ANSWERS Lesson No. 44 Test C Lessons 32-43 Form B Double Time Fonn A 531813 9776756 5353488 6987 Form B 510157 7676759 75844608 7897 Contents Page Personal Note to Teachers 3 Ten Essential Points 3, 4 Section I General Description , 5 Program 6 Section II Detailed Instructions — Monday f Tuesday 7-11 Wednesday 11-13 Thursday 13-16 Friday 16 Monday 16, 17 Tuesday 17 Wednesday, Thursday, Friday 17, 18 Monday 18-30 Section III Diagnosis and Remedy of Individual Defects — Cheating 30, 31 Transfer 33 Efficiency 33 Types 33 Age 33 Temperament 33, 34 Physical Condition 34, 35 Mental Traits 25 Speed 36 Mental Deficiency 36, 37 Miscellaneous 37 Practice Lesson ] 37-39 3 39,30 3 30,31 4 31 5 31,33 6 33,33 " " 7 33 8 34 • " " 9 34 59 60 STANDARD PRACTICE TESTS Page Practice Lesson 10 34 11 35,36 13 36 13 36,37 U 37 15 37 16 38 17 38 18 38 19 38 20 38,39 21 39 23 40 23 40 24 40 25 40 26 41 27 41 28 41 29 41 30 43 31 42 33 42 33 43 34 43 35 43 36 43 37 43 38 43 39 43 40 43 41 43 43 43 43 43 44 43,44 45 44 46 44 47 44 48 44 Teacher's Records — Daily Record 45-50 Report of Tests 51 Summary 52, 53 Ind ex Addition Lessons — Lessons 1, 5, 8,12,16,20,23,37,32,36,40 Page 27, 31, 34, 36, 38, 38, 40, 41, 42, 43, 43 Alternative Methods 12 Answers — Lessons 9 Tests 54-58 Reading of 9 When correct 9 Attention Span 38 Austrian — Division 35 Subtraction 30 Borrowing — subtraction 29 Bridging Tens , 31 Carrying — Addition 36 Subtraction 29 Multiplication 32 Division 33 Cases in Division — I 38 II 40 III 41 IV 41 Combinations — Addition 27 Subtraction 39, 30 Multiplication 30, 31 Division 31 Copying , 43 Correction of Lessons — Children 9 Teacher 11 Detailed Instructions 7 Diagnosis of Defects 20 Difficulties 20 61 .63 STANDARD PRACTICE TESTS Division — Lessons 4, 7, 11, 15, 19, 33, 36, 39, 35, 39, 43 Pages 31, 33, 35, 37, 38, 40, 41, 41,^43, 43, 43 Efficiency 33 Elimination 11 Forms A and B , . 5 General Description 5 Graphs — Drawing of 18 Me^ming 19 Samples ^ 19 Use 30 Habits of Work- Addition 27-39 Subtraction 39, 30 Multiplication 33 Division 33 Home Study 16 Illustrations — Diagnosis 15-38 Division 35 Graphs 19 Records 15, 18 Immaturity 23 Instructions .* . 'i Judgment — In Rescoring ' 14. , In Standards 14' Measurement '.2, 7-11 Memory 25, 38 Mental Deficiency 26 Mental Traits 25 Multiplication — Lessons 3, 6, 10, 14, 18, 31, 25, 38, 34, 38, 43 .' Page 30, 33, 34, 37, 38, 39, 40^ 41, 43, 43, 43 Nervousness , 24 Periods of Growth .24 TEACHER'S MANUAL ^ Physical Condition 24 Practice . .^ 16, 38 Precocious Children 33 Process — Addition 27 Subtraction 29 Multiplication 30 Division 31 Program 6 Records — Children 18 Teachers 15, 45-50 Reliability of Results 10 Reports of Tests 51 Research Tests 43 Retarded Children 23 Sample Records — Graphs 19 Scoring — Children 10 Speed 36 Subtraction — Lesson 2, 9, 17, 24, 33, 37, .41 Page 29, 34,> 38, 40, 43, 43, 43 Summary , 52, 53 Teacher's Record — ' Scoring , 14, 15, 45-50 Reaching — Graphs , 19 How to Study 16 Temperament |3 Tests A 6,7-10, 36 Tests B : 6, 12, 43 ■ Tests C . . .-. 6, 12, 43 Time Allowances 9 Transfer 32 Types 33 Warnings •. 12 Courtis Standard Practice Tests IN THE FOUR OPERATIONS WITH WHOLE NUMBERS Sheet-Package Edition PRACTICE TESTS Two series — Form A and Form B — of 48 lesson sheets in packages, each package con- taining 150 copies of one lesson. Each form covers the same growid and is designed to provide greater variety of practice than is afforded by a single series. FORM A — A series of 48 lesson sheets in packages, each package containing 150 copies of one lesson. Sold only in sets. Price, per set of 48 packages, net $8.64. FORM B — A series of 48 lesson sheets in packages, each package containing 150 copies of one lesson. Sold only in sets.. Price, per set of 48 packages, net $8.64. STUDENT'S RECORD A pamphlet containing daily record sheets and graph sheets for recording the tests, to- gether with instructions for using. Price, per package of 50 pamphlets, net $1.00. TEACHER'S MANUAL A 64-page pamphlet containing all the nec- essary instructions for the proper use of the material. Price, net 30 cents. TEACHER'S RECORD Pages 45-53 inclusive of Teacher's Manual. Price, net 5 cents. SPECIMEN SET— I Teacher's Manual, I Student's Record, [ copy of each lesson sheet in both Forms A and B — 96 sheets. Price, net 50 cents, postpaid. Card-Envelope Edition PRACTICE TESTS Two series — Form A and Form B — of 48 lesson cards, one envelope containing one card of each lesson. Each form covers the same ground and is designed to provide greater variety of practice than is afforded by a single series. FORM A — Envelope of 48 cards. Price, net 30 cents. FORM B — Envelope of 48 cards. Price, net 30 cents. STUDENT'S RECORD AND PRAC- TICE PAD A tablet containing (i) daily record sheets and graph sheets for recording the 48 tests, together with instructions for using them, and (2) tissue sheets upon which the prob- lems are worked. Price, net 10 cents. TEACHER'S MANUAL ^ A 64-page pamphlet containing all the neces- sary instructions for the proper use of the material. Price, net 30 cents. TEACHER'S RECORD Pages 45-53 inclusive of Teacher's Manual. Price, net 5 cents. SPECIMEN SET — I Teacher's Manual, I Student's Record and Practice Pad, and I envelope of both Forms A and B. Price, net $1.00, postpaid. Card-Cabinet Edition CABINET I — For a class of so pupUs. 720 cards in cabinets, with 48 separators, or guide cards. Sold only by the cabinet. Price, net $6.00. CABINET II — For a class of zo puinls. 288 cards in cabinets, with 48 separators, or gtiide cards. Sold only by the cabinet. Price, net $3.60. STUDENT'S RECORD AND PRACTICE PAD— The same as for the Card-Envelope Edition. Price, net 10 cents. TEACHER'S MANUAL — A 64-page booklet containing all the necessary instructions for the proper use of the material. Price, net 30 cents. TEACHER'S RECORD — Pages 45-53 inclusive of Teacher's Manual. Price, net 5 cents. SPECIMEN SET — The same as for the Card-Envelope Edition. See above. WORLD BOOK COMPANY, PUBLISHERS YONKERS-ON-HUDSON, NEW YORK CHICAGO ATLANTA DALLAS MANILA Vi-V't - ^v'^'A^^m ■;n.