Analysis of reading vocabulary in grades four, five, and six

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(1)Boston University OpenBU. http://open.bu.edu. Theses & Dissertations. Dissertations and Theses (pre-1964). 1947. Analysis of reading vocabulary in grades four, five, and six https://hdl.handle.net/2144/14714 Boston University.

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(4) BOSTON DIVERSITY SCHOOL OF EDUCATION. THESIS. ANALYSIS OF READING VOCABULARY IN GRADES FOUR, FIVE, AND SIX. Submitted by Josephine Anne Piekarz (B. S.. in Ed., Teachers College of Connecticut, 1943) In partial fulfillment of the. requirements for the degree of. Master of Education. 19. First Reader. :. Second Reader: Third Reader. :. 4 7. Dr. D, D. Durrell, Professor of Education Dr. Helen Blair Sullivan, Professor of Education Dr. M. Agnella Gunn, Associate Professor of Education. I. Boston university School of Education.

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(6) ACKNOM.EDGEMENTS I. wish to express my sincere appreciation to. Dr, Donald D. Durrell, Dean, Boston University School of. Education, for suggesting the problem and guiding the study.. Thanks are due to Miss Alice Crossley, Instructor of Education, for her willing co-operation and guidance. I also wish to thank. assistance and encouragement.. my many friends for their.

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(8) TABLE OF CONTENTS CHAPTER I.. PAGE. STATEim^T OF. PROBLEi'/[. AND REVIEW. OF RESEARCH II.. III. IV.. 1. PLAN AND CONDUCT OF STUDY. 12. ANALYSIS OF DATA. 17. SmClARY AND SUGGESTIONS FOR FURTHER. RESEARCH. 46. BIBLIOGRAPHY. 50. APPENDIX. 53.

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(10) LIST OF TABLES TABLE I.. II.. III.. IV.. V.. VI.. VTI.. VIII.. PAGE Comparison of Percentage of Fourth, Fifth, and Sixth-Grade Reading Vocabulary Learned at Three Levels.. 18. Comparison of Percentage of Fourth, Fifth, and Sixth-Grade Reading Vocabulary Learned in Higher Grades on Bucicingham-Dolch List, in Higher Grades on Thorndike List, and in Same Grade. 20. Comparison of Rank Order of Frequency of Usage of Parts of Speech in DurrellSullivan Intermediate Grade Vocabulary.. .. .. 21. Comparison of the Percentage of Parts of Speech in Durrell-Sullivan Intermediate Grade Vocabiilary. 22. Comparison of Percentage of Parts of Speech Learned in Grades Four, Five and Six at Same Level, Later in Writing, and Later in Reading. 23. Percentage of Parts of Speech in Fourth-Grade Reading Vocabulary Learned in Higher Grades on BuckinghamDolch List, in Higher Grades on Thorndike List, and in Same Grade on Both Lists. 27. Percentage of Parts of Speech in Fifth-Grade Reading Vocabulary Learned in Higher Grades fctn Buckingham- Do Ich List, in Higher Grades on Thorndike List, and in Same Grade on Both Lists,. .. .. 28. Percentage of Parts of Speech in Sixth-Grade Reading Vocabulary Learned in Higher Grades on Buckingham- Dolch List, in Higher Grades on Thorndike List, and in Same Grade on Both Lists.. .. •. 29.

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(12) LIST OF TABLES (continued) TABLE IX.. X.. XI.. XII.. XIII.. XIV.. XV.. PAGE. Rank Order of Frequency of Usage of Roget»s Twenty-four Classifications in Fourth-Grade Reading Vocabulary. 30. Rank Order of Frequency of Usage of Roget»s Twenty-four Classifications in Fifth-Grade Reading Vocabulary. 31. Rank Order of Frequency of Usage of Koget^s Twenty-four Classifications in Sixth-Grade Reading Vocabulary. 32. Percentage of Roget^s Classifications Included in Fourth, Fifth and SixthGrade Reading Vocabulary. 33. Comparison of Rank Order of Frequency of Usage of Durrell-Sullivan FourthGrade Reading Vocabulary Classified According to Roget on Three Levels of Learning. 35. Comparison of Rank Order of Frequency of Usage of Durrell-Sullivan FifthGrade Reading Vocabulary Classified According to Roget on Three Levels of Learning. 36. Comparison of' Rank Order of Frequency of Usage of Durrell-Sullivan SixthGrade Reading Vocabulary Classified According to Roget on Three Levels of. Learning XVI.. XVII.. ,. 37. Comparison of Percentage of Usage ofRoget *s Classifications in Fourth, Fifth and Sixth-Grade Reading Vocabulary Divided into Three Learning Levels. 38. Percentage of Roget »s Classifications in Fourth-Grade Reading Vocabulary Learned in Higher Grades on Thorndike List, in Higher Grades on BuckinghamDolch List, and in Same Grade on Both Lists. 43. -.

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(14) LIST OF TABLES (continued) TABLE XVIII.. XIX.. A.. B.. C.. PAGE. Percentage of Roget's Classifications in Fifth-Grade Reading Vocabulary Learned in Higher Grades on BuckinghamDolch List, in Higher Grades on Thorndike List, and in Same Grade on Both Lists. 44. Percentage of Roget's Classifications in Sixth-Grade Reading Vocabulary Learned in Higher Grades on BuckinghamDolch List, in Higher Grades on Thorndike List, and in Same Grade on Both Lists. 45. Division of Durrell-Sullivan FourthGrade Reading Vocabulary According to Differences in Assigned Grade Ranks on Thorndike and Buckingham-Dolch Lists. .. •. 54. Division of Durrell-Sullivan FifthGrade Reading Vocabulary According to Differences in Assigned Grade Ranks on Thorndike and Buckingham-Dolch Lists. .. •. 5B. Division of Durrell-Sullivan SixthGradd Reading Vocabulary According to Differences in Assigned Grade Ranks on Thorndike and Buckingham-Dolch Lists. .. .. 61.

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(16) CHAPTER I STATEMENT OF PROBLEM The purpose of this study is to discover the types of. words learned more easily and used most frequently in the. reading vocabulary of grades four, five and six» While many studies have been made in the field of. vocabulary to determine the quantity of words known at. various grade levels, investigations related to the types of these words have been few.. There appears to be little. agreement as to which words are learned in the intermediate grade range.. It has been the practice to select any words. needed to tell a story adequately.. Exposure of children. to a great number of words, many of which are too difficult,. results from such practice. 1/. Several years ago Durrell and Sullivan,. after. compiling a reading vocabulary list from the books read by children in the fourth, fifth and sixth grades, concluded, there are a great many words which appear in the . . . child's writing vocabulary, as shown by the Buckingham-. D. D. Durrell and H. B. Sullivan, 'Vocabulary Instruction in the Intermediate Grades," Elementary English Review May 1938. Vol. 15, p. 192. 1/. ,.

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(18) Dolch list, before they aopear in his reading vocabulary. The5.e words with lower Buctcingham-Dolch rating are particularly significant for the teaching of reading, since it is probably true that the child has found need for the use of the words in these earlier grades. 1/. Recently Watts. added a note of concern to the. problem when he stated, It is clear, therefore, that vocabulary research will have to take into account to an increasing extent the range and quality of the words the children use, and this will mean that the attempt must be made to classify the kinds of words acQ_uired at different ages and an account given of what is implied by the results of such classifications.. Study of the problem indicates that a knowledge of the types of words used by children at various levels and. rates of retention would seem to be valuable to authors of children*. s. of repetition.. books in choice of vocabulary and frequency Therefore, this study is an analysis of. the reading vocabulary in grades four, five and six and. seeks to answer the following questions: 1.. Vi/hat. portions of words are:. a. Learned at the same grade level for reading as. for writing? b.. Learned later for reading than for writing?. c.. Learned later for writing than for reading?. 1/ A. F. Watts, The Language and Mental Development of Children, London: George G. Harrap and Co., Ltd., 194^. pTTC.

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(20) 2.. What portions of the parts of speech are: a. Learned at the same grade level for reading. as for writing? b. Learned later for reading than for writing? c. 3. TWhat. Learned later for writing than for reading? portions of Roget*s twenty-four minor categorie. are: a. Learned at the same grade level for reading. as for writing? b. Learned later for reading than for writing? c.. Learned later for writing than for reading? REVIEVv OF RESEARCH. 1/. A study by Wilfcing. is one of the few previous. investigations in the area of classification of children* vocabulary.. In this study the establishment of the rank. order of frequency of usage of the twenty-four minor. categories into which Roget classified English words and. phrases was a prerequisite for the construction of a. reading vocabulary test.. 1/ Stephen V. Willing, The Construction and Evaluation of a Measure of Reading Vocabulary , UnpuFllshed Master *s thesis, Boston, Boston University, 1940..

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(22) In Roget's International Thesaurus. words are. tJie. classed according to connotation in a philosophical. There are six primary or major classes of. manner.. categories: 1. Abstract Relations 2. Space 3.. Material V/orld. ^. 4. Intellect 5.. Volition. 6. Sentiment and Moral Powers. The major categories are broken down into twenty-. four minor classes, and these in turn, into one thousand sub-divisions.. A single word, because of its varied. meanings, may be, and generally is, classified in several categories.. Tabulation of the words on the Furrell-Sullivan 2/. Minimum Essential Word List. revealed to Wilking the use. of fourth-grade reading words in the following order of. frequency: 1. Individual Volition 2. Organic Matter. S . Mawson , Roget s International Thesaurus of English Words and Phr ases , New York: Thomas Y. CrowelT. 1/ C. .. 0. .. *. Co£pany,"T:^."pp. xii-xxxi 2/ D. D. Durrell, Improvement of Basic Reading Abilities New York: World Book Company, 1^0. pp. 360-3881. ,.

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(24) 3.. Personal Affections. 4* Motion 5.. Intersocial Volition. 6, CojMiuni cation of Ideas. ?• Dimensions 8,. Formation of Ideas. 9. Quantity. 10, Moral Affections 11, Causation. 12, Sympathetic Affections .13.. Form. 14. Inorganic Matter 15. Space Generally. 16. Order. '. 17. Affections Generally 18. Time 19. Religious Affections 20. Relation 21. Number 22. Existence 23. Change. 24. Matter Generally. This study provided Willing with evidence on which was. based the selection of words included in the reading. vocabulary test..

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(26) Experimenting has been carried on by Watts. in. England while studying the growth of children in the. mastery of vocabulary.. Classifications were formulated. as results of these studies in terms of the "feisling tone** of words and this type of categorization was formed: 1. Neutral Terms. a. Hames of common things, actions, and states b. Technical terms c. Names for collections of things. d. Abstract terms and concepts e. Vague terms 2. Elevated Terms. a. Formal terms b. Euphemisms c.. Poeticiams. d. Genteelisms e.. Archaicisms. f. Alienisms g.. Vogue words. h. Romanticisms i. 3.. Dignified terms. Debased Terms a. Vulgarisms b. Stump words. 1/ A. F. Watts, op. cit,, pp. 224-225..

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(28) c.. Trade names. d. Babyisms e.. Make-do»s. f . Facetious terms g. Empiiaticisms. Watts listed examples under each of the categories, but did not attempt to classify all the words which. children use nor list the classifications in order of. frequency or importance. The chief contributions of Thorndike to the solution of vocabulary problems have been through the medium of. the frequency of usage of specific words.. However, an. awareness of the problems of word meanings and classific1/ ation is manifested in the Teachers College Record where it is reported that there are several types of words,. namely: 1. Words which always or almost always have the. same meaning 2. Words which have several clearly distinct. meanings, the intended meaning usually being indicated by the context 3. Words. which have meanings fluctuating by fine. shades or degrees and require consideration of the. context as well as considerable experience on the part of the reader in order to interpret correctly what the. author has written. T7 E. L. Thorndike, "Improving the Ability to Read,** Teachers College Record, October 1934. 36:7.

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(30) 4. Words whicli are so varied in their meanings. that particular expressions containing them must be learned as totals.. No indication of the frequency of use of such type nor the rate of learning is offered by Thorndike.. About twenty years ago Dolch. y stated. that as the. new words "increase in number, the process of reading becomes harder and more vague until after a time the text ceases to yield any ideas whatsoever.". Through the analysis of a vocabulary test of his 2/. own construction, Dolch 1.. classified vocabulary as:. Words which describe familiar ideas, but are. poetic or literary equivalents for other words which. children ordinarily use. 2.. Words which signify things or actions with. which few children anywhere have occasion to come in contact. 3.. Words which are familiar to children in. particular localities. 4. Vôrds which act as symbols for abstractions or. generalizations To test correspondence between difficulty and frequency of use, the words were looked up in three word lists made on a basis of frequency: one from l7. E. W. Dolch, Reading and Vyord Meanings Ginn and Company, 1927. p. 24. 2/. Ibid, pp. 56-58. ,. Boston:.

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(32) pre-school conversation, another from adult correspondence, and the third from reading matter, A rough correspondence was found, but there was marked failure of the word counts to include all those words on the test that judgment would expect to include. This failure can be ascribed either to incompleteness of the counts or to failure of higher frequency of use 1/ to correspond with real familiarity to the children. The classification of adult vocabulary by Faucett and Maki. was specifically compiled to provide teachers. and students of the iinglish language with means of dis-. tinguishing indispensable from special. words.. ,. essential , and useful words. Low frequency on the Horn and. Thorndike lists, for the most part, determines special words,. 2/. A study. covering a long period of time, by a con-. temporary student of semantics established the following classifications for general vocabulary: 1. Pictured names 2. (Qualities. 3.. Adverbs. 4. General names 5. Operations 6. Verbs and auxiliaries. 1/. Ibid, p. 5^. 2/ L. j?'aucett and I. Maki, A Study of ^jinglish Word Values Statistically determined from the Latest .extensive Word Counts Tokyo, Japan: Matsumura Sanshodo, 1932, p, TI ,. 3/ H, R. Walpole, The Nature of Words and Their Meanings New York: W. W. Norton and company. Inc., 1941. p. 199. ,.

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(34) Organization of the system of Basic iCnglish by 1/. Ogden. led to the evaluation of vocabulary.. The eight. hundred and fifty words comprising the total vocabulary of Basic Jjaiglish are divided among five classifications.. Things, general. 400 words. Things, picturable. 200 words. Operations. ...... Qualities, general. 100 words •. 100 words. Qualities, opposite. 50 words. Transference of the above numbers of words into percentages indicates that Basic English consists of: 47.06 per cent general things 23 .53 per cent picturable things. 11.76 per cent operations. 11.76 per cent general qualities 5.89 per cent opposite qualities It is evident that word classification is not new.. However, the majority of studies undertaken have been. concerned mainly with categorizing words in a general sense.. There is relatively little accomplishment in the. area of classification of children's vocabularies or the. discovery of the types of words that are learned more easily and used more frequently by children at various T7 G. K. Ogden, The System of Basic English, Nev/ York; Harcourt, Brace and Co . 193^^7 pp. 35-64 ,.

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(36) grade levels.. Therefore, this study was undertaken to. discover the types of words learned more easily and used. most frequently in the reading vocabulary of grades four, five, and six..

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(38) CHAPTER II. PLAN AND CONDUCT OF STUDY In attempting to analyze the words used in reading by children in grades four, five, and six, it was necessary to work with an authoritative reading vocabulary list.. The Durr ell-Sullivan Heading Vocabulary for the Inter-. mediate Grades'" was used for this purpose.. This reading. list was compiled by counting words in fourth, fifth and. sixth-grade reading and social studies books.. Seventeen. books were used for the fourth-grade list, twenty books for the fifth-grade, and nineteen books for the sixthgrade list,. A word was included only if it appeared in. seven or more books at a grade level,. V/ords. which occurred. in lower grade lists were not repeated in later lists and. any words appearing in the Gates Primary List were not. recorded.. In this manner 69I words were selected for the. fourth-grade list, 525 words for the fifth-grade list, and 849 words for the sixth-grade list.. All the words from the Durrell-Sullivan Inter-. mediate Vocabulary were located on, and assigned a grade 2/. rank from the Thorndike T7. D. D. Durell,op.. 3/. and the Buckingham- Dolch. Lists;. cit., pp. 355-391. 2/ E. L. Thorndike, A Teacher* s Word Book of Twenty Thousand Words , New York: Bureau of PublicatTons, Teachers College, Columbia, 1931 2/ B, E. Buckingham and E. W. Dolch, A Combined Word List , Boston: Ginn and Company, "'Q'^^..

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(40) the former being a reading vocabulary and the latter a. writing vocabulary. The Thorndike List is a collection of words. obtained by count of general literature or the words found. most frequently and widely in general reading for children and young people.. Thorndilce rated words according to the. thousand as they appeared in the count.. In an article. describing a word count of eight fourth-grade boots, which. m. appeared. 1/. the Teachers College Record. ,. Thorndike. stated,. each word in the least important 7500 of the • • Thorndite 10,000 was also allocated to its proper class in the Thorndifce List as follows; .. Grade 3 B words from Grade 4 A words from Grade 4 B words from Grade 5 A words from Grade 5 B words from. 2501 3001 3501 4001 4501. to to to to to. 3000 3500 4000 4500 5000. Thorndike grade ranks were assigned to the words under consideration by use of the same method. The Buckingham- Dolch List is a writing vocabulary list, the result of a free-association method of acquiring. words.. This study involved over 20,000 children.. sheets of paper were distributed.. Blank. In a period of fifteen. minutes each child wrote down as many isolated words as possible.. A total of over 2,700,000 words was obtained.. 1/ E. L. Thorndike, "Improving the Ability to Read," Teachers College Record, 36:125, November 1934..

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(42) Tentative lists for grades two through eight were set up The tentative lists were then combined. from these data.. with eleven other important vocabulary studies and the 1/ finished study was called A Combined Word List . Since first-grade children were not involved in the experiment, 2/. the words which appeared on the Kindergarten Union List. were considered pre-school and first-grade words. Upon the completion of Thorndike and Buckingham- Do Ich grade assignments to the words of the Durrell-Sullivan. Intermediate Vocabulary, tables were set up for grades four, five, and six.. Only words were included which were common. to the Thorndike and Buckingham- Dolch Lists and which had. grade ranks of one through eight on both these lists.. This. was done to discard those words considered as adult vocabulary on the Thorndike List.. This step eliminated 125 words. from the Durrell-Sullivan List on the fourth-grade level, 154 words on the fifth-grade level, and 485 words on the. sixth-grade level.. The remaining lists were comprised of. these numbers of words:. Fourth grade. 566 words. Fifth grade. 371 words. Sixth grade. 364 words. E. W. Dolch, "Side Lights on a Combined Word List", 1/ Elementary English îeview, 14: 22, January 1937.. 2/ A Study of the Vocabulary of Children Before Entering the Eirst Grade , The Child Stuly Committee of the Interna tionaFlcTMer gar ten Union, Baltimore, 1928..

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(44) Tables A, B, and C, wJaich appear in the appendix,. were set up by comparing the writing vocabulary (BuckinghamDolch List) with the reading vocabulary (Thorndike List), Words having the same grade rank on both lists were recorded in a column headed zero... .. If there were differences between. grade ranks, the differences were obtained and the words. were recorded the correct number of columns away from the zero column under the headings Grades Higher on Thorndike. List and Grades Higher on Buckingham- Dolch List .. The. tables had a spread of difference from zero to five grades. higher on the Buckingham- Dolch List in one direction and from zero to seven grades higher on the Thorndike List in the other direction.. By setting up Tables A, B, and C in this manner, the Buckingham- Dolch and rhorndike grade ranks were lost.. However, the words learned later in writing than in reading. were separated from those words which were learned later in. reading than in writing on each of the intermediate grade levels. The work so far showed the positions of specific. words in the vocabularies of grades four, five, and six. it seemed advisable at this point to classify the words. and generalize in order to make the study more valuable. for those concerned with children's vocabularies.. The. parts of speech and r.oget's categories were selected for.

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(46) tile. two types of classifications to be used.. 1/. The Thorndike-Century Junior Dictionary. was. selected to be the authoritative reference for the basis of classification according to parts of speech.. Words. were recorded under as many parts of speech as listed by Thorndiice.. A large part of the words, therefore, appeared. under several headings. The second type of classification for organizing. random vocabulary chosen for this study was Roget*s twenty-four minor categories.. As in the previous method. of classification, words again were listed under as many. headings as indicated by authority. The words on Tables A, B, and C, were categorized. according to both classifications without losing their locations on the tables.. With the information available. at this point, it was possible to discover the portions. and the types of words learned at various levels.. For. purposes of convenience, portions were described according to percentages throughout this study.. 1/ E. L. Thorndilce, The Thornd ike-Century Junior Dictionary , New York: D. Appleton-Century Company, 1935. 2/ 0. 0. S. Mawson, Roget's International Thesaurus New York: Thomas Y. Crowell Company, 1925.. ,.

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(48) CHAPTER III Al^TALYSIS OF. DATA. The data obtained throup-h the classification and. tabulation of intermediate grade reading vocabulary were analyzed to find the answers to the following questions: 1.. ViThat. portions of words are:. a. Learned at the same grade level for. reading as for writing? b. Learned later for c.. 2.. reading than for writing?. Learned later for writing than for reading?. Vftiat. portions of the parts of speech are:. a. Learned at the same grade level for reading. as for writing? b. Learned later for reading than for writing? c. 3.. Learned later for writing than for reading?. What portions of Roget's twenty-four minor. categories are: a. Learned at the same grade level for reading. as for writing? b. Learned later for reading than for writing? c.. Table. Learned later for writing than for reading? I. shows a comparison of the percentages of. Durrell-Sullivan Intermediate Grade Reading Vocabulary learned at the three levels v;hich resulted when Thorndifce and Bucliingham-Dolch grade ranks were compared..

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(50) TABLE I. FIFTH AND SIXTH GRADE READING VOCABULARY LEARNED AT THREE LEVELS. COfylPARISON CF PERCEI\"TAGE OF FOOETH,. DurrellSullivan Grade. Later in BuckinghamDolch Writing Vocabulary. Same Level. Later in Thorndike Reading Vocabulary. Four. 28.62. 18.55. 52.83. Five. 37.47. 21.29. 41.24. Six. 37.91. 24.18. 37.91. Total. 33.74. 20.91. 45.35. An analysis of Table. I. reveals that on the fourth-. grade reading level more than half of the total reading. vocabulary is learned later for reading purposes than for. writing purposes.. On this same level, more than a quarter. of the total number of words is learned later for writing. purposes.. The smallest portion, about one-sixth of the. total number, is learned at the same grade level for both purposes. On the fifth-grade level, the difference between. those words learned later for reading and writing purposes is smaller.. Over a third of the words at the fifth-grade. level is learned later for writing and two-fifths are. learned later for reading, while about a fifth is learned.

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(52) at the same grade levels.. The sixth-grade list shows equal amounts on both the higher Thorndike and higher Bucfcingham-Dolch categori and brings those words learned at the same levels up to. one-fourth of the total number..

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(56) An examination of Table II shows a comparison of the percentage of Durrell-Sullivan worcls which fell higher. on the Bucicingham-Dolch than Thorndike List; higher on the. Thorndike than the Buckingham-Dolch List; and those that fell at the same grade level on both lists. In grades four and six the amount of words learned at the same level on both lists is slightly higher than. in any one level where there is a difference between the. lists.. On the fifth-grade level, however, the number of. words which is learned one grade later for writing exceeds the amount learned on the same level for both lists.. Parts of Speech Analysis of parts of speech in relation to the. reading vocabulary of the intermediate grades shows that there is little difference in the rank order of frequency of usage of the parts of speech in grades four, five and six.. TABLE III. COMPARISON OF RANK ORDER OF FREQUENCY OF USAGE OF PARTS OF SPEECH IN DURRELL-SULLIVAN INTERIvdSDIATE GRADE VOCABULARY Grade Four 1. 2. 3. k* 5. 6. ?• 8.. Nouns Verbs Adjectives Adverbs Conjunctions Interjections Prepositions Pronouns. Grade i?ive 1. 2. 3. 4. 5. 6. 7. 8.. Nouns Verbs Adjectives Adverbs Prepositions Conjunctions Interjections Pronouns. Grade Six 1. 2. 3. 4. 5. 6. 7. 8.. Nouns Verbs Adjectives Adverbs Prepositions Conjunctions Interjections Pronouns.

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(58) Table IV cites the percentage of the total number of wor(3s in the reading vocabulary of grades four, five. and six that each part of speech comprises.. TABLE IV. COMPARISON OF THE PERCENTAGE OF PARTS OF SPEECH IN DURRELL-SULLIVAN INTERMEDIATE GRADE VOCABULARY. Grade Four. Nouns. Pronouns Verbs. Adverbs Adjectives. Grade Five. Grade Six. 47.30. 44.69. 49.28. 0. 0. 0. 35.62. 32.40. 30.52. 1.01. 2.43. 1.03. 15.84. 20.11. 18.97. Prepositions. 0. .37. .21. Interjections. .11. .19. 0. Conjunctions. .11. .19. 0. Nouns, verbs and adjectives, in respective order of. frequency of usage, mate up the bulk of the complete. reading vocabulary.. Since all pronouns are learned in. the primary grades, they do not appear in Table IV at all». Table V shows a comparison of the frequencies of the parts of speech in relation to whether words were. learned later for reading, later for writing, or at the same time for both..

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(60) TABLE V COMPARISON OF PERCENTAGE OF PARTS OF SPEECH LEARNED IN GRADES FOUR, FIVE AND SIX AT SAME LEVEL; LATER IN WRITING; AND LATER IN READING. Part of Speecli. DurrellSullivan Grade. Later in V/riting. Vocabulary. Four Five Six. 37.60 39.15 44.26. Four Five Six. ©. Verbs. Adverbs. Nouns. Later in Reading Vocabulary. Same Level. 48.21. 50.61 47.83 54.74. 0. 0 0 0. 0 0. Four Five Six. 38,84 35.45 38.25. 34.87 32.20 30.35. 34.29 30.00 23.15. Four Five Six. 2.48 2.65 1.09. 1.69. Adjectives. Four Five Six. 21.07 22.22 16.39. 13.16 16.95 21.43. 14.08 20.00 20.00. Prepositions. Four Five Six. 0 0 0. 0 .85 0. 0 .43 .53. Pronouns. 0. 51.96. 0 0. !. 0. .61. 1.74 1.58.

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(62) TABLE V (continued). COMPARISON OF PERCENTAGE OF PARTS OF SPEECH LEARNED IN GRADES FOUR, FIVE AND SIX AT SAI'^ LEVEL; LATER IN VffilTING; AND LATER IN READING. Part of Speech Interjections. Conjunctions. DurrellSullivan Grade. Four Five Six Four Five Six. Later in Writing Vocabulary 0 .53. 0. 0 0 0. Same Level. Later in Reading Vocabulary. 0 0 0. .20 0 0. 0 .85. .20 0 0. 0. The next phase of vocabulary analysis to be. considered is the comparison of the portions of the. several parts of speech in grades four, five and six in. relation to the number of words learned later on the. Buckingham-Dolch List; learned later on the Thorndifce List; and learned at equal grade levels on both lists.. In the. fourth grade, 51.96 per cent of the words learned at the same grade levels and 50.61 per cent of the words learned. later for reading purposes are nouns.. Only 37.60 per cent. of the words learned later for writing are this part of. speech.. In the fifth grade, the first two divisions. mentioned above drop to percentages of 47.46 and 47.83,.

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(64) while the percentage of those words learned later for. writing purposes rises to 39.15 •. In the sixth grade,. the portions are regrouped, having nouns comprise 48,21 per. cent of all words learned at the same level and 54.74 of. those learned later for reading purposes, but only. 44.26 per cent of those learned later for writing. The verbs show a different pattern.. Where nouns. comprised the smallest percentage of words learned later in the writing vocabulary for grades four, five and six,. the verbs comprise the largest percentages for the three. grades in this category.. Adjectives are a less predictable part of speech. At the fourth grade, the category that contains the largest percentage of adjectives is the one where vocabulary is learned later for writing purposes.. maintained at the fifth grade level.. This same relation is. At the sixth grade. level, however, adjectives comprise the largest percentage of the words learned at the same grade levels and the. smallest percentage of those learned later for writing.. New conjunctions, interjections, prepositions, and pronouns are learned so infreauently at the intermediate grade level that they do not appear to show noticeable. relationships.. Adverbs appear less frequently in learning. at the same level for both lists than either later for. writing or later for reading..

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(66) Tables VI, VII and VIII show what percentage the. various parts of speech are of the total number of words learned at specific grades higher on the Buclcingham-Dolch. Writing List and the Thorndike. jrieading. List..

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(74) JO. Roget*s Twenty»four Minor Categories The third major consideration in this study is the. analysis of the reading vocabulary of intermediate grade children in relation to Roget*s twenty-four minor categories*. Tables IX, X and XI show the rank order of frequency of usage of Roget*s categories, when the total reading. vocabularies of grades four, five and siz are taken into consideration.. The tables are obtained, when words are. classified in respect to all possible meanings rather than one most common meaning.. TABLE IX RANK ORDER OF FREqUENCY OF USAGE OF ROGET»S TWENTY-FOUR CLASSIFICATIONS IN FOURTHGRADE READING VOCABULARY 1. Individual Volition. 13. Form. 2.. Personal Affections. 14. Order. 3.. Organic Matter. 15. Space Generally. 4. Communication of Ideas 5.. Motion. 16. Sympathetic Affections. 17. Time. 6. Intersocial Volition. 16. Relation. 7. Dimensions. 19. Affections Generally. 8.. Quantity. 9. Formation of Ideas. 20. Number 21. Existence. 10. Causation. 22. Religious Affections. 11. Moral Affections. 23. Change. 12. Inorganic Matter. 24. Matter Generally.

(75) 0. R. *.

(76) TABLE X. RANK ORDER OF FREQUENCY OF USAGE OF ROGET^S TWENTY-FOUR CLASSIFICATIONS IN FIFTHGRADE READING VOCABULARY 1. Individual Volition. 13. Sympathetic Affections. 2.. Organic Matter. 14. Form. 3.. Personal Affedtions. 15. Time. 4.. Motion. 16. Change. 5.. Communication of Ideas. 17. Inorganic Matter. 6.. Intersocial Volition. 18. Space Generally. 7. Foriaation of Ideas. 19. Affections Generally. 8. Dimensions. 20. Number. 9. Quantity. 21. Relation. 10. Causation. 22. Religious Affections. 11. Moral Affections. 23. Existence. 12. Order. 24. Matter Generally.

(77) Hi.

(78) TABLE XI. RAM. ORDER OF FREQ,UENCY OF USAGE OF ROGET»S TWENTY-FOUR CLASSIFICATIONS IN SIXTHGRADE READING VOCABULARY. Individual Volition 2. Personal Affections 3.. Communication of Ideas. 4. Intersocial volition 5.. Motion. U.. Time. 15. Form. 16. Religious Affections 17. Inorganic Matter. 6. jj'ormation of Ideas 7. Organic. Matter. 8. Dimensions 9. Moral. 13. Sympathetic Aff ectioj. Affections. 18. relation 19. Space Generally 20. Number. 21. Affections Generally. 10. (Quantity-. 22. Change. 11. Causation. 23. jiixistence. 12. Order. 24. Matter Generally. Tabulation of vocabulary reveals that with minor changes of placement, the rank order of frequency of usage of the twenty-four categories remains approximately the same,. individual Volition, with the rank order of one;. Matter Generally, with the rank order of twenty-four; and Number, with the rank order of twenty; are the three. categories that correlate perfectly on the three grades. Organic Matter and Inorganic Matter show the greatest changes in order of rank.. Organic Matter holds places. three and two respectively on the fourth and fifth grade.

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(80) vocabularies, but it slips down to seventh position on the grade six vocabulary,. inorganic Matter holds twelfth place. at fourth-grade level, but descends to seventeenth place on the fifth ani sixth-grade lists.. Table XII is a list of the percentage of each of. Roget's classifications included in the total reading vocabulary of grades four, five and six. TABLE XII. PERCENTAGE OF ROGET*S gLASSIFI CATIONS INCLUDED IN FOURTH, FIFTH AND SIXTH-GRADE READING VOCABULARY Classification. Grade Four. Existence Relation. 1.21 1.66 5.63 3.01 1.41 2.43 1.09 4.28 2.94 5.81 3.20 6.65. 1. 2. 3. 4. 5. 6. 7. 8. 9.. 10. 11. 12. 13.. u. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.. (Quantity. Order Number Time Change Causation Space Generally Dimensions Form Motion Matter Generally Matter Inorganic Matter Organic Formation of Ideas Communication of Ideas Individual Volition Intersocial Volition Affections Generally Personal Sympathetic Moral Religious. Grade Five .62. 1.64 4.21 3.18 1.64 2.77 2.46 3.90 2.46 5.44 2.97 6.87. Grade Six 1.00 1.57 4.00 3.23 1.69 2.67 1.33 3.67 1.57 5.12 2.00 6.56. .64. .41. .67. 3.26 6.71 5.50 6.65 15.21 6.33 1.60 6.78 2.88 3.84 1.21. 2.46 7.90 5.85 6.56 14.26 5.95 2.26 7.38 3.08 3.38 1.33. 1.57 6.01 6.35 7.79 16.35 7.79 1.34 8.45 2.77 4.56 2.00.

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(82) The above table reveals that the category,. Individual Volition. holds rank one on all the grades by. ,. percentages much larger than those which place the remaining categories.. The average difference between ranks one and. two for the three grades is seven.. This difference appears. to be significant, when it is noted that the difference. between any two of the remaining twenty- three categories,. including the three grades, is always less than two per cent. The next three tables show another rank order of. frequency of usage of Roget*s classifications.. Here, the. rank order of those words learned later on the BuckinghamDolch List; learned later on the Thorndike List; and learned at the same time; is depicted for each of the intermediate. grades.. To save space and to make the charts more easily. readable, a code is employed.. Each of Roget's classifications. is represented by a single letter.. A represents Existence B C. D E F G. H J. K L. M. represents represents represents represents represents represents represents represents represents represents represents. N represents Matter Generally P represents Inorganie Matter Q represents Organic Matter R represents Formation of Ideas S represents Communication of Ideas T represents Individual Volition U represents Intersocial Volition V represents Affections Generally represents Personal Affections represents Sympathetic Affections represents Moral Affections represents Religious Affections. Relation Quantity Order Number Time Change Causation Space Generally Dimensions Form Motion. W X Y Z.

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(84) TABLE XIII COiWARISON OF RANK ORDER OF FRE'ÛENCY OF USAGE OF DORRELL-SULLIVAN FOURTH-GRADE READING VOCABOLARY CLASSIFIED ACCORDING TO ROGET ON THREE LEVELS OF LEARNING. Rank Order. ?. Same Level. !. T. 1 2. Later on B u c k i n gh am- Do 1 c. —. 4 -i. 8 9. 10 11 12 13 ll^. 15 16 17. 18 19 20 21 22 23. W u R. M. Later on Ttiorndike T. T S. M. u. 1 W. t w R. S. s C. 5. H Y K. K. J. M. U. D z. R. t X. X D F. V L B G E. t. J-. H. Y. B F. F D. ^. V. '. i. E. P. N G V. Z. E. A. B i. N. i N.

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(86) TABLE XIV COivIFAHISON OF HANK ORDER OF FRE(Û"ENCY OF QSAGE OF DURRELL- SULLIVAN FIFTH- GRADE READING VOCABULARY CLASSIFIED ACCORDING TO ROGET ON THREE LEVELS OF LEARNING. Later on Bu c k i n gh am- Do 1 c h. Rank Order 1 2. —. -73. ". Same Level. T. T. W. TT. Later on TnorndiKie. :. m T Q. U. R. Q,. 0 0. K. W M. U. s. s. 6 7 8 9. K. K. u. 16 11 12 13. G D F. 5. C. M. M. R. Y W X H. K c. H. Y. d-. D. H. c. X. lif. J. 15 16. X Y V. L P. '. 17 IS 19 20 51 52 55 2i,. P B L. D F Z V. —. !. 1. Z. E. A N. A N. i '. L ^ G J-. '. P. V B E Z. A N.

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(88) TABLE XV. ORDER OF FREQUENCY OF USAGE OF DURRELL-SOLLIVAN SIXTH-GRADE READING VOCABULARY CLASSIFIED ACCORDING TO ROGET ON THREE LEVELS OF LEARNING COIvIPARISON OF ram:. Rank Order 1. Later on Buckingham-Dolch T. o. w U. k. s. 3. T 6 7 8. Same Level. i. m. !. Later on Thorndike i. m T q o. U. M W. R. M. ^. K. H R. ^. Y. M U w R. D. Y K. 10 11 12 13. H. C. C. D. X. C. K Y. F. Z. Ik. X. X. 15. B. 16 17 IS 19 20 21. E. E F. J". A. L Z G P. 23. V A. 24. N. G. L F H P D V z. J. N P. —f-. E G. i. V. ^ B. N.

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(90) When reading vocabulary is separated into such divisions as illustrated in the previous tables, it is. apparent that there is a considerable amount of change among the rank orders for those categories among grades four, five. and six.. One of the purposes set up at the beginning of this study was to discover how Roget*s classifications were. divided among the words which were learned later for reading;. among the words learned later for writing; and among those learned at the same time for both purposes.. Table XVT. gives the desired information.. TABLE XVI COlvIPARISON OF PERCENTAGE OF USAGE OF ROGET»S CLASSIFICATIONS IN FOURTH, FIFTH AKD SIXTH GRADE READING VOCABULARY DIVIDED INTO THREE LEARNING LEVELS. Classification Existence. Relation. (Quantity. Order. DurrellSullivan Grade. Higher on BuckinghamDolch List. Four Five Six. 1.71. Four Five Six. 1.92 1.93 2.47. Four Five Six. 5.54 4.70 3.29. Four Five Six. .27. 2.77 3.87 3.59. Higher on Thorndike List. Same Level .74 .51 1.05. 1.09. 2.60 1.02. 1.21 1.68 1.16. .48. 1.75. .53. I. ,. 5.58 3.05 4.21 4.83 2.54 4.74. j. 5.69 4.33 4.65. 2.54 2.88 2.03.

(91) •. 1.

(92) TABLE XVI (continued). COMPARISON OF PERCENTAGE OF USAGE OF ROGET»S CLASSIFICATIONS IN FOURTH, FIFTH AND SIXTH GRADE READING VOCABULARY DIVIDED INTO THREE LEARNING LEVELS. cxSLssinca. uion. Number Time Ciiange. Causation Space Generally. Dimensions. Form Motion Matter Generally Inorganic Matter. Organic Matter. Formation of Ideas Communication of Ideas. DurrellSullivan Grade Four Five Six Four Five SIX Four Five OlX Four Five blX Four Five blX Four Five blX Four Five olx Four Five Six Four Five OlX Four Five Six Four Five Six Four Five Six Four Five Six. Higher on BuckinghamDoicn List 1.71 1.92^ o—WW 2.77 3.31. Same Level .74 1.52 1.58 1.86 2.03. 1. T. ^ .29. 1.71 4.14 TOO 1.3/ 4.90 3.04 3*59 3.20. i. '. 1.45 1.92 1.45 2.54 2.64 2.02. eft. ^ A' 1.12 ^. '. .73. .51 i.up. 1.92 1.45. 2.o0 4.57. 4. 4.0. 5. 1. /. g. 4.33. • /'9. 2778. Z. /O. T. 3.55 i.op 3.72 5.58. TOO. 4.2o 5.25. Higher on Thorndike List. i. !. ^ft. 1.45 7.38 5.53. ? .40. 4.'^1. 5. 2 . 13. 2.97 3.05. 3*87 3.85 2.91 8.11 9.62 7 . 27. 1.93. 1. 1 .92. 5.97 4.42 5.48 .64 .28. .53. ^. 3.35 5.58 7.37 1.12. ;. i.4«>. J. '. !. .. J.. 1,28 2.21 1.10 4.69 5.25 5.21 6.52 7.46 6.58 5.76 6.63 7.12. 1. [. 1. '. 2.54 1.05 S.IS 7.61 6.32 5.9^ 7.61 5.79 S.55 6.60 8.95. ;. 1. i. i. .23. .48 .72 .0/. 4.96 2.64 2.32. 10.34 6.69 4.66 3.61 6.40 6.54 6.49 7.85. —.

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(94) TABLE XVI (continued) COMPARISON OF PERC^TAGE OF USAGE OF ROGET'S CLASSIFICATIONS IN FOURTH, FIFTH AND SIXTH GRADE READING VOCABULARY DIVIDED INTO THREE LEARNING LEVELS. Classification Individual Volition Intersocial Volition. Affections Generally. Personal Affections Sympathetic Affections. Moral Affections Religious Affections. DurrellSullivan Grade Four Five Six Four Five Six Four Five Six Four Five Six Four Five Six Four Five Six Four Five Six. Higher on BuckinghamDolch List 17.06 15.19 16,16 7.04 6.35 8,22 2.35 2.49 1.10 7.25 9.12 10.96 2.09 2.76 2.47 4.ifS. 2.76 4.66 1.07 1.93 1.64. Higher on Thorndike List 14.04 13.22 15.12. ,. Same Level 15.61 14.72 18.95 7.43 9.14 8.42. f. 1. ^. .74 1 '. i. i '. ,. \ '. 1. 1.52 .53. 5.95 5.08. 6.84 1.86 4.57 2.11 6.32 5.08 3.16 3.75 2.03 3.16. i. i. 5.57 4.09 6.98 1.45 2.40 2.03 6.78 6.97 6.69 3.15 2.64 3.49 2.66 3.12 5.23 .48 .48. 1.75. Table XVI discloses that Individual Volition, which. holds first place in. ranlc. order of frequency, is used. proportionatly most frequently in the section of words learned later for writing in grades four and five, and in the section where vocabulary is learned at the same time. for reading and writing on the sixth-grade level.. The last. ranking category, Matter Generally, is used proportionately. most frequently where writing vocabulary is learned later on the fourth-grade level and where reading vocabulary is.

(95) r. r.

(96) learned later on the fifth and sixth-grade levels.. The. only category which is consistent through the three grades. On. in the order of greater proportion of usage is Time,. each of grades four, five and six, it is used to the. greatest degree where writing vocabulary is learned later and to the smallest degree where words are learned at the. same time for reading and writing vocabularies.. The. categories which are similar in the respect that they are used proportionately most frequently on one area for the. three grades are: Form and Inorganic Matter used most. frequently where reading vocabulary is learned later, Personal Affections used where writing vocabulary is learned later, and Communication of Ideas and Religious. Affections used where words are learned at the same time. The categories which are similar in the respect that. they are used proportionately least frequently on one area for the three grades are: Intersocial Volition, Formation of Ideas, and Individual Volition used least frequently where. reading vocabulary is learned later; Organic Matter used least frequently where the reading vocabulary is learned later; and Affections Generally used least frequently where. words are learned for reading and writing at the same time. Tables SVII, XVIII and XIX show the percentage of. Roget*s classifications which fell higher on the BuckinghamDolch List than on the Thorndike List; and also those which.

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(98) fell higher on the Thorndike List than on the BuckinghamDolch; as well as those which fell at the same grade level. on both.. Each figure is a per cent of the words which are. learned only in that column of the table..

(99) t.

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(105) !. «. *. «. •. I. I.

(106) CHi^PTER IV. SUMM/IRY. A summary. of the findings of this study reveals. the following things: I. Grade Placement of Vocabulary. A. Tabulation of the Durrell-Sullivan Reading. Vocabulary words shows that: 1. Some intermediate grade. reading words are. assigned the same grade ranks on the Thorndilce. Reading List and on the Buckingham-Dolch Writing List. 2. Some words are assigned higher grade ranks. on the Thorndifce Reading List. 3. Some. words are assigned higher grade ranks. on the Buckingham- Dolch Writing List, B. Analysis of the Durrell-Sullivan fourth-grade. list reveals that: 1. The. majority of words are assigned higher. grade ranks on the Thorndike List. 2. The smallest. proportion of words are assigned. the same grade value on both lists. C. Analysis of the Durrell-Sullivan fifth-grade. list reveals that: 1. There is a considerably smaller proportion of. words assigned to higher grades on the Thorndike.

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(108) list than at the fourth-grade level, 2. There is a. larger proportion of those words. which are assigned higher grades on the Buckingham-Dolch List than at the fourth-grade level. D. Analysis of the Durrell-Sullivan sixth-grade. list reveals that the proportions of words assigned to. higher grades on the Thorndike List and to higher grades on the Buckingham- Dolch List are exactly equal, E. Analysis of the lists for the three grades. indicates that there is a slight increase from grade four through grade six in the proportion of words assigned to the same levels on both lists,. II. Parts of Speech. A. Analysis of the Durrell-Sullivan reading. vocabularies for the intermediate grades indicates that: 1. The noun is the most frequently used part of. speech. 2. Verbs hold second rank. 3.. Adjectives hold third rank.. 4. The remaining parts of speech are much less. frequently used. B. Analysis of the Durrell-Sullivan Lists for each. grade divided according to grade placements on the. Thorndike and Buckingham- Dolch Lists reveals that:.

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(110) 1. Nouns, verbs, and adjectives, respectively,. retain the same. ranlc. positions on each grade for:. a, V/ords assigned higher grades on the. Thorndike List. b. Words assigned the same grade levels on. both Thorndike and Buckingham- Do Ich Lists. 2. The order of rank for nouns and verbs is. reversed on the Durrell-Sullivan fourth-grade level for those words assigned higher grades on the Buckingham-Dolch List. III. Roget*s Classifications. A. Analysis of the rank orders of frequency of. usage of total Durrell-Sullivan vocabularies for each grade indicates that: 1. There apparently is a close relationship. among the rank orders of frequency of usage for grades four, five, and six. 2. Individual. Volition is the most frequently. used category for the intermediate grades. 3.. Matter generally is the least frequently. used category for the intermediate grades. B. There is a definite shifting of the orders of. frequency of usage, when the Durrell-Sullivan words are divided according to grade placement on the Thorndike and Buckingham-Dolch Lists..

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(112) SUGGESTIONS FOR FURTHER RESEARCH 1. Study of the types of words used in children*. books that are of low frequency on the Thorndike List, (They are omitted from this study.) 2. Study of the kinds of words learned in grades IV,. V and VI, when word meaning is taken into account and only the most common meaning is used. 3» Repetition of this study using some other reading. vocabulary than the Thorndike List which resulted in the discarding of many words for this study, 4. Analysis of reading vocabulary with classification. of words in terms of abstractions..

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(114) BIBLIOGRAPHY.

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(116) BIBLIOGRAPHY Buckingham, B. R., and E. W« Dolch, A Combined Boston; Ginn and Company, 1936. r84pp. V/ord. List. ,. Child Study Committee of the International Kindergarten Union, A Study of the Vocabulary of Children Before Entering the First Grade, Baltimore: 1928. 36 pp. Dolch, E. V/., Heading and VJord Meanings Company, 192?"^ pp. 24-59.. ,. Boston; Ginn and. "Side Lights on a Combined V/ord List," Elementary English Review , 14:22, January 1937. ,. Durrell, Donald D. Improvement of Basic Reading Abilities New York: Vvorld Book Company, 1940. pp. 355-390. ,. ,. and H. B. Sullivan, "Vocabulary Instruction in the Intermediate Grades," Elementary English Review , 15:192, May 1938.. Faucett, L. and I. Maki A Study of English V/ord Values Statistically Determined from the Latest Extensive" V/ord Counts. Tokyo, Japan; iviatsumura Sanshodo, 1932. p. 11. ,. Mawson, C. 0. S., Roget's International Thesaurus of English V/ords and rhrases New York; Thomas Y. Crowell Company, 1925. 741 pp. ,. Ogden, C. K., The System of Basic English , New York; Ear CO 'art Brace and Company, 1934T pp. 3 5-64.. Thorndike, E. L., "Improving the Ability to Read," Teachers College Record , New York; Teachers College, Columbia University, 3^:7-125, October, November 1934.. New York: A Teacher's Word Book of 20,000 V/ord Columbia University, Bureau of Publications, 1931. 182 pi .. ,. The Thorndike-Century Junior Dictionary Appleton-Century Company, 1935. 970 pp. ,. D.. ,. New York;. Walpole, H. R., The Nature of V/ords and Their Meanings New York: VV. V/. Norton and Company, Inc., 1941. p. 199 ,. # Boston university '. toool. of Educati(if^.

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(118) Watts, A. F., The Language and Ivlental Development of Children , London: George G. Harrap and Co., Ltd., 1944. pp. 31-225.. Willing, S. v., ^Construction and Evaluation of a Measure of Reading' Vocabulary " Unpublished Master' Thesis, Boston: Boston University, 1940, ,.

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(120) ^5. APPENDIX.

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(128) f7. TO. i. LISTS. DOLCH. ACCORDING. BUCKINGHAM-. VOCABULARY. AND. READING. THORNDIKE. (continued). ON FOURTH-GRADE. A. Thorndike. RANKS. TABLE wrench. on GRADE. Higher. DURRELL-SULLIVAN. ASSIGNED. wreaxn. zone Grades. IN. OF. DIFFERENCES. Level. DIVISION. U <D Same. 0). Xi 0<-P. 0) <D. g«HH (DXJ. 03. t5D-P. 'H. -HOW. O (D-H-H.

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(134) •. LISTS. TO. LCH. DO ACCORDING. BUCKINGHAM-. VOCABULARY. AND. (continued). READING. THORNDIKE. Thorndike. baggage. B. trudge. ON TABLE. FIFTH-GRADE. on RANKS. vO decorate. paddle. yeast Higher. GRADE. Grades. dipper. tunnel. croak. bulb. haul. DURRELL-SULLIVAN. ASSIGNED. o o. H IN. o OF. cjH-PJ:la>+*+3j*laJX>wofH.H0 ol>jida g>»a)-HaJOHoM::Ja>oc5gHfHâj(ij.HffJ oooHcjc!o+3+3+5|4c}(i)(i)00<i)xjx{a>. o o. (D. rH. DIFFERENCES. 1^ DIVISION. tjD. •H 03. i E cd. d. -O id ClJ. rH. p. o. d O. (D. rH. oJ. >>. g H. -P. 3 C. -H H oo© (D+3+>0 o 03 ^< d h -Pdoi-P +3 Vi xiid4^ra(Dd 0) PÔdW^^cd^^lHg<D::^<D(D•Hdol(l)gd:::JO a>.H od © <D-P (U^-PTJ tiOm o d u o o+^'H+^'o <D. Ca. OtlStlD. 'H. 0). HOd ooH a}<Do>H^ft>'OirHHod3t)Df^fHCdîoodoi«»Hd cd. P^fH?Hoaa)<D<DQ)doo-p-PdQ>xj^tddd©«Hô. p^p,P(^^f^f^^Llf^^^0lM0llQW•P^-^+^4a^Jd^>l>>>>.

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