# The effects of the use of adding machines on the arithmetical ability of bookkeeping students

код для вставкиСкачатьTHE EFFECTS OF THE USE OF ADDING MACHINES ON THE ARITHMETICAL ABILITY OF BOOKKEEPING STUDENTS A Thesis Presented to the Faculty of the School of Education The University of Southern California In Partial Fulfillment of the Requirements for the Degree Master of Science in Education by Jay Wilson Cummings June 1941 UMI Number: EP53994 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation PWisMng UMI EP53994 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 O T h is thesis, w r it t e n u n d e r the d ir e c t io n o f th e ^ J j^ J ? , C h a ir m a n o f the candidate*s G u id a n c e C o m m itte e a n d a p p r o v e d by a l l m em bers o f the C o m m itte e , has been p resen ted to a n d accepted by the F a c u lt y o f the S c h o o l o f E d u c a t io n in p a r t i a l f u l f i l l m e n t o f the re q u ire m e n ts f o r the degree o f M a s t e r o f Science in E d u c a tio n . Datel^..h...l^. ......... Guidance Com m ittee E. G. Blackstone Chairm an P. J. Weersing Irving R. Melbo TABLE OF CONTENTS XxE THE PROBLEM . . . ..................... ". . The problem Minor problems . .. ....... 11 ............. 2 REVIEW OF RELATED STUDIES.................. 3 Social uses of arithmetic ................ 4 . Business arithmetic textbooks ............. 5 A study of everyday uses of arithmetic . .. 6 Mathematical requirements of commercial .. 7 . .. 8 positions open to high school graduates Summary of reviews of related studies THE METHOD OF PROCEDURE.................... Preliminary situation . .. 10 10 Period of time of the study.............. 11 Procedure of the study 11 .................. Testing materials rev i ew e d . .. 13 .............. 16 Results of the arithmetic tests . . . . . . . 16 Results of the bookkeeping tests 16 COMPARISON OF TESTING SCORES ......... Comparison of scores in arithmetic and bookkeeping ........................... 17 Explanation of tables .................. 17 Comparison of arithmetic and bookkeeping groups with their I.Q,. scores . . . . . . . 23 iii CHAPTER PAGE V.DIVISION OF CLASS GROUPS . . . . . . . . . . . . Based on arithmetic scores........ Based on I.Q,. scores 26 ............. Based on bookkeeping s c o r e s ...... Summary of class grouping ..... 26 30 ....... VI.. TESTING RESULTS AFTER SIX MONTHS.... Arithmetic testing 26 33 38 .......... 38 Class using adding machines, . ........... 38 * Class not using adding machines ....... 47 Bookkeeping progress comparisons . . . . . . . 51 Arithmetical progress of class using machines 48 Arithmetical progress of class not using machines .................. Summary. ....... 48 ........................... 54 ........... 55 VII. SUMMARY AND CONCLUSIONS Summary .............. Conclusions ....................... 55 55 Recommendations.......................... .56 BIBLIOGRAPHY .............. 57 LIST OF TABLES TABLE PAGE I. Arithmetic Scores Before Class Division . . . . 18 II. Distribution of Arithmetic Scores . . . . . . . 19 III. Bookkeeping Scores Before Class Division ... IY. Distribution of Bookkeeping S c o r e s ... Y. I.Q,. Scores of Students of Bookkeeping gi g'g .... £4 VI. Distribution of I.Q,. Scores......... ....... £5 VII. Class Division Based on Arithmetic Scores . . . £7 VIII. Class Division'Based on I.Q. Scores.... IE. . Class Division Based on BookkeepingScores X. Arithmetic Scores After Six M o n t h s ... 51 . . 3.4 37 XI. Distribution of Arithmetic Scores After Six Months ......................... .. XII. Arithmetic Scores After Six Months of Assigned to Use Machines . Class ............. XIII. Arithmetic Scores After Six Months of Assigned Not to Use Machines . 39 40 Class ......... 4£ XIY. Comparison of Arithmetic Scores After Six Months Class Assigned to Use M a c h i n e s.... 44 XY. Comparison of Arithmetic Scores After Six Months Class Assigned Not to Use Machines ..... 45 XYI. Summary of Comparison of Arithmetic Scores After Six Months ......... 46 V TABLE PA® XVII. Composite of Scores Arithmetic and Bookkeeping of Class Assigned to Use Machines . .. . . .. . 4-9 XVIII. Composite of Scores Arithmetic and Bookkeeping of Class Assigned Not to Use Machines . . . . XIX* Bookkeeping Scores After Six' Months . . . . . . 50 52 XX. Distribution of Bookkeeping Scores After Six Months ’............ . 53 CHAPTER I THE PROBLEM It is a controversial question whether the free use of adding or calculating machines by students of bookkeeping tends to increase their arithmetical ability more than a strict adherence to mental solutions of arithmetical problems. Some teachers contend that the free use of adding machines increases arithmetical ability of bookkeeping stu dents because the mind is greatly relieved of the mental effort during calculations, being concerned only with the outline of the process necessary for solution of-the problem. They think that the mechanical operation of the machine be comes largely a habit and does not interfere with the problem solving activities of the mind, and when the process of solution has been decided, concentration can be made upon the mechanics of machine operation and thus assure a correct solution. Other teachers think that the use of the adding machine acts as a distractor to the mental processes. Too much attention is taken away from problem solution in order properly to manipulate the machine. Or, unless each book keeping student.is equipped with an individual machine at his own desk, the student’s attention is diverted when he walks across the room to a machine. Unless a large number of machines are available, students will waste their time wait ing for their.turns to use a machine. • With the possible exception of long problems in addition, as when taking a trial balance, most of the prob lems in arithmetic found in the. bookkeeping course are not very long or involved. However, there are many problems in volving both common and decimal fractions, percentage, and discount in addition to problems in addition, subtraction, multiplication and division. Many of the problems involve two or more different processes for their solution whether a machine is used or the student must rely upon his own mental ability for speed and accuracy of solution. . The major problem is whether the use of an adding machine increases the arithmetical ability of the bookkeeping student more than a strict dependence upon his own mental ability. Some minor points which the experiment might reveal would be (1) whether the use of machines helped to increase bookkeeping efficiency by requiring less time for completion of exercises, and (2) whether the use of the machines tended to increase the bookkeeping abilities of the class and be revealed by a higher average of scores in the regular book keeping tests. CHAPTER II REVIEW OF RELATED STUDIES Studies have been made to determine the arithmetical needs of individuals employed as office workers in many dif ferent kinds of business such as insurance, manufacturing, retail store clerks, salesmen of different, commodities; the arithmetical needs of skilled and semiskilled trade workers; and the arithmetical needs of housewives and home owners* Each of these studies has shown that the arithmetic textbook writers have shown little concern about the needs of in dividuals* They continue to fill their books with a great mass of material that never will be needed by the average individual. Because so much of the student’s time is consumed in gathering some familiarity about many topics, not enough time is permitted to make them really proficient in those arithmetical skills most needed in life’s occupations* The great majority of teachers of arithmetic are not aware of the degrees of skill attained, nor do they know what learning difficulties are present that prevent the student from attaining satisfactory skills* Usually, arithmetical skill deficiency is not discov ered until employment is secured, or until the individual realizes later in his life activities when he suffers an 4 economic loss or is compelled to seek the help of others. Guy M. Wilson^ found from his study of social uses of arithmetic that the textbooks are burdened with nonessential problem material* From his survey, he found forty-three types of arithmetical processes used. But from his analysis it was learned that only six types of problems were needed by 90 per cent of the cases interviewed. These six processes that were the only needs of 90 per cent of the individuals, in the order of use frequency, are: 1. Multiplication (whole numbers) 2. Addition (whole numbers) 5. Subtraction (whole numbers) 4. Division' 5. Fractions 6. Accounts A seventh process, percentage, would have added S per cent to the usage total. None of the other thirty-six processes were used by as much as 1 per cent of the group. A. 0. Bowden2 found from his 1929 study that the ^ Guy M. Wilson, A Survey of the Social and Business Usage of Arithmetic (Teachers College Contributions to Education, No. 100. New York: Teachers College, Columbia University, 1919) , p. 35. 2 A. 0. Bowden, Consumers Uses of Arithmetic; an In vestigation to Determine the Actual Uses Made of Arithmetic in Adult Social Life, Exclusive of Vocational Uses (Teachers College,Contributions to Education, No. 340. New York: Teachers College, Columbia University, 1929), 69 pp. arithmetic textbooks contained 85 per cent more problem process material than would be needed♦ He found that 60 per cent of the individuals in his study never used more than the first four fundamental operations as named by Guy M. Wilson.3 A study of "Business Arithmetic Textbooks," by 1. R. Bassett4 reveals that the schools are not teaching arithme tic in harmony with the needs of business* The schools con tinue to use textbooks that are written without regard to the needs of business workers* He cites several well-known authorities, including Cameron Beck, 5 Personnel Director of the New York Stock Exchange; Earl W. Kempton,^ Educational Director of the American Steel and Wire Company, Cleveland, 7 Ohio; Ira W* Kibby, Director of Business Education, State Board of Education of California; Dr* F. I* Weersing,8 School of Education, The University of Southern California, Los Angeles, California. 3 Wilson, op. clt*, p. 35. 4 E. R. Bassett, "Business Arithmetic Textbooks," (unpublished Master’s thesis, The University of Southern California, Los Angeles, 1934), pp. 15-32. ^ Ibid., p. 15. ° boc. clt. 7 boc. cit. 8 Ibid., p. 23* 6 A survey of the arithmetic used by workers in busi ness occupations in California^ made by the California Bureau of Business Education caused them to come to the con clusion that the secondary schools should offer remedial work in arithmetic, A study of the essential everyday uses of arithmetic made by Katherine Spiers,^ included the following topics in the order given; 1. Cash accounts, children and family expense. 2. Addition, including fractions. 3. Checks and paying bills. 4. Multiplication of fractions*. 5. Subtraction of fractions. 6. Banking operations In-this same study, it was learned that the essentials required in arithmetical knowledge 1. Addition (whole numbers) byemployingfirms were: 100 per cent of firms 2. Multiplication (whole numbers) 98 per cent of firms 3. Division (whole numbers) 92 per cent of firms 9 "Arithmetic Used by Workers in Business Occupations,” (unpublished survey of the California Bureau of Business Education, Sacramento, California, November, 1931), 4 pp. 10 Katherine Spiers, ,fA Study of Eliminations, Inclu sions, and Social and Business Requirements of Arithmetic,” (unpublished Master's thesis, University of California, Berkeley, California, 1921), pp. 87-96. 7 4. Subtraction (whole numbers) 88 per cent of firms 5. Decimals 82 per cent of firms 6. Fractions 78 per cent of firms 7. Percentage 62 per cent of firms Lucien Blair Kinney11 found in his study of 828 inter views representing 4,812 workers that the calculating machine enters into the daily use of a considerable percentage of clerical workers. It appears that machines are used extensively by clerical workers who perform operations with whole numbers. Most of those who use an adding machine, how ever, use it for only a part of their calculations. In the other calculations with whole numbers, the pro portion of clerical workers who use a machine occasion ally is small. This may be due to the fact that it is quicker for one who is not accustomed to a machine to subtract, multiply, or divide without a machine than to use one. This is not the case with a long column of addition. The number of clerical workers who have no occasion to use decimal fractions is much greater than the pro portion who have no occasion to perform the operations in whole numbers. About one-third of those who use decimals, perform the operations entirely on the machine. This proportion is much greater than in whole numbers. The reason is that common fractions cannot be handled on a calculating machine and have to be converted into decimals. Kinney goes on to say that the fractions that most frequently occurred in business were mainly fractions of Lucien Blair Kinney, "The Mathematical Requirements of Commercial Positions Open to High School Commercial Graduates," (unpublished Doctor’s dissertation, The University of Minnesota, 1931 reprint loaned by the University of Minnesota). pounds, yards, feet, dozens, or gross* Consequently, it was found that the fractions 1/2, 1/3, 1/4, 1/6, and 1/8 consti tuted 93*6 per cent of those that were used. Summary of reviews of related studies. Studies that have been made of the arithmetical needs of individuals em ployed as office workers in many kinds of business, of salesmen of different commodities, skilled and semiskilled trade workers, and the needs of housewives and home owners show that the writers of arithmetic textbooks have shown little concern about the needs of individuals. They continue to fill their books with a great mass of material that never will be needed by the average individual. Usually, arithmetical skill deficiency is not discov ered until employment is secured, or until the individual realizes later in his life activities when he suffers an economic loss or is compelled to seek the help of others. Guy M. Wilson found from his study of social uses of arithmetic that the textbooks are burdened with nonessential problem material. He found forty-three types of arithmetical processes used, but his analysis revealed that only six types of problems were needed by 90 per cent of the cases inter viewed. A. 0. Bowden found from his 1929 study that the arithmetic textbooks contained 85 per cent more problem 9 material than would be needed* He found that 60 per cent of the individuals in his study never used more than the first four fundamental operations as named by Guy M* Wilson* S* R. Bassett made a study of "Business Arithmetic Textbooks," which reveals that the schools are not teaching arithmetic in harmony with the needs of business* He cites several well-known authorities who confirm his findings* A survey of the arithmetic used by workers in the business occupations in California was made by the California Bureau of Business Education. They came to the conclusion that the secondary schools should offer remedial work in arithmetic* Lucien Blair Kinney found in his study of 822 inter views representing 4,812 workers that the calculating machine enters into the daily use of a considerable percentage of clerical workers. He also found that the fractions that most frequently occurred in business were 1/2, 1/3, 1/4, 1/6, and 1/8, constituting 93*6 per cent of those that were used. CHAPTER III THE METHOD OF PROCEDURE Preliminary situation. In order to obtain two classes in bookkeeping as nearly identical in- ability as possible, a series of tests in arithmetic and in bookkeeping were given to forty students of bookkeeping. student was obtained. Also, the I.Q.’s of each These forty bookkeeping students were divided into two classes, one of which was provided with.one adding machine for each two students; the other class was denied the use of any mechanical aid during the period of the experiment. Each class was taught by the same teacher. The class periods were the same in length of time, and both classes were scheduled during the afternoon of the school day. Each bookkeeping class numbered twenty students at the beginning of the experiment, but due to dropouts and transfers, the number was two or three less at the end of the six-month interval. The classes were made up of tenth grade and eleventh grade students, as equally divided as was possible from the results of the arithmetic tests, the bookkeeping tests, and their I.Q,. scores. The experiment was conducted at the Orange Union High School, Orange, California. The machines provided for the use of the group of 11 students assigned to mechanical aids for their arithmetical problems incidental to their bookkeeping work were: 2 Sundstrand adding machines - 10-key type 2 Victor adding machines - 9-bank type 2 Monroe calculating machines - crank driven type 2 Comptometers - key driven type 2 Burroughs bookkeeping machines set for addition- subtraction 10 machines - one for each two students Period of time* The experiment extended over a period of six months of the school year* During this interval, one bookkeeping class was denied the use of any mechanical aid for their related arithmetic. The other bookkeeping class was encouraged to use mechanical aid whenever possible. The individuals were given personal instructions on the operation of each type of machine, and additional help was-given when ever needed. No arithmetical instruction was given to the other bookkeeping class, except to explain interest calcula tions. Procedure. Early in October, the tests in arithmetic and mental ability were given. Five bookkeeping tests were given on bookkeeping theory as the classes progressed in their beginning work. The arithmetic tests were Schorling-Clark- 12 Potter.*1* The 1.^. test was the Terman Group Test of Mental Ability.2 From the results of the arithmetic tests, see Table VII, page 27, two classes were arranged with each group con taining students matched with equal scores. This preliminary grouping was compared with a grouping resulting from their bookkeeping scores. grouping. The comparison revealed a very accurate The standard error of means was 2.4, and the standard difference of error of means was only 3.95, which reveals a high degree of accuracy in grouping based on either the arithmetic scores or the bookkeeping scores. When the I.Q. of each student in the two groups was matched and a frequency table was constructed, it was again found that the comparison revealed a very accurate grouping. The standard error of means was 2.08, and the standard dif ference of error of means was only 3.75. As nearly as was possible, an equal number of tenth and eleventh grade students were placed in each group. This was done so as to have the two classes divided as nearly . equal as possible based upon their physical ages. 1 Schorling-CIark-Potter Arithmetic Test, Form A (The World Book Company, Yonkers-on-Hudson, New York). 2 -Terman Group Test of Mental Ability, Grades Seven to Twelve (The World Book Company, Yonkers-on-Hudson, New York). 15 One class was given access to the ten machines previously mentioned and was encouraged to use them whenever an opportunity was provided in the solution of arithmetical problems presented itself in their bookkeeping work* The majority of problems were in addition, multiplication and subtraction of whole numbers, or in dollars and cents. The second class was denied the use of any mechanical aid and all arithmetical problems were solved at their desks. Testing materials reviewed. The test in arithmetic used in this study was the Schorling-Clark-Potter Arithmetic Test, published by The ?/orld Book Company. The authors are Raleigh Schorling, John R. Clark and Mary A Potter. made up of two tests, Form A and Form B. upon 3,545 cases. It is Norms are based The reliability coefficient between the two forms for a single grade is .85. It consists of six sections: 1. Addition 10 problems 2. Subtraction 10 problems 5. Multiplication 17 problems 4. Division 16 problems 5. Fractions, Decimals Per cents 37 problems 6. General list Total 10 problems 100 problems 14 The first four sections of these tests include examples in integers, fractions, decimals, and denominate numbers. The general list includes problems on averages, ratio and pro portion, interest, and discount (sales discount). The New Stanford Arithmetic Test (for ninth grade). The authors are Truman L.. Kelley, Giles M. Euch, and Lewis M. Terman. It is made up of four tests, Forms V, W, X, Y. The World Book Company is the publisher. Otis Arithmetic Reasoning Test. The author is Arthur S. Otis. It is composed of•two tests, Form A and Form B. It is for grades four to twelve. The World Book Company is the publisher. ! Objective Tests in Business Mathematics. The author is R. Robert Rosenberg. It consists of a series of six achievement tests in business mathematics. Gregg Publishing Company offers this test. Progressive Achievement Tests. The authors are E. W. Tiegs and W. W. Clark. Test 3 is on Mathematical Reasoning, Test 4 is on Mathematical Fundamentals. and Form B. It comes in Form'A California School Book Depository is the pub lisher. Terman Group Test of Mental Ability. The author is Lewis M. Terman. This test is for determination of I.Q. and Mental Age for grades seven to twelve. Company is the publisher. The World Book 15 Bookkeeping Tests. The author is Paul L. Carlson. Portions of his tests were used for the testing of each chapter of the "bookkeeping text. -South-Western Publishing Company publishes this testing series. The tests given at the beginning of this experiment were Schorling-Clark-Potter Arithmetic Tests, Form A, the Terman Group Test of Mental Ability for I.Q,. scores, and a series of five chapter tests in bookkeeping theory taken from Paul L. Carlson’s Bookkeeping Tests written for the SouthWestern Publishing Company. Results of these tests showed a high degree of correlation as a basis for division of book keeping students into two class groups. At the end of a six-month period, Form B of ShorlingClark-Potter Arithmetic Tests was given, and bookkeeping theory tests from the same source were used. CHAPTER' IY COMPARISON OF SCORES The comparison of the scores made at the beginning of this experiment in arithmetic and in bookkeeping reveal no appreciable difference in the mean or the median scores. Results of the arithmetic tests. The Schorling-ClarkPotter Arithmetic Test, Form A, given to forty students in two bookkeeping classes early in October, revealed some very important facts as shown in Table I, page 20. From a pos sible score of one hundred, the student scores ranged down ward from ninety-three to nine. The mean was a score of 54.6; the median was a score of fifty-one. An extremely wide range of arithmetical ability was revealed by this test. There were many students who made errors in problems involving addition, subtraction, multiplication and division of integers. However, the greatest number of errors occurred in the problems involving fractions, decimals and percentage. Many papers did not show one correct answer to these types of problems. Results of the bookkeeping tests. Five tests were given covering the progress of each student in bookkeeping theory. From the cumulative totals, a distribution of scores revealed a range from 106 downward to forty-three. (Table Ill, page 21). The mean was a score of 75.8 and the median score was 72.3. (Table IY, page 22). Comparison of scores in arithmetic and bookkeeping. Computations revealed a standard error of means of 2.4. standard error of difference of means was 3.93. The This shows that no appreciable difference existed between the ability of students in arithmetic and their ability in bookkeeping as a group. From these results it was not a difficult task to assign students into two class groups so as to have each group have an equal range of ability in both arithmetic and bookkeeping. These scores were compared with those made by the same group of students at the end of the six-month interval to determine the general progress in bookkeeping ability. The results of bookkeeping progress is then compared with the progress in arithmetical ability. Explanation of tables. 1. Schorling-Clark-Potter Arithmetic Test, Form A. This was the test first given to the entire group of forty bookkeeping students before a division was made into two class groups. Previous to this time, the two classes had received identical instruction in bookkeeping theory by the same instructor during two afternoon periods. 18 TABLE I 'ARITHMETIC SCORES BEFORE CLASS DIVISION Possible score 100 99 98 97 96 95 94 93 92 91 •90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 Number of students 1 2 1 1 1 2 2 1 Possible score 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 '28 27 26 25 24 23 22 21 20 Number of students 1 1 2 1 1 1 1 2 1 1 2 1 1 1 1 2 2 2 2 2 10 9 1 19 table ii DISTRIBUTION 03? ARITHMETIC SCORES Number of students 10 9 8 7 6 5 4 3 3 2 1 1 0 Score range to rH 1 OS 03 1 O rH Score 02 to O CD sjt -sj* 1 I 1 02 to to lO 89-96 81-88 73-80 65-72 57-64 49-56 41-48 33-40 25-32 17-24 9-16 H to to cO 02 o O CD I I o (D CD 1 1 1 rH o> to to to E> CD to o> 1 o> CD 1 students 3 1 6 6 4 6 5 3. 4 1 Mean score Median score 54,6 51 so The median arithmetic score was found to he fiftyone. The mean was 51.4, with a standard deviation of 20.8. Further calculations revealed a probable error of 3.IS. 2. Bookkeeping tests. Five objective tests in bookkeeping theory were com piled by the selection of material from tests by Paul L. Carlson,^ so that a test could be given for each chapter of the text in bookkeeping that was studied before the time the students were' divided into t?/o class groups. The textbook used was Twentieth Century Bookkeeping and Accounting, 17th Edition, by Baker, Prickett and Carlson, published by South-Western Publishing Company. The range of scores shown on page 22 show a high of 106 and downward to a score of forty-three. These scores are shown in distribution table, Table II, on page 19-. median bookkeeping score was 72.34. The The mean score was 75.8 with a standard deviation of 16.08 scores. Further calcula tions reveal a standard error of mean to be 2.4. The stand ard error of difference between the arithmetic test and the bookkeeping test was found to be 3.93. This indicates no significant difference between the two means. 2 ^ Paul L. Carlson, Bookkeeping Tests for the SouthWestern Publishing Company, Cincinnati, Ohio. 2 Ernest W. Tiegs, Tests and Measurements in the Improvement of Learning (lie?/ York: Houghton Mifflin Company, 1939) ,' p7 368. TABLE III BOOKKEEPING SCORES BEFORE CLASS DIVISION Possiblescore 110 109 108 107 106 105 104 103 102 101 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 Number of students 1 1 1 2 1 2 2 1 1 1 1 3 1 2 3 Possible score 69 68 67 66 66 64 63 62 61 60 59 58 57 56 55 54 53. 52 51. 50. 49. 48. 47 46 45, 44 43'. .42. 41 40, 39 38 37 36 35, 34 33 32 31 30. Number of students 1 2 2 1 1 1 1 1 1 2 1 1 1 • 1 TABLE IY DISTRIBUTION OF BOOKKEEPING SCORES Number of students 10 9 8 8 7 6 5 4 3 3 2 1 1 0 Score range GO 1 CO sH in i as o to i to i W IN 1 IN m tO tO cO in ■. H GO IN 1 CO IN CO 1 a> IN o CQ os Os o GO o i 1 rH rH 1 rH in GO tO as CN a> t CO o rH 103-108 97-102 91-96 85-90 79-84 73-78 67-72 61-66 55-60 49-54 43-48 3 3 2 3 2 5 6 8, 5 2 1 Mean 75.8 Median 72.3 Standard error of means 2.4 23 3* Terman Group Test of Mental Ability* Testing of the fortjr members of the two bookkeeping classes disclosed an I.Q. score ranging from 1*29 downward to .71* This represents.a very heterogenous grpup of mental abilities for any group that is to receive the same instruc tions in any subject. This wide range of ability made a rather poor class for such exacting efforts as is necessary in arithmetic and in bookkeeping. However, it made it easy to divide the pupils into two groups of about equal range of abilities. The number of students of the different I.Q. scores, is found on page 24. Table VI, on page 25, shows the dis tribution of I.Q.- scores on a frequency table. The median score was found to be an I.Q,. of 102.75, higher than a normal average of a class group. However, the median score in the arithmetic test was found to be 51.4, or 3 per cent above the actual midpoint of the one hundred prob lems in the test. The mean I.$. score was 103.5, with a standard deviation of 13.9 scores. mean was found to be 2.08. The standard error of A comparison with the results of the arithmetic test revealed a standard error of difference of means of only 3.75. A comparison with the results of the bookkeeping test revealed a standard error of difference of means of only 3.17. TABLE V I.Q. SCORES OF STUDENTS OF BOOKKEEPING Score 1.30 1.29 1 •SB 1.27 1.26 1.25 1.24 1.23 1.21 1.20 1.19 1.18 1.17 1.16 1.15 1.14 1.13 1.12 1.11 1.10 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 1.00 0QQ %t%/ .98 .97 .96 .95 .94 .93 .92 .91 .90 .89 •88 .87 .86 Number of students 2 1 1 1 2 1' I 1 1 1 1 1 1 1 1 2 1. 1 1 1 1^ 2 1 1; 1 1 3 2 2 Score .85 .84 .83 . •82 .81 .80 .79" .78 .77 .76 .75 .74 .73. .72 .71 .70 Number of students 25 TABLE VI DISTRIBUTION OF MENTAL ABILITY SCORES (I.Q,.) Number* of students 10 9 8 7 6 5 4 3 2 1 1 1 0 Score range CO o1 cti <o CO o1 co CO 1 a» C" CO CO i 00 CO CO I CO co CO CO i CO o rH 1 o> o> CO o rH 1 o rH 129-133 124-128 119-123 114-118 109-113 104-108 99-103 94-98 89-93 84-88 79-83 74-78 69-73 2 students 2 1 5 45 4 57 3 1 0 1 to rH rH I o> CO rH rH 1 rH rH rH o CO CV2 rH I o> rH i— 1 Mean 103.5 Median 102.75 Standard error of Means 2.08 00 <ra rH I nH C\2 rH CO CO rH 1 CJ» oa rH CHAPTER V DIVISION OF CLASS GROUPS Based on arithmetic scores. Because it was the pur pose of this problem to determine the effect upon the arithmetical ability of bookkeeping students who used, or did not use adding machines, ..a division of a group of bookkeeping students into two class groups was first based upon the re sults of a test of arithmetical ability. After the division was made upon this basis, the two groups were compared by tests in bookkeeping ability, and by a comparison of their I.Q,. scores. Each of these comparisons were found to be in harmony with the first division made from the arithmetic test. The results of this test in arithmetic is shown on page 18, with scores ranging downward from ninety-three to nine out of a possible one hundred score. Starting at the top of this list, an attempt was made to place an equal number in each group of as nearly equal ability as was pos sible, yet keep the mean score of each group at the same point. This helped to create a favorable attitude from the students. There were students of equal abilities together in each class. No one felt that he had been placed in a class arbitrarily. Based on I.£. scores. The list of I.Q. scores for the forty bookkeeping students is shown on page £4. The 27 TABLE 711 CLASS DIVISION BASED ON ARITHMETIC SCORES Possible score Assigned to use machines 100 99 98 97 96 95 94 93 92 91 90 89 Assigned not to use machines * ' 93 88 87 86 85 84 83 82 81 • 80 79 78 77 76 75 74 73 72 71 70 69 86,86 83 78 72 69 68 67 66 67,67 69 28 TABLE VII (CONTINUED) CLASS DIVISION BASED ON ARITHMETIC SCORES Possible score 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51. 50 49 48 47 46 45 44' 43 Assigned to use machines Assigned not .to use machines 65 60 - 59,59 61,61 60 55 53 50 50 48 45 44 43 4.9 41 40 39 38 37 ' 36 35 34 33 32 31 41 41 39 38 35 35 34 29 TABLE VII (CONTINUED) CLASS DIVISION BASED ON ARITHMETIC SCORES Possible score SO 29 28 27 26 25 24 23 Assigned to use machines Assigned . not to use machines 29 28 26 22 21 21 21 20 20 20 19 18 17 16 15 14 13 12 11 10 9 9 8 7 6 5 4 3 2. 1 20 students 20 students 30 scores range downward from 1.29 to .71. Starting at the top of the two groups just shown, the I.Q,. scores were matched and the resulting group of scores were compared with those of arithmetic grouping and found to "be very accurate. Based on bookkeeping scores. The list of bookkeeping scores for the forty bookkeeping students is shown on page 18. The scores range downward from 106 to forty-three. These scores were matched with the names as previously divided into the two groups. Comparisons made with the arithmetical ability and the I.Q,. scores found the division very satisfactory from the viewpoint of bookkeeping ability. Summary of test grouping. The first division of the forty bookkeeping students was made from, the resulting scores from the arithmetic tests. After the bookkeeping scores were determined and the individual scores placed opposite the names of students in each group, it was found that the groups were very nearly equally divided. In other words, if the division of students into two groups had been first made upon the basis of their bookkeeping scores, it would have compared very favorably with the results of the arithmetic scores. As a further approval of grouping, the I.Q,. scores were matched with the names of the students in the two groups. The distribution of I.Q,. scores (see Table VIII, pages 31-32) revealed that the grouping was equally 31 TABLE VIII CLASS DIVISION BASED ON I.ft. SCOPES Possible score 1*30 1.29 1.28 1.27 1.86 1.25 1.24 1.23 1.22 1.21 1.20 1.19 1.18 1.17 1.16 1.15 1.14 1.13 1.12 1.11 1.10 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 1.00 .99 .98 Assigned to use machines 1.29 Assigned not to use' machines 1.29 1.26 1.25 1.21 1.18 1.18 1.17 1.16 1.14 1.13 1.11 1.10 1.09 1.08 1.07 1.06 1.04,1.04 1.03 1.01 1.00 .99 TABLE VIII (CONTINUED) CLASS DIVISION BASED ON I.Q,. SCOPES Possible score Assigned not to use machines .97 .96 .96 .95 .94 .-92 .91 .90 .89' .88 .90,.90 •89- CD • .97 .96 .95 .94 .93 .92 .91 .90 .89 ,88 .87 .86 .85 .84 .83 .82 .81 .80 .79 .78 .77 .76 .75 .74 .73 .72 .71 .70 Assigned to use machines .79 .71 - 20 students , 20 students 33 satisfactory* The two classes were then given the same instruction in bookkeeping, together with related arithmetic, by the same instructor for a period of six months. One class was furnished with one adding machine for each two students. They were frequently urged to use these machines freely for all their problems in arithmetic that they could solve by use of a machine. The other class was denied the use of any mechanical aid for their arithmetical calculations. They were urged to solve their own individual problems or seek aid from the teacher. At the end of this six-month period, the two groups were again tested in arithmetical ability by using Form B of the Sehorling-Clark-Potter Arithmetic Test used at the beginning. Testing to determine .bookkeeping progress was also done. See Table XVII, page 49, and Table X7III, page 50. 34 TABLE IX CLASS' DIVISION BASED ON BOOKKEEPING SCORES Score 110 109 108 107 106 105 104 103 102 101 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 Assigned to use machines Assigned not to use machines 106 104 103 101 101 98 91 90 91 90 85 84 80 77 TABLE IX (CONTINUED) CLASS DIVISION BASED ON BOOKKEEPING SCORES 74,74 74 73 71 70 71 o 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 Assigned not to use machines o Score Assigned to use machines 68 66 65 64 66 65 63 62 61 60 56 57 56 55 53 50 43 20 students 20 students CHAPTER VI TESTING RESULTS AFTER SIX MONTHS At the end of a six-month interval (October to April) the Schorling-Clark-Potter Arithmetic Test, Form B, was given to each bookkeeping class. Fortunately, there were very few dropouts during this period of time. At the same time that the arithmetic tests were given, current tests in bookkeeping were also given to determine whether the students had improved their positions in their respective groups. Arithmetic testing. Table X, pages;.37-38, shows the result of the second testing in arithmetical ability for the entire group of forty students in the two bookkeeping classes, Table XII, pages 40-41, shows the test scores in arithmetic for the class assigned to use machines during the six-month period. Table XIII, pages 48-43, shows the test scores in arithmetic for the class assigned not to use machines during the six-month period* Table XIV, page 44, shows the comparison of arithmetic scores of the members of the class assigned to use adding machines during the six-month period* The class as a group showed wonderful improvement in their arithmetical ability. Fourteen of the twenty students showed an increase in 37 TABLE X ARITHMETIC SCORES AFTER SIX MONTHS sil or< October April score score 1 1 1 1 2 86 2 1 1 1 2 2 2 1 1 66 65 64 63 1 1 1 1 1 2 1 1 2 1 1 1 r lr l 1 1 H 1 1 1 1 2 HH 2 68 67 2 1 r| 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 1 > HH 87 2 2 2 rl 1 88 - 62 61 60 59 58 57 56 55, 54 53, 52 51 50 49 48 47 '46 45 44 43. 42 41 40 39 38 37, 36 35 34 33 32 31 30 29’ 28 27 26 25 April score rH 99 98 97 96 95 94 93 92 91 90 89 - October score I—I CQ CV2 00 Possible score 1 1 1 38 TABLE X (CONTINUED) ARITHMETIC SCORES■AFTER SIX MONTHS Possible score October score April score Possible .October score score April score 24 23 22 21 2 20 2 19 18 17 16 15 14 13 12 11 10 9 1 8 .7 6 5 4 3 2 1 Mean score Median score Form A Test October 51.4 Form B Test April 64.4 Increase 13.0 51.' 65.1 14.1 59 TABLE XI DISTRIBUTION OF ARITHMETIC SCORES AFTER SIX MONTHS Number of students 10 9 8 7 r 6 5 4 5 2 1 1 0 Score range O- 03 1 rH <X2 CO 1 o o 03 rH 1 lO CO co wi Score 98-104 91-97 84-90 77-83 70-76 63-69 56-62 49-55 42-48 35-41 28-34 21-27 to to t CJ> 03 tO 1 to in o> to i CO to t o oo1 CN CO 00 1 Cs Cs o o> 1 00 o- CJi 1 rH -o> O i —1 1 oo o> 1 student 2 35 4 5 6 2 4 1. 3 1 Mean 64# 4 Median 65.1 40 TABLE XII ARITHMETIC SCORES AFTER SIX MONTHS (CLASS ASSIGNED TO USE MACHINES) Possible score 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 October score April score 1 1 1 1 2 1 1 1 1 1 1 2 1 1 . Possible score 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 • • 34 33 32 31 • 30 29 28 27 26 25 October April score score 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 41 TABLE XII (CONTINUED) ARITHMETIC SCORES AFTER SIX MONTHS (CLASS ASSIGNED TO USE MACHINES) Possible score 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 o w 1 October April score score 1 1 Possible score October April score score 42 TABLE XIII ■ARITHMETIC SCORES AFTER SIX MONTHS (CLASS ASSIGNED NOT TO USE MACHINES) Possible score 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 October score April score 1 2 1 2 2 1 1 1 2 1 1 Possible score 62 .61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 October April score score 2 1 2 1 1 1 1 1 1 • 1 1 1 1 1 1 1 1 1 45 TABLE XIII (CONTINUED) ARITHMETIC SCORES AFTER SIX MONTHS' (CLASS' ASSIGNED NOT.TO USE MACHINES) Possible score October score 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1 April score Possible score October score April score 4(4 TABLE XIV COMPARISON 'OF ARITHMETIC SCORES AFTER SIX MONTHS (CLASS ASSIGNED TO USE MACHINES) Student Form A October Form B April 'Points improved 5 10 12 31 13. 1 2 3 4 5 93 69' 21 29 60 98 79 33 60 73 6 7 ,8 9 10 41 4538 59 67 27 36 68, ■ 74 75 30 15 8 11 12 13 14 15 35 78 26 53 50 34 92 45 61 57 14 19 8 7 16 17 18 19 20 67 44 20 . 59 83 67 60 0 16 81 81 22 Not improved 14 9 1 0 2 210 14 students improved a total of 210 points, an average of 15. 4 students decreased a total of 26 points, an average of 6-J-. 1 student with no change. 1 student dropped out. ‘26 45 TAELS XV COMPARISON OF ARITHMETIC SCORES AFTER SIX MONTHS (•CLASS ASSIGNED NOT TO USE MACHINES) Student Form A October Form B April Points v improved 1 2 3 4 5 34 28 9 39 41 43 29 48 51 42 9 1 39 12 1 6 7 8 9 10 69 21 60 . 35 50 90 76 83 49 69 * 21 55 23 14 19 11 12 13 14 15 65 55 86 61 86 83 63 95 61 90 18 8 9 0 4 16 17 18 19 20 48 61 20 43 72 50 69 2 8 88 62 45 Points not improved 288 17 students improved a total of 288 points, an average of 17* .1 student decreased a total of 10 points. 1 student with no' change. 1 student dropped out. 20 10 46 TABLE XVI SUMMARY OF COMPARISON OF ARITHMETIC SCORES AFTER SIX MONTHS Class assigned to use machines Class assigned not to use machines Number of students increasing in ability 14 17 Number of students decreasing in ability 4 1 Number of students with no change in ability 1 1 Number of students dropped out 1 1 20 20 15 17 Average number of points increased ability Average number of points decreased ability 6i* 10** * Four students made a lower score **. One student made a lower score From the above data it is plain (1) a definite im provement in arithmetical ability resulted from a study of bookkeeping, and (2) those students not using adding machines improved slightly more than those who did use adding machines. 47 ability by a total of £10 points, or an average improvement of fifteen points each. As the arithmetic test had one hundred points, this means an improvement of 15 per cent. Four of the students showed a decrease in arithmetical ability by a total of twenty-six points, or an average de crease of six and one-half points. efficiency of per cent. This means a decrease of There was one student with no improvement, and one student dropped out. Table XV, page 45, shows the comparison or arithmetic scores of the members of the class assigned not to use add ing machines during the six-month period. This class as a group showed more improvement than the class assigned to use 'adding machines. Seventeen of the t?renty students showed an increase in ability by a total of £88 points, or an average improvement of seventeen points each. in efficiency of 17.per cent. This is an increase Only one student showed a de crease in arithmetical ability, ten points. There was one student that made no improvement, and one student dropped out. Table XI, page 39, indicates the Schorling-ClarkPotter Arithmetic Test, Form B, given in April showed a mean score of 64.4, and a median score of 65.1. Form A test October Form B test April Increase Mean score 51.4 64.4 13.0 Median score 51. 65.1 14.1 Tables XVII and XVIII, pages 49-50, are a composite of scores resulting from both the Form A and Form B arith metic tests, together with the bookkeeping scores of the first quarter of the school year and the scores of the third quarter— the six-month period of this study. Table XVII, age 49, shows the data about the bookkeep ing class assigned to use adding machines. This table shows that fourteen students made higher scores in the last arith metic test, totaling 210 points, or an average of fifteen points each. At the same time, four students made lower scores totaling twenty-six points, or an average of six and one-half points each. There was one student who made the same score on the second test, and one student dropped out. This same table'shows the bookkeeping scores of the first quarter of the school year, and the third quarter. Two students received the same score position in their class group, five students made a better score, eleven students made a lower score, and two students dropped out before the final examinations of the quarter and received no grade. Table XVIII, page 50, shows data about the bookkeeping class assigned not to use adding machines for the six-month period. This table shows that seventeen students made higher scores in the arithmetic test, totaling 288 points, or an average of seventeen points each. At the same time, one student made a lower score of ten points. There was one 49 TABLE XVII COMPOSITE OF SCORES - ARITHMETIC AND BOOKKEEPING CLASS ASSIGNED TO USE MACHINES Student I.Q. Arithmetic Form A Form B October April per cent f Bookkeeping f October April per cent 1 2 3 4 5 1.29 1.14 1.03 .79 1.21 93 69 21 29 60 98 79 33 60 73 5 10 12 31 13 100 90 66 59 80 100 68 51 66 58 0 -22 -15 7 -22 6 7 8 9 10 .92 .97 .90 1.06 1.04 41 45 38 59 67 27 36 68 74 75 -14 - 9 30 15 :8 74 65 94 71 74 79 71 61 69 5 6 -33 - 2 out 11 12 13 14 15 .99 1.18 .96 1.08 .90 35 78 26 53 50 34 92 45 61 57 - 1 14 19 8 7 90 91 70 70 100 88 75 68 69 93 - 2 -16 - 2 - 1 - 7 16 17 18 19 20 1.10 .89 1.04 1.26 1.11 67 44 20 59 83 67 60 0 16 72 69 81 81 22 -2 63 -65 56 100 56 9 4 out - 1 0 Arithmetic 14 4 1 1 student s increased 210 students decreased 26 student no change student dropped out Average increase 15 points Average decrease 6 points - 99 56 Bookkeeping 5 students 11 students 2 students 2 •students increased 31 decreased 123 no change dropped out Average increased 6 points Average decrease 11 points 50 TABLE XVIII COMPOSITE OF SCORES - ARITHMETIC AND BOOKKEEPING CLASS ASSIGNED NOT TO USE MACHINES Student I. Q. Arithmetic Form A Form B October April per cent Bookkeeping ♦ October April per/cent 43 29 48 51 42 9 1 39 12 1 57 55 64 "-50 68 61 55 -51 57 65 90 76 83 ■ 49 69 21 55 23 14 19 84 76 77 62 74 81 56 76 55 70 65 55 86 61 86 83 63 95 61 90 18 8 9 0 4 85 61 100 60 100 54 82 100 56 96 -31 21 0 - 4 - 4 48 61 20 43 72 50 69 2 8 43 71 53 91 66 47 76 4 5 out -14 - 2 1 2 3 4 5 1.00 .91 .84 .89 .88 34 28 9 39 . 41 6 7 8 9 10 1.01 .95 .96 .71 1.16 69 21 60 35 ,50 11 12 13 14 15 1.17 1.07 1.29 .90 1.25 IS 17 18 19 20 .94 1.18 .88 1.13 1.09 — 88 62 45 -10 studentsi increased 288 student decreased 10 student no change student dropped out Average increase 17 points Average decrease 10 points - 3-20 - 1 - 7 - 4 Bookkeeping Arithmetic 17 1 1 1 77 64 4 0 -13 7 - 3 5 12 2 1 students increased 41 students decreased 106 students no change student dropped out Average increase 8 points Average decrease 9 points 51 student who made the same score on the second test, and one student dropped.out. This same table shows the bookkeeping scores of the first quarter of the school year and the third quarter. Two students received the same score in their class group, five students made a better score, twelve students made a lower grade, and one student dropped out before the third quarter examinations. . Table XIX, page 52, shows the bookkeeping scores re sulting from the tests at the end of the six-month interval. There were only thirty-seven students who took this test. V Table XX, page 53, shows the distribution of the bookkeeping scores resulting from the tests given at the end of the six-month period. These scores are shown in Table XIX on page 52. Computations reveal a mean score of 70.0, and a median score of 68.14. The standard error of the mean is 2.25, and when compared with the bookkeeping test scores of October, a standard error of differences between the means of 3.3 is found. This indicates that the relative bookkeeping ability of the class as a whole is of no appreciable difference than it was in:October. October April Mean 75.8 70.0 Median 72.34 68.14 52 TABLE XIX BOOKKEEPING SCORES AFTER SIX MONTHS Possible score 100 99 98 9? 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 ’ Number of students 2 1 1 1 1 1 1 1 1 2 1 Possible score 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 Number of students 1 1 1 3 2 1 1 1 2 1 1 3 2 1 2 1 55 TABLE -XX DISTRIBUTION OF BOOKKEEPING SCORES AFTER SIX MONTHS Number of students 10 9 8 7 6 5 5 4 4 4 3 5 4 3 2 1 1 1 0 Score o o rH 1 to o> to o* 1 1— i o> 96-100 91-95 86-90 81-85 76-80 71-75 66-70 61.65 56-60 51-55 46-50 o o 1 to o 00 1 CO 1 to 1—1 CO 00 to o* 4 .students 1 1 2 4 3 7 4 5 5 1 to £N 1 rH O O D-1 to to LO O to to 1 rH to to 1 LO to to 1 rH O to 1 to to Mean score 70.0 Median score 68.14 Standard error of mean 2.25 Standard error of difference of means 3.3 Summary. A study of Table XVII and Table XVIII, pages 49-50, reveals that students in bookkeeping show a great im provement in arithmetical ability during a period of six months. It will be seen, too, that those bookkeeping stu dents who were compelled to solve their bookkeeping arithme tic mentally made a greater progress in arithmetic than those who were given the free use of adding machines. CHAPTER VII SUMMARY AND CONCLUSIONS A number of significant facts seem to present them selves from this study* During the study of bookkeeping, the student is called upon to solve many problems in arith metic. The majority of these problems are simple processes of addition, subtraction, and multiplication. However, there are occasions where a knowledge of percentage is imperative, and where the computation of interest is necessary. There are long columns of figures to be added when taking a trial balance, and multiplication problems involving decimals. Whether the use of adding machines helps to improve the arithmetical ability of bookkeeping students, or whether it retards their improvement, is not shown in a decisive' * manner from this study. However, there does seem to be a rather slight tendency for greater improvement in arithmeti cal ability when onljr mental ability is used for problem solving* The following rather significant facts do seem to be important: 1. Nearly all students in bookkeeping improved in arithmetical ability* 2. Those students who were compelled to use only their mental faculties for problem solving do improve in 56 arithmetical ability slightly more than those who were given free use of mechanical aids* 3. There is a conservation of the time of students by not having to make ready to use a machine. 4 ’s* There is less confusion in the classroom when no /machines are in use. 5. Students using machines do gain an additional business skill. 6. It would be expensive to provide enough machines to avoid confusion from noise and movement. 7* Mental calculations give confidence to the student. Too often a student thinks the results obtained from the machine is a correct answer— he is reluctant to check the machine tape for a possibility of error. Recommendations. From this study, the following recommendations are suggested: 1. That students in bookkeeping be encouraged to rely upon their mental abilities for solving arithmetical problems occurring in the bookkeeping work, except long lists in addition, and multiplication when proving invoices. 2. The gaining of an additional business skill in machine operation is to be desired* BIBLIOGKilPHY BIBLIOGRAPHY A. BOOK Tiegs, Ernest W., Tests and Measurements in the Improvement of Learnings New York: Houghton Mifflin Company, 1959. 490 pp. B. PERIODICAL ARTICLES Kinney, Lucian B., "Mathematical Requirements of Business," Journal of Business Education, VII (February, 1932), pp. 15-14, (March, 1932), pp. 13-14. C. PUBLICATIONS OF LEARNED ORGANIZATIONS "Arithmetic Used by Workers in Business Occupations." Un published survey of the California Bureau of Business Education, Sacramento, California, November, 1931. 4 pp. Beck, Cameron, "The Necessity of Closer Relationship Between Business and the Schools." Monograph report prepared for the Business Education Division of the National Education Association Convention, July, 1930. 48 pp. Bowden, A. 0., Consumers Uses of Arithmetic; an Investigation to Determine the Actual Uses Made of Arithmetic in Adult Social Life, Exclusive of Vocational Uses. Teachers College Contributions to Education, No. 340. New York: Teachers College, Columbia University, 1929. 69 pp. * "Commercial Workers’ Biographical Survey." Unpublished survey of the Los Angeles Department of Education, Los Angeles, California, 1924. 4 pp. Kibby, Ira W., "Arithmetic Used by Workers in Business Occupations." Unpublished survey of the California Bureau of Business Education, Sacramento, California, November, 1931. 4 pp. , "What Arithmetic Should be Taught in the Secondary Schools." Mimeographed report of the California Bureau of Business Education, Sacramento, California, 1932, p. 3. 59 Wilson, Guy M., A Survey of the Social and Business Usage of Arithmetic. Teachers. College Contributions to Education, No. 100. New York: Teachers College, Columbia • University, 1919, p.. 35. X). UNPUBLISHED MATERIALS Bassett, E. R., "Business Arithmetic Textbooks." Unpublished Master’s thesis, The University of Southern California, Los Angeles, 1934. 118 pp. Fisk, William, "The Relation Between Business Arithmetic and Business Practice." Unpublished Master’s thesis, The University of Southern California, Los Angeles, 1926. 126 pp. Kinney, Lucien Blair, "The Mathematical Requirements of Commercial Positions Open to High School Commercial Graduates." Unpublished Doctor’s dissertation, University of Minnesota, 1931. (Reprint loaned by the University of Minnesota Loan Library.) McCall, Beth Ada, "The Contribution to Skill in Arithmetic Made By a Study of the Use of a Calculating Machine." Unpublished Master’s thesis, The University of Southern California, Los Angeles, 1931. 69 pp. Putman, Helen, "A Study to Determine the Arithmetical Processes Used by f/orkers in Offices." Unpublished Master’s thesis, The University of Southern California, Los Angeles, 1936. 134 pp. Spiers, Katherine, "A Study of Eliminations, Inclusions, and Social and Business Requirements of Arithmetic." Unpublished Master’s thesis, University of California, Berkeley, California, 1921. 223 pp.

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