Q I :1 “ .‘I i“: .- ‘ '74 <~i I; i ‘1‘ L . a." u This is to certify that the thesis entitled A Study of the Relationship Between Sociocultural Variables and Geometric Problem Solving Performances of Disadvantaged Children presented by Steven New stat has been accepted towards fulfillment of the requirements for Ph. D. Curriculum degree in Date . fig/52’ o-mo-- TZ'W. 730 3 Met“ ABSTRACT A STUDY OF THE RELATIONSHIP BETWEEN SOCIOCULTURAL VARIABLES AND GEOMETRIC PROBLEM SOLVING PERFORMANCES OF DISADVANTAGED CHILDREN BY STEVEN NEWSTAT The purpose of this research study was to determine if sociocultural variables of socioeconomic status, "father" present in the home, and crowding in the home influenced the learning of geometric constructions by culturally impoverished Junior high school students. A geometry workbook was designed to minimize the influence of reading by presenting each geometry lesson via an audio tape. Each taped lesson was approximately fifteen mdnutes in length and contained all of the necessary information for learning specific types of geometric constructions illustrated in the workbook. In ‘37 :heories were Pedagc zatical coma; theories discu mepurpose of individual dif iifferential 17 these modes to iiscussed. F .EC '93 the various €53 “ eutial for t i'QOQolosy for Tue da: (a .‘4- “hit of the tea In this :eth'ea ~n social In this study a review of the literature pertaining to the cognitive theories of psychology was presented. These theories were based upon Piaget, Bruner and Ausubel. In general, the cognitive theorists attempted to explain the develOpmental learning patterns of the organism. These learning patterns were descriptions of the organism's capability for operational thinking. Pedagogical implications for learning mathe- matical concepts are prevalent throughout the cognitive theories discussed in this investigation. Although the purpose of this investigation was not to study individual differences, some generalizations as to differential modes of intellectual growth for applying these modes to solving mathematical problems has been discussed. Recognition of the capabilities suggested by the various phases of intellectual growth are essential for the development of an adequate teaching methodology for the culturally impoverished learner. The data analyzed in this research study included achievement test scores, course grades assigned by teachers, certain cultural variables, and scores on the test instru- ment of the teaching method being evaluated by this study. In this study the predicted non-correlation between social and familial variables and student achievement correlation: for ccrrela: significance The familial cha. a "father" 1: Systematic e: on the teach: It wo achievement were found. The non-significance of these correlations were determined by a two-tailed t test for correlated means and the t ratio for testing the significance of a correlation coefficient. The results of this study indicated that familial characteristics, the presence or absence of a "father" in the home, and crowding produced no systematic effect upon the performance of students on the teaching method in question. It would appear, from this study, that socio- cultural variables are not correlated with students performance on the test instrument; and vocabulary deficiencies are not a barrier to successful learning when the disadvantaged child is presented with a teaching methodology that does not emphasize reading skills. Further research should be focused on environ- mental variables and their relationships to physical characteristics, personality development, achievement data, and any changes in the socioeconomic status between infancy and adulthood. This chain like cause and effect relationship, between the disadvantaged child and his environment, should provide further nierstanding t: that would over; social deprivat; understanding toward the develOpment of a curriculum that would overcome the multilateral influence of social deprivations on learning. A STUDY OF THE RELATIONSHIPS BETWEEN SOCIOCULTURAL VARIABLES AND GEOMETRIC PROBLEM SOLVING PERFORMANCES OF DISADVANTAGED CHILDREN A DISSERTATION SUBMITTED TO THE FACULTY OF INSTRUCTIONAL DEVELOPMENT AND TECHNOLOGY OF THE COLLEGE OF EDUCATION OF MICHIGAN STATE UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY STEVEN NEWSTAT OCTOBER, 1972 COPYRIGHTED BY STEVEN NEWSTAT 1972 ii I would Charles F. S Of my reseax doctoral co: S‘NGIES in . program. I would enc‘mmiiéeme Possible tit years. 501 which has I ACKNOWLEDGEMENTS I would like to express my appreciation to Professor Charles F. Schuller for assisting me in the completion of my research study. I am indebted, as well, to my doctoral committee who aided and guided me in my studies in educational theory during my doctoral program. I would also like to thank my parents for their encouragement and timeless cooperation which made possible the completion of my studies over the past years. Both they and my wife have provided a model which has been a constant source of inspiration. iii ,Hr‘y‘yvv n n“.- lr| L.;.‘\UNLJ.DJ§_'*. LIST 0? TABLE; Chapter 1. IN ‘A‘Vh- Purpog Need 1 TABLE OF CONTENTS Page ACKNOWLEDGWNTS O O O O O O O O O O O O O O O O O O O O O O O O O O O 0 0 iii LIST OF TABLES O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 0 0 v1.1 Chapter 1. INTRODUCTION Purpose of the Study.................. 1 Need for the Study.................... 4 References CitedOOOOOOOOOOOOOOOOOOO... 16 2. BASIS FOR THE STUDY The Disadvantaged Child............... 20 Euclidean Geometry as a Basis for Research Material Used in this Study.. 2h Birkhoff and Beatley's Geometry....... 25 THEORIES OF COGNITIVE PSYCHOLOGY RELATIVE TO THE DESIGN OF THE STUDY The Geneva School................. 27 The Harvard School................ 30 iv a I I n _ Teach, advan“ Refere RESEAE Samplg The I: Data L Evalu: Bella: Stands the Te Test \ StanE The "t ReseaI Refere David Ausubel..................... Teaching Mathematics to Dis- advantaged Children......... ..... .... References Cited........ RESEARCH DESIGN AND SAMPLING PROCEDURES sample sectionOOOOOOOOOOOOOOOOOO0.0... The Index of Socioeconomic Status..... Data Gathering Procedures.. Evaluative Instrument................. Reliability of the Instrument......... Standard Error of Measurement of thevTestOOIOOOOOOOOOOO00.000.00.000... TeSt validityOOOOOOOOOOO. ....... 00.... Statistical Procedures...... .......... The "t" TeStooooooooo Research Hypotheses................... References Cited.... 33 3A 47 57 58 61 63 67 71 72 73 76 78 80 whammy , CONCl Concl Reco: APPENDIXES A. Socic 8- Quesq C' Geome D ° Pre-a E. Scat: RESEARCH FINDINGS The Research Hypotheses and the FindinESOOOOOOOOOOOOOOOO00.0.0 00000000 83 References Cited...... ...... . ........ . 98 5. CONCLUSIONS AND RECOMMENDATIONS Conclusions........................... 99 Recommendations............ ......... .. lOl BIBLIOGRAPHY.................... ....... ....... 106 APPENDIXES A. Socioeconomic Index................... l3fl B. Questionnaire......................... 1A3 C. Geometry Workbook..................... 150 D. Pre-and Posttest...................... 199 E. Scatterplots.......... ..... ........... 200 vi A... -C IllII-IIIH HI . u .. l c a n n. F» M. r.» .L .6» v. o 5. Tc .1: Au ... . i P .C n. it P In P G a P it .2 Ag “G 2.. a,“ n. S h; .9 n. no h. F. .n. nu AG r.“ n .v f,“ w). 0 n 0 A.» 0 e 0 WV.» Q» 0 Q.» ”L in . nC fr. 33 n9 TI h» b. . C N. . C LL uh. 0v we... nu .JI‘ n1,“ .(0v .5. .nNH fr” 710 FV! Table LIST OF TABLES Analysis of Variance of 10 Items in Geometry, Administered to 100 StudentSoooo 000000000000 ..0.0....00000 Analysis of Test Instrument by Item... Analysis of Mean Scores of Test Data.. Correlations Between SES and Test Instrument.00.0...0. ...... 0.0.0....... Correlations Between Father and The Test Instrument....................... Correlations Between Crowding and The TeSt Instrument...00000000..0.00..0..0 Correlations Between Verbal Achievement by Grade Level and The Test Instru- ment0000000000..0.000..000000000000000 Correlations Between The Test Instru- ment and Mathematics Achievement by Grade Level..00000..........0.0.00000. vii Page 70 75 814 88 89 90 92 9M O ua/ "fl .Jo lO. Correlations Between The Test Instru- ment and Mathematics Grades........... Correlations Between The Test Instru- ment and English Grades............... viii 96 5, A” E V amt? 0* ” H' a 9"“ I . ' a...-\3V‘* - (I R was-..“ .‘0 d. 1“ u": “h Au: “0:sz or ”I C :c‘és'h 4'" I ‘ x .n .— &¢.-m-“ 0 9:11 .tcial defend V‘ Per mom i“ Eadie-4 4- ' vu to 112‘: iicajvaur; Chapter I INTRODUCTION Purpose of the Study The educational achievement of the disadvantaged student is a product of a variety of factors such as apti- tude, perserverance, experience, motivation, and intelli- gence. It appears from a review of studies concern— ing major psychological theories and related research findings that most of these factors are influenced by the conditions of the disadvantaged child's environment. Other factors such as motivation, the ability to learn, and maturation were also affected by certain 1 environmental conditions. The research studies by Irwin, Gould,2 and Jordan3 demonstrated the influence of the en- vironment as it applied to the achievement motivation and educational behavior of the disadvantaged child. The social demands for educational achievement, parental as- pirations for the educational accomplishments of the child, peer group influences, and other environmental conditions tended to influence the educational achievement of the disadvantaged child. _ _ c m. : . A: .»u D» e .2 a. I . a. C .5” h” at a. “a ab 7 a a; a. .. .nu «Nu Iv .1 Q}. n... HIRE-vi, . It . .4 w. L . .env acnieve. The intellectual deveIOpment of the disadvantaged child, which contributes to his educational progress, is also influenced by the characteristics of his environment. Piaget observed that ”intelligence can be conceived as consisting of a series of attempts, inspired by implica- tions that regulted from them but selected by the external environment.“ Hebb concurred with Piaget when he observed that the early experiences of the disadvantaged child may 5 influence his basic learning abilities. The research findings of Deutsch,6 Coleman,7 Newton,8 Bruner9 and others demonstrated that the environ- ment produced a multilateral influence on the educational achievement of the disadvantaged child. The environment influenced his potential academic achievement directly by determining the kind and quality of educational experi- ences. At the same time, it also influenced the disadvan- taged child's academic growth indirectly by conditioning his motivation for learning and by stimulating his develop- mental and maturation processes. It is, therefore, im- portant to ascertain information concerning the influ- ence of the environment upon the academic achievement of U - fl .5" .. 3 n L . a“. “U. Ma. 0 E VUSV CORGI d. 33 S 5 “an ' \I F quI #2.: bu; re C. a» . x .F. N . h. .3 .n. C at “w go it +c aw 1i 0 0 1A 0 hs .n . nu. .5 F .O 9 .C e m i .f. u. ‘ a 5.. h. n Liv e a» VI :. «0 AU «6 ad .nu nu n. .s. n» HI. nu Hu 0» D. we Cu VJ +b .l. ‘U Awe .n u a A... at .. . . . «O “a to rd L . W. A... T a . v n .3 :,. a . fly at «xv QC .WL wk ANA-I1!" 3! var ‘ls...v-I4kd the disadvantaged child in order to better understand his educational behavior. In this study an Index of Socioeconomic Status (SES) will be utilized to determine the type of environment in which the population, used in this study, was raised. In order to study the multilateral influences of social deprivation on learning one would have to include both cognitive and psychomotor experiences. The environmental conditions which met these dual criteria were then viewed as social deprivations and comprised the variables which were combined into a composite SES score. The particular variables selected for this study and their mode of combination will be discussed in a later chapter. The purpose of the present investigation was to explore the educational environment in terms of specific ongoing processes and forces that may be related to the educational achievement of the population under investigation. It involved the identification and measurement of environmental factors in terms of general I ‘_ - ins.ru~€nt- a. +u h. «9 . .1 a. D. o.‘ g e 0:17.: ei. 0 ‘ EI‘EI’IC .voVoIU ’1 Hr; A .L- O of re. 6 env: : e V 5 st ,n'r ‘ . a ‘3- 6 “'0‘- .... All 3‘.H status characteristics such as social class, and father's occupation as they are related to performance on the test instrument. Need for the Study This research study concerned itself with aspects of environmental factors that influence the academic achievement of disadvantaged children. The environment was studied in relationship to its influence on verbal learning and intellectual achievement. The more constricted an individual's social frame of reference and the greater his distance from the cultural mainstream, the less meaningful and the less effective are the dominant cultural values that impinge on the disadvan— taged learner in the schools. Thus, the behavior of a disadvantaged child becomes less interpretable by standard— ized measuring techniques, as these techiques are more foreign to hislgocial frame of reference. Gordon stressed that if psychological appraisal is to concern itself with the problems of educational A y Q.‘ 0121’ 0033‘: s: S ar‘.’ .n. J 1531"}: at .C E .. a: A; .A ... t ~ u as P. t ad 13:. l a; s A.“ a r 2 a. E S O S C .7. a; .1 ":h “r“ fin‘ u. . .11. A: ha nlu Hi 2. "V x .. O «.J Wu :3. no. :4 n“ flan a a: .5 V 441...... all 5.! -.. Ell—V. r101 5.921391: '9 planning for the socially disadvantaged, researchers should concentrate on the development of new teaching instruments and techniques. They would provide education- al planners with the means to evaluate potential for learning, styles of learning, and patterns of learning disabilities. Such a procedure, according to Gordon, would make the appraisal process one of qualitative analyses rather than of quantitative assessment. He advanced the position that it is through qualitative appraisal that the educator will gain prescriptive direc— tion for ameliorating the learning difficulties encountered by disadvantaged children as they progress through school. It must be recognized that cultural deprivation and educational deprivation are not necessarily mutually exclusive, but may reinforce one another in a negative manner. Thus, the result for disadvantaged children is usually a cumulative deficit in learning. According to Kenneth Clark, 1. ... r“ o I“ . go.* 3 r” n. 0 Au 4; e H H a. e. 9. n. 3 e ”a a m S C a. T. ._ Z a e a a. .3 T f «I. n. Au .ns ad 1 .73. C ab .1. e my. D» .nl. .2 Flu. “i c ‘U a: O 2. ‘b n. a» 9 .u C .I. n n e e a» .ru .3 ‘1 .r« J a. 3 A v fl. HA— C» 6b v a . . . Li... L. __.e :_ a. ;\ s. s a u n s e s e i .1 r. 0 v 1 i d .r. n i r d f i 9 *9 cl ‘1‘ Q.— .slv 0L 1. V 3‘ P a; n... y- o . ..v e E i .3 .3 .f. .w... o 6 ma t r. t 3 S a .l S a .3 .C .1 .n... fv mu 1 U. Q» 96... t at a k .. t V . . . low-status minority children [are] literally abandoned by our public schools, in terms of any meaningful definition of the term education, are suffering from a pattern of unresolved educational problems. But the data support the fact that the retardation is cumulative; that the longer the children remain in school, the further behind they fall in the basic subjects. 11 The learning environment of the disadvantaged student has been described by Ausubel as one that lends credence to the cumulative deficit theory. According to Ausubel, His cumulative intellectual deficit is almost invariably, in part, the cumulative impact of a continuing and consistently deficient learning . environment. . .Thus, most of the lower—class child's alienation from school is in great measure a reflection of cumulative deficits of a curriculum that is too demanding of him, and impaired self- confidence that he must bear.12 Deutsch concurred with Ausubel when he observed, . .that when a disadvantaged student broadens his environmental contacts by going to school, he is made aware of his inferior class status and this has the same depressing effect on his performance that his inferior class status had all along. 3 Furthermore, it has been shown, statistically, that the longer a disadvantaged student remained in -‘\ 7‘ -V-fln- an-‘O talc ernstei. 2 a 7&9“” v u a -o -..o v-» Lilithwn ., «o «b nu 14 school, the lower their tested reading ability becomes. The theories advanced to account for this cumula— tive learning deficit are usually based on the concept that the educational materials require greater environ- mental and cultural experience than is possessed by the culturally disadvantaged student. Deutsch stated that,, . . .it would appear that when one adds four years of school experience to a poor environment, plus minority status what emerged are children who are apparently less capable of handling standard intellectual and linguistic tasks.l5 In a study by Milner it was found that a lower- class life results in a restrictive use of language.16 Bernstein has described this language as following a restricted linguistic pattern that hinders the development of an extensive functional vocabulary which keeps thought at a low level of conceptualization.l7 The importance of these different orientations to language was that the culturally disadvantaged student was not as equally suited to school instruction as his middle- class counterpart. Almy and Chittenden have determined v .x u... a» w 1.. S .1. .au a» . . a g. 8 Q . e. 1 a .«AV “I. Nu 5W n3 0 fl. .rv m!” w 5* ad V. .r” 5 Ltd .«a $9 0.. a v 1. AG 1 SO"“C€S «C ”A . I‘V'n... Q L... ‘..\ re «C u A o i r . . C i Q a i t that the cognitive performance of disadvantaged children 18 is markedly inferior to that of a middle—class student. It would seem reasonable, therefore, to assume that a dis- advantaged youth upon entering school with these limited resources is going to find learning a frustrating experi- ence unless the schools deve10p educational materials designed to overcome these deficits. In a study by Coleman et. al. it was shown that there was reasonable convincing evidence that the home background of students was a major determinant of their 19 expected rate of progress. Deutsch tended to agree with this finding when he concluded from his study that Children with deficits in learning and cognitive skills should be approached with methods to learn skills that would have been used at an earlier time had they not been disadvantaged in either their home or school environment. Unless these differences are realized, the culturally deprived student will derive little of educational value from the years spent in public schools. I n.‘- --e A‘A .3 e .hu ...A. K» . 'l‘h 5“ 4-11.." ...- .3 vl/n .44. it: C) x. _. ““g ... The disadvantaged child was characterized by Beilin and Gotkin as being enactive and less able than the middle- class child to deal with concrete materials, and much less with their pictorial or schematic repre— sentation. . . the disparities become greater as the middle-class child acquires competence in the symbolic reasoning while the lower—class youngster continues to struggle with concrete materials. . .21 Whiteman tended to agree with this point of view when he observed that, The lower achievement level may even feed back on the slower development of the originally lowered cognitive skills. A series of interactions between underlying abilities, overt achievement and inward self-confidence may take place resulting in lower abilities producing lower achievements, and inducing diminished self—confidence, which in turn feeds upon achievement and so on.22 These deficiencies in cognitive and psychomotor experiences make it more difficult for the disadvantaged student to comprehend and successfully compete in a curriculum which presupposes a variety of cognitive and verbal experiences which disadvantaged students often do not possess. The learning difficulties encountered by the socially disadvantaged student are often characterized as .: t-A" 3-.3 cu“ ‘n ”‘3 J... S- 'p,‘ y,oy‘1'n 1....0'u-.-.‘ fi“: ivc‘ u-v ‘I ‘ *no fi‘ncnngH V..U UnhyLam ~.4. ‘ J "”1 ‘I‘ ‘ - - . ”a: 19”.; '3'\ “my d...»v-v¢ —. o < ”‘q 3' ‘1‘: n - Aagag “O ‘4 . H Q q. W uv»,‘~ V. ”-S e". :_ 'R an' . F“ 7.. “ V.-.al m I“ .c A «'- H lO 'beaing somewhat universal in nature. That is, all individuals agretin some manner intellectually, socially and culturally inmpoverished. This viewpoint does not recognize that there £1143 intellectual and social characteristics unique to the disadvantaged youth. An impoverished environment resulted in what Jensen hens labeled a ”higher threshold” for verbal mediation.23 TTnis would mean that the disadvantaged youth, as a result of liis experiental background, is less able to solve problems by wrerbal mediation than would be true of a student with gre21ter language experience. The potential importance of thijs for learning cannot be overestimated, in view of the fact: that mathematical problems whose solutions were facili- tatead by verbal mediation were not limited to verbal problems, or eaven to problems verbally stated. In many so-called non- vertnil tasks verbalization plays an integal role and many Imnraverbal problems are solved with the use of verbal mediation. Human learning is sufficiently complex to justify the development of alternate teaching strategies for no single apprc to accommoda' by students educational curr of experI cannot t as much disabil: child. fie skil baCkgI‘ou should b Which wi 0f the c directed deficit, Bloc What We have tim1to find master the S meet this Oh curriculum Ci 11 single approach is likely to have sufficient sophistication to accommodate all the varied cognitive patterns employed by students and their teachers. In general, compensatory educational programs involved curricula which simply present a cafeteria of experience which do not include some direction, cannot be expected to succeed - or to accomplish as much in ameliorating the school learning disabilities manifested by the disadvantaged child. Therefore, the evaluation of the speci— fic skills and deficits of children from varying backgrounds should continue, and the attempt . should be made to devise curricula and experience which will be consistent with the current skills of the child and which will be effectively directedzfioward his growth in the areas of deficit . Bloom maintained that "most students can master what we have to teach them, and it is the task of instruc- tion to find the means which will enable our students to master the subject under consideration."25 In order to meet this objective, Bruner believed that the format for curriculum designs should begin with a theory of instruc- t1°n sPecifying Ills... _..I. E d a. a... T 3 n. 1* o‘.‘ .1 b n L 0 ad a. . .Azu .. v +9 In..|n..|||.nr I1. at 318 t n t upo St eve: ~5:. . A «v: l2 . . the ways in which a body of knowledge should be structured so that it can be most readily grasped by the learner. . .since the merit of a structure depends upon its power for simplifying_information, for generating new propositions, and for increasing the manipulability of a body of knowledge. . . A theory of instruction should specify the most effective sequences in which to present the materials to be learned.26 One difficulty in determining this body of knowledge was the failure, for the most part, of educa— tional researchers to plan and conduct empirical studies that included parameters which had a significant influence upon the type of learning being appraised. According to Tyler, the most important of these parameters, and the least evaluated were: 1. the abilities, interests, and relevant background of the students; 2. the extent to which the environment of the school, home and neighborhood encourage or discourage school learning..., 3. the extent to which...program appro— priately fits in with the total pattern of con— ditions required for effective learning.27 Av C a h“. UM Q. 030 Ten ! I“ 1. .‘\ -.E \1 1782"- 10 __,II.||Iu-.|ullfll.9|!r \l.|l .Illeu up. n... .C E H C C .l P. «w .l a P a S C 2.1 P D.~HM n t h; s i i d r a i t .lOUE a... 38.1.4 .nt EEa 0.1 at 13 Brown and Deutsch tended to agree with Tyler's observations when they noted that a sizeable error variance occurred when racial groups were treated as 28 homogeneous entities. Moreover, investigators have largely failed to pursue the identification of specific features of the lower-class environment which are associated with cognitive and verbal development. . .We must identify environmental factors which, when present or absent, can be related to perform- ance on these abilities.29 When the parameters of these environmental factors have been identified viable compensatory education programs can be developed for socially disadvantaged students. Essen- tially, this would involve the writing and filling of educational prescriptions concerning the total process of learning. Such a process involves a sequence in which the student turns his attention to the learning situation, seeks to practice the things he is to learn, obtains guidance as needed in making his efforts successful, gains satisfaction from successful performance and continues the practice until the things become part of his available repertoire. Typically, a learning procedure or device is developed to aid in some part or parts of the learning process but not all of it.30 v: .2 '..~‘ u~h n. .3 .14 .. M... ‘5‘. ..IL 1H Rosner points out that the "areas of intellectual performance which show the least difference in level of performance are those associated with mathematical 31 reasoning.“ Beilin has demonstrated that disadvantaged children are more likely to succeed initially with subjects that are not too culturally laden. . . such as mathematics ggich is relatively more cultural—free than others. Thus, one reference point from which to begin the abatement of intellectual impoverishment of the disadvantaged youth is in the area of mathematics. Mathematics, however, is both an organized body of knowledge and a set of methods of critiquing and extending that knowledge. Both aspects are equally important. Either aspect, or both, may hold transient attention for solving the mathematical problem—at-hand. The mathematics curriculum planner therefore, cannot, select a particular psychologically-based strategy of instruction. He must first identify the terminal characteristics of the subject—matter to be learned.33 These terminal characteristics become the course objectives. Also, the mathematics curriculum designer must specify the student population taking these mathematical courses. Only after this is determined, can the curriculum designer make an appropriate selection of a teaching strategy to be employed. a: _: Lb 2. am. a: 15 The purpose of the present research study was as follows: 1. To determine whether the relationship between specific environmental factors and performance on the test instrument were independent of socioeconomic status. 2. To explore whether some specific environmental factors interact jointly with the socioeconomic status of the disadvantaged child and do thereby affect his performances on the test instrument used in this study. To accomplish the above, a pOpulation of dis— advantaged children in Philadelphia were selected from a Junior High School in a racially encapsulated area. f'“ V'-\. V 7 ~— ~ r . . e a C .3 5.x «CV 5. ~ 16 Chapter 1 REFERENCES CITED 1. C. Orvis Irwin, “Language and Communications,” Handbook of Research Methods in Child Developmggt, Edited by Paul H. Mussen, New York: John Wiley and Sons, 1960, Chapter 12. 2. Rosalind Gould, ”Some Sociological Determinants of Goal Strivings,” Journal of Social Psychology, 13: 461-73, May, 1941. 3. Thomas E. Jordan, ”Early Developmental Adversity and Classroom Learning: A Prospective Inquiry," American Journal of Mental Deficiency, 69: 360-71, November, 1964. 4. Jean Piaget, The Origins of Intelligence in Children, translated by Margaret Cook, New York: International Universities Press, Inc., 1952, p. 358. 5. D.O. Hebb, Organization of Behaviog, New York: Science Edition, Inc., 1961. 6. Martin Deutsch, Minority Group and Class Status as Related to Social and Personality Factors in Scholastic Achievement, Society for Applied Anthropology, Monographs No. 2, Ithaca, N.Y., Cornell University, 1960. 7. J. Coleman, et. alt,_Equality of Educational Opportunity, United States Office of Education, Washington, D.O., 1966. 8. Eunice Shaed Newton, "Planning for the Language DeveIOpment of Disadvantaged Children and Youth,” Journal of Negro Education, 33: 264—74, Summer, 1964. 9. Jerome Bruner, ”The Cognitive Consequences of Early Deprivation,” Sensory Deprivation, edited by Philip Solomon and others, Cambridge, Mass.: Harvard University Press, 1961, Chapter 13, pp. 195-207. NJ. 2. a q a. .1 ‘q.. us. «C A}; o.\ a... u~..\. 5|; “4 p. .v .m. a: no .5 m. a \n. 0; ~‘ 17 10. Edmund W. Gordon, ”Counseling Socially Disadvantaged Children,“ in Mental Health of the Poor, edited by Frank Riessman, Jerome Cohen, and Arthur‘Pearl, New York: Free Press of Glencoe, 1964, pp. 275-82. 11. Kenneth B. Clark, ”Unstructuring Education,” in New Relationships in ITV, Educational Media Council, Inc., 1967. 12. David Ausubel, ”How Reversible are the Cognitive and Motivational Effects of Cultural Deprivation? Implications for Teaching the Culturally Deprived,” Urban Education, 1: 18, Summer, 1964. 13. Martin Deutsch, ”The Role of Social Class in Language Development and Cognition,” American Journal of Orthopsychiatgy, 35: 85, January, 1965. 14. Martin Deutsch, "Social Intervention and the Malleability of the Child,” Annual School of Education Lecture, Cornell University, Ithaca, New York, 1965, p.24. 865. Deutsch, ”The Role of Social Class,” Op. Cit., p. 0 l6. Esther Milner, ”A Study of the Relationship Between Reading and Readiness in Grade I School Children and Patterns of Pattern-Child Interference," Child Development, 22: 95—112, 1951. 17. Basil Bernstein, ”Language and Social Class,” British Journal of Sociology, 11: 275, September, 1960. 18. M. Almy and E. Chittenden, ”Young Children's Thinking: Understanding of the Principle of Conservation," Paper Presented at the Biennial Meeting of the Society for Research in Child Development, Berkley, California, 1963.(Mimeo) 19. James Coleman and others, Equality of Educational Opportunity, United States Office of Education, Washington, D.C., 1966. 20. Deutsch, ”Social Intervention,” Op. Cit., p. 13. TIA l—\ L. y Irv um a... Au} :w AIV ‘6 Q" vOCn {9W , n -n d bfin4 1? J I. 18 21. Harry Beilin and Lassar G. Gotkin, "Psychological Issues in the Development of Mathematics Curricula for Socially Disadvantaged Children," Paper Presented to the Conference on Mathematics Education for Below Average Achievers held by the School Mathematics Study Group in Chicago, April 10-11, 1964, p. 15. (Mimeo) 22. Martin Whiteman, "Developmental Theory and Enrichment Programs," in Environmental Deprivation and Enrichment, New York, Ferkhauff Graduate School, Yeshiva University, 1965, p. 56. 23. A.R. Jensen, "Verbal Mediation and Education- al6gotential," Psychology in the Schoolgj 3: 99-109, 19 o 24. Jerome S. Bruner, The Process of Education, Cambridge, Harvard University Press, 1960, pp. 203—204. 25. Benjamin Bloom, "Learning for Mastery,"Evaluation Comment, University of California, Los Angeles, California, May, 1968, p. l. 26. Jerome S. Bruner, Toward a Theory of Instruction, W.W. Norton Publisher, 1968, p. 41. 27. Ralph W. Tyler, "The Possibilities of Educational Evaluation," in School and the Chgglenge of Innovation, John Burns (Chairman), Committee for Economic Development, New York, p. 81. 28. Martin Deutsch and Bert Brown, ”Social Influence in Negro-White Intelligence Differences," Journal of Social Issues, 20: 28, April, 1964. 29. Ibid., p. 30. 30. Ralph W. Tyler, Op. Cit., p. 83. 31. B. Rosner, Community Socioeconomic Status in Mental Organization, Unpublished Doctoral Dissertation, Teachers College, Columbia University, 1955, p. 71. 32. R. Kelson, New Curriculum and the Teaching of the Disadvantaged, McGraw-Hill, New York, p.’16} 33. Lee S. Schulman, "Psychology and Mathematics Education," Mathematics Education, Sixty—Ninth Yearbook of National Society for the Study of Education, Part I, University of Chicago Press, Chicago, 1970, p. 71. l m 19 Chapter 2 BASIS FOR THE STUDY Factors associated with learning disabilities of disadvantaged children are identifiable but they Operate neither independently nor with a clearly predictable pattern. Future efforts to characterize, identify, and select the socially disadvantaged student must be directed toward the identification of their learning disabilities. This is basic to, and a pre-requisite for, implementing new curriculum developments and experimentation with different approaches to teaching the disadvantaged. This chapter is concerned with Specific research relative to the study as follows: 1. The learning disabilities of disadvantaged children which affect their academic achievement. 2. Sociocultural variables that may account for differences in achievement and learning capabilities 20 within disadvantaged groups. Additional purposes of this chapter are (l) to provide some historical perspective of the test instrument; (2) to present a background of cognitive psychology associated with learning mathematical concepts. The Disadvantaged Child There are different types of disadvantaged children. The group or subgroup in question may be easily identi- fiable, as ethnic groups, or relatively difficult to distinguish as in groups of individuals with common interests, such as an athletic team. Culturally influenced behavior may be formal and deliberate or incidental and subtle. A review of the literature shows that a variety of different terms are used interchangeably when identifying a population as being disadvantaged. Anastasi referred to culturally deprived children as "persons exposed to inconsistent and often incompatible 1 mores, goals, and social pressures." Kerber and as I. .II.II it. I“. ...nmr _..I .... . . .v _( fl ‘1. 21 Smith used the term culturally deprived children but in reference to those who "do not know enough of our cultural heritage, do not have the possession, rewards, competences, or knowledge which are too much taken for granted as given everybody in the American Society."2 Deutsch and his associates used the term minority- group children to apply to the absence of the "home, neighborhood, and school environment that might enable them [the disadvantaged] to utilize their ability and personality pofientials fully."3 Passow has used the term culturally disadvantaged when referring to the economic state in which they live. He also described culturally disadvantaged children, as being synonymous with the following terms: socially handicapped children; culturally different children; culturally impoverished children; children with inferior educational background; children of low social origin; the diverse, low income groups; children of dgpressed parents; and children of depressed areas. Deutsch has observed that the home of a disadvantaged youth is 0 0.” Vol 22 characterized by . . A scarcity . . . of books, toys, puzzles, pencils and scribbling paper. It is not that the mere presence of such materials would necessarily result in their productive use, but it would increase the child's familiarity with the tools he'll be confronted with in school. Actually, for the most effective utilization of these tools, guidance and explanations are necessary from the earliest time of exposure. Such guidance requires not only the presence of aware and educated adults, but also time - a rare commodity in these marginal circumstances. In a study by Ausubel, it was shown that a delay in the acquisition of certain formal language forms resulted in difficulty in the transition from concrete to abstract modes of thought.7 Deutsch found lower-class children to be inferior in abstractSconceptualization and categoriza- tion of visual stimuli. A similar result was found in a study by Bean, who had discovered that lower-class children tended to be relatively poor in visual imagery, abstraction and verbalization.9 The research of Spain10 states, that for the most part, the major difference between the culturally deprived and non-culturally deprived child was the slower increase 23 in the functional use of language by the culturally deprived children. Gordon11 held that all organized patterned behaviors are reflections or interactions between the organism and its environment. Deutsch and Brown,12 found a similar interaction position, and suggested making an analysis of social factors, of social class components, and of the interaction of the two. Huntl3 focuses more directly on the developmental dimension and he emphasizes the hierarchical and sequential arrangement in developing intellectual capacities. Chilmanlu pursued the dimensions of deve10pment still further by suggesting that dis- advantaged children have a pragmatic, concrete and personal style, that is, the style of an immature person. Reissinan15 defines a series of euphemisms such as culturally deprived, educationally deprived, deprived, underprivileged, disadvantaged, lower-class, lower socioeconomic group as interchangeable. He stated that 24 While lower socioeconomic groups lack many of the advantages (and disadvantages of middle-class culture), we do not think it is appropriate to describe them as "culturally deprived" . . . The term "culturally deprived" refers to those aspects of middle-class culture - such as education, books, formal language - from which these groups have benefited. However, because it is the term in current usage, we will use "culturally deprived" interchangeably with "educationally deprived" to refer to the members of lower socioeconomic groups who have had limited access to education.16 Throughout this study, the term culturally disadvan- taged is used according to the definition set forth by Reissman in the preceding paragraph. Euclidean Geometry as a Basis for Research Materials Used in this Study_ Euclid composed the Elements, in which he col- lected many of the geometric discoveries of Hermotimus, Pathagoras, Eudoxus, completed many of the theorems developed by Theatetus, and supplied then irrefutable mathematical proofs of geometric concepts which had1 not been mathematically proven by his predecessors. The logical structure of Euclid's Elements fulfilled Aristotle's desire to develop a science based 25 upon the "primitive elements, on definitions and axioms."2 Each of Euclid's thirteen books began with newly introduced concepts. The first book was divided into the following areas: (1) the primitive notions of geometry (point, line, surface, angle, boundary, and figure), and (2) the basic geometric figures (right angle, acute and obtuse angles, triangle, circle, quadrilaterals, and parallel lines). These explanations were followed by the postulates, and then by the axioms. Together, they comprised the mathematical foundation upon which Euclid developed a theory of geometry. This foundation (Book I) served as a base for the material utilized in the test instrument employed in the present investi- gation. Birkhoff and Beatley's Geometry_ Generally, the format of a geometry course has followed the pattern established by Euclid over two- thousand years ago. Throughout history mathematicians have sought to modify and clarify Euclid's geometry in an 26 attempt to make its mathematical basis more rigorous. The past century has seen considerable improvement upon Euclid's treatment of geometry with the emergence of alternative systems. Perhaps the most significant attempt to structure demonstrative geometry was undertaken by George Birkhoff and Ralph Beatley.l Beginning with an article in 1930 in the Fifth Yearbook of the National Council for the Teachers of Mathematics entitled "A New Approach To Elementary Geometry" and culminating with the publication in 1940 of the textbook Basic Geometgy, they presented a logically sound elementary system of geometry which provided an alternative approach to the teaching of traditional Euclidean Geometry.2 This approach was the basis for the workbook containing the geometric constructions used in this investigation. Theories of Cognitive Psychology Relative to Teaching Mathematics The purpose of this section of the study is to review the literature pertaining to cognitive psychology as (DOD—‘- 27 it applies to the teaching of mathematical concepts to disadvantaged students. The importance of psychological theory, as it is related to learning geometry, is that it 1. Can provide information as to the nature of each act of learning and the conditions affecting it. Each act of learning contains . . . the whole problem of learning. 2. Can formulate an economics of learning, that is to say, a theory and a practical art for selecting optimal rates and order of presentation when there are several or a large number of items to be learned.1 2 Beilin and Gotkin suggested that the mathematics curriculum for disadvantaged pupils be subjected to a cogni- tive analysis in order to know what is to be taught and what behaviors and cognitive processes the disadvantaged learner is assumed to have in order to cope with mathematical problems. According to them, . . . the disadvantaged child who is lacking in most cases the relevant cognitive structures or the symbolic means of representing his eXperience, may PIKDfit from being provided with approgriate logical models or problem solving strategies. 229 Geneva School The Geneva School was represented by Jean Piaget. His theory was closely associated with the study of mathe— matical, learning. Piaget's theory of cognition supported their 28 4 5 6 by the works of Flavell, Furth, Sigel and Hooper, can be interpreted as a group Of three theories: a metatheory, a stage—independent theory, and a stage dependent theory.7 The stage-dependent theory is relevant to the mathematical concepts used in this study. Stage-Dependent Theory. As a stage-dependent IB' theory, Piaget's work embraced the nature of the human learner, the nature of knowledge, and the nature of the general development of the learner. This theory provided the human learner with inborn structures, capable of a limited number of perceptions.' This was considered as an Operational mode common to all living organisms in their interaction with reality. This Operational mode can be interpolated to the area of geometry. To assist the disadvantaged child in solving the construction problems in the workbook used in this research the psychological principles discussed above were incorporated in the design of the material. «no .nlv 310V 1. «Q Q ,s c.” 29 These materials were designed to encourage the student to move from the stage-dependent theory to combinatorial analysis which resulted in his ability to seek solutions to geometric constructions by deductive reasoning. Formal Stage Theory. Research by Inhelder 9 and Piaget on the reasoning capacity of children of particular ages has led them to the conclusion that development of the capacity for hypothetical reasoning or formal aspects of logic began at about age eleven. In a study by Hill1 it was shown that children between the ages of six and eight had a considerable intuitive grasp of many principles of logical inferences. In addition, these children demonstrated their understanding in reasoning from hypothetical premises. Her results also indicated that simple demonstrations improved children's performance in recognition of valid inferences. A study by Yudin and Katesll investigated concept attainment of adolescents. Their findings were consistent with Inhelder and Piaget's assertion that the age of 3O twelve is the beginning of formal Operations. The educationally disadvantaged individuals did not begin to fully employ formal operations until the ages of fourteen to sixteen but did show significant gains during these two years though equilibrium was not yet attained. Factors of culture, socioeconomic status, and formal education, are recognized as variables which can promote or deter educational develOpment and Specifically the develOpment of the capacity for hypothetical reasoning. The Harvard School The Process 9£_Education, a report by Jerome 12 Bruner became the focal point for the learning by discovery approach. Although Bruner's theory was not original, he managed to embody the letter and spirit of the reform movement to renovate mathematics education during the decade of the 1950's. These talents have enabled Bruner to present educational theories in a manner which have had a pervasive influence on the 31 contemporary educational scene. While recognizing that these theories were not new, it is still important to realize that they are significant and challenging to the teaching of mathematical concepts. Bruner's concept of knowledge structure was related to the writings of Alfred North Whitehead.l3 His educational psychology about learning by discovery was based upon Piaget1 and included ideas from the 15 16 writings of Dewey, and Scott. Bruner classified the modes Of representation as enactive, iconic, and symbolic. These three learning sequences designated ways in which the learner made discoveries which were necessary for the teaching of transferrable principles and processes. The deficits in symbolic representation and language development are reflected in studies of concept development in disadvantaged children. Concept formation in disadvantaged students has been found, by Reissman, as being content-centered rather than form-centered and whose reasoning has been described as more inductive than gene DPEC effe ch11 the ; t . in: Lacs. 5? B: the I: i '0 1e 32 17 deductive. This conceptual style was reported by Gordon18 to limit the child's ability to make accurate generalizations from the Specific to the general and to transfer knowledge utilizing previously learned concepts. Although Bruner did not concede the necessity or the possibility Of linking specific age limits or deprivation levels to these representational modes, he generally compared his levels to Piaget's stages of preoperational, concrete, and formal intelligence. According to Bruner, any subject can be taught effectively in some intellectually honest form to any 19 child at any stage of development. Bruner emphasized the kind of processes learned by the student, in contrast to the specific subject matter 20 taught, that is, "knowing is a process, not a product." Peel21 discussed the learning strategies reported by Bruner, Goodnow and Austin. He recommended instruction which recognized individual differences and suggested the possibility of develOping a new strategy appropriate to learning formal mathematical operations. 33 David Ausubel 22 The Theory. Ausubel recognized the careful sequencing of instructional eXperience so that the teaching of any mathematics unit was clearly and logically related to the units that precede it. His theory of learning concentrated on meaningful learning requiring that the learner utilized a meaningful set and that the material learned have potential relevance for the learner. The characteristics of a meaningful learning set included the ability to relate new material to correspond- ing features of existing cognitive structures and the capacity for incorporating the various relationships of the new material into present cognitive structure. For new material to be learned, a more general concept must already have been incorporated into the cognitive structure. These principles were some of integral features of the test instrument used in this study. Ausubel23 conceived of the cognitive organization of meaningful learning by the learner as a hierarchical system. Rote learning resulted from materials not inherently meaning- vPU Lb .r.\ CL 19 ac . n-“ . I . C . n C QM 1 g a e t - ... .1: ,. a ~19 ll? 1-! l4 34 ful, or at least not meaningful to the learner, or with potentially meaningful materials not approached with the prOper learning set. This notion was similar to Hunt's theory of learning. He proposed that learning tasks can be divided into those which require complete information transmission (rote learning), information reduction (concept learning), and information production (probabilistic learning).2u The arrangement of curricular materials can be governed by Ausubel's subsumption theory, a theory which assumed a hierarchical organization of knowledge.25 Ausubel suggested the use of advance organizers prior to each unit and subunit. These organizers would contain the particular unit which they preceded; they would be general in nature and formulated in terms familiar to the student. These principles were incorporated into the teaching methodology employed in this study. Teaching Mathematics to Disadvantaged Children A theory of developing cognitive structure was oriented toward providing the disadvantaged learner with l! (5.1.... J1! I .Q .. 35 a logical structure which he may apply to a variety of mathematical relations. These relations would be develOped in a logically ordered fashion so that the disadvantaged student acquires fundamental logical principles in a sequential order gradually developing more complex and SOphisticated mathematical skills. Such a procedure would allow the disadvantaged child to "bypass the Often arduous and frustrating task of attempting to discover mathematical principles which come more easily to middle—class children (who have considerably broader referential systems)."1 To overcome the disadvantaged student's achievement deficit on tests measuring cognitive ability, the school, being the primary method of socializing and teaching the disadvantaged youth, must also accept its own failures whenever any such child fails. TO ignore this fact means that the school will only tend to increase the achievement deficit and further impoverish the intellectual talents of the disadvantaged youth. 2 Martin Deutsch, in his study concerning the social milieu of the disadvantaged child and its effects upon the that skilj Bald} 36 learning process, concluded that the lower-class child enters the school situation so poorly prepared to produce what the school demands that initial failures are almost inevitable and the school eXperience becomes negatively rather than positively reinforcing. Educators must not allow themselves to believe as self-evident and self-fulfilling the cumulative- deficit theory. Instead the schools must undertake to decrease this intellectual impoverishment Of the culturally disadvantaged. According to Cynthia Deutsch, Environmental background factors can be very important in the training of problem solving abilities and that these underlying skills are most crucial in the learning process in school. It has been shown by Piaget, Baldwin, and others that conceptual thinking and fundamental problem solving skills begin to develop during the early preschool period. Baldwin summarizes Piaget's findings as follows: '1’ ,m,,. ‘Lu- lrl'le;" ~—~ 37 After infancy the cognitive development of the child consists largely of the develOpment of conceptual schemata. At the end of infancy he can exhibit the behavior that follows the simple logical rule. . .The course of the development of this conceptual schemata is from the specific to the general. The child first recognizes relationship in the one situation, then gradually generalizes until finally it becomes an abstract schema. Nelson observed that "children as young as three years have the ability to use a simple form of rational learning, and they can discover the rational organization of the learning problems with which they are confronted." These evidences suggest that the higher cognitive processes and mental skills which are very important to learning begin to develop at a very early age, much before the child begins to go to school. Consequently, the intellectuality in the home, the kind of complex and challenging environment provided to the child in the home contribute to the development of these abilities and skills. The influence of the home in this respect can continue even after the disadvantaged child begins formal schooling. 8 Bruner,6 Sigel and McBane,7 and Bernstein have shown that the home environment plays a very important n. ....; n~——-———-~—-——-—— m-m- —- role 1 a part school the k1 at the 38 role in the development of the child's verbal facility as a part of the socialization process much before he enters school. The quality of his language usage depends upon the kind of language models available to him in the home at the initial stages of his language develOpment. The cognitive development of disadvantaged children is not as adequate as that of their advantaged peers. Weak— nesses in language, limited range of cognitive and verbal experiences, and restricted stimulation of an intellectual nature all produce certain cognitive deficiencies. In particular, culturally deprived children seem to have special difficulty in developing concepts of an abstract generalizing nature. Empirical evidence supported the notion that school achievement of disadvantaged [children] is characterized by a cumulative-deficit phenomenon. The children begin school with certain inadequacies in language development, perceptual skills, attentional skills, and motivation. Under the usual school cur- riculum, the achievement pattern of deprived children is such that they fall increasinglg behind their non- deprived peers in school subjects. These cognitive deficiencies become most evident in the later elementary and Junior high school grades when the 39 subject matter typically requires such abilities. In a cross-cultural study of the acquisition of 10 arithmetic concepts, Montague found that lower—class students performed better in mathematics than in reading. 11 Deutsch also found arithmetic scores to be higher than reading scores in a population of lower-class children. Both of these researchers tended to agree 12 with the early finding by Siller that disadvantaged children are most proficient in such academic areas as arithmetic. 13 in Davis and Jensen have shown that status differ- entiations have the effect in varying degrees of defining and limiting the intellectual environment of the dis- advantaged student. They maintained that SES was an important factor in determining the development of mathematical concepts. Findlay and McGuire15 found that children from lower status backgrounds eXhibited a lower degree of’problem solving capacity than higher status children. l6 17 18 Studies by Deutsch, Newton, Montague, 19 20 21 22 23 Dunkley , Dutton , Binkley , Searle , Skypek , Statu cone: ObSEr child abstz to d: tevwn. 36am j13a proc! DPOO: #0 2H 25 Wahlstrom, and Erickson investigated the relationship of socioeconomic environment and mathematics achievement. They found that the lower the level of socioeconomic environment the lower the school mathematics achievement. This relationship indicated that children from low socioeconomic background had a scholastic handicap in direct prOportion to the degree of their disadvantaged status. 26 27 Davis, Lorge and Thorndike have found that low status children tended to Operate, as a group, at a more concrete level than do high status children. They observed that the early deprivation in the disadvantaged child's development resulted in a lessened ability to form abstractions and that limited verbal develOpment is related to difficulty in learning mathematics. Mathematics instruction should be considered in terms of matching the proper instructional module and teaching strategy to the unique characteristics of the disadvantaged learner. According to Dode, this matching process is very difficult because there " is no decisive proof'that any particular teaching method . . . will -.>v——-_.4_... Q-‘l'\t guara; so fa: H1 guarantee better results than any other method or philosophy, so far as achievement is concerned."28 Instead, it becomes a matter of determining the most effective learning sequence and combination of the instructional methods necessary for solving different types of mathematical problems. Ralph Heimer observed that such a determination is very complex because "the extent of substantive knowledge about construction of efficient instructional sequence in mathematics is at present desperately sparse."29 Moreover, Suppes, Hyman and Jerman concurred with Heimer when they observed that "in the cognitive domain mathematics provides one of the clearest examples of complex learning and performances, for the structure of the subject itself provides numerous constraints on any adequate theory."30 Kruteskie31 has identified the two general components of mathematics learning as a visual image component and verbal-logic component. He established that there was a marked relationship between the ability to perform well in mathematics and the ability to deal with N2 symbolic and abstract representations of problems, whether verbally or non-verbally. Havighurst tended to agree with Kruteskie when he observed that "the difference between the socially disadvantaged and the mass majority is less on tests of certain non-verbal skills than on tests of more verbal and abstract abilities."32 This relationship is further enhanced because disadvantaged children do not show a deficit in the conceptualization task in its performance aSpect.33 Thus curriculum materials specially designed for the disadvantaged child should prove superior to materials designed for "average" students. Reissman observed that visual aids are "useful for eliciting the special cognitixe style and creative potential of deprived children."3 Newton tended to agree with Reissman when he observed that auto-instructional devices enhanced the learning environment of disadvantaged children because "they favor concrete, stimulus—bound cognitive processes which involve learning." ‘43 Jerome Bruner, emphasizes the kinds of processes learned by the student, rather than the specific subject- matter products he may acquire. This idea was reflected in his statement that We teach a subject . . . to get a student to think mathematically for himself. . . to embody the process of knowledge-getting. Knowing is a process, not a product. Bruner, in The Process of Education, states that the development of cognitive strategies are enhanced by providing the learner with intervening opportunities for trial and error in solving problems. This kind of exposure will increase the intellectual and social inter- change between teacher and pupil. Robert Gagne concurs with Bruner's emphasis that the process of learning was more important than its product. Gagne, however, is much more concerned with the teaching of the rules or intellectual skills that are relevant to particular instructional disciplines. He observed that when solving "a mathematical problem the individual . . . may have acquired a strategy of applying relevant subordinate rules in a certain order - but he must also have a and G: the Sc learnf given that 44 38 have available the mathematical rules themselves." In contrast to the educational philOSOphy of Bruner and Gagne, Ausubel maintained that the primary objective of 39 the school is the transmission of knowledge. Meaningful learning, according to Ausubel, occurred . . . if the learning task can be related in non- arbitrary, substantive fashion to what the learner already knows, and . . . if the learflgr adopts a corresponding learning set to do so. Lloyd Scott concurs with Bruner's theory that given sufficient prerequisite understanding in a given time period any child can learn any subject. Scott states that "any concept may be taught a child of any age in some intellectually honest manner, if one is abli to find 1 the prOper language for expressing the concept." Kelson tends to reflect upon Scott's statement when he observed that "disadvantaged students, given enough time, can.equal achievement levels oi "suburban" children even 2 with highly abstract content." Similarly, John Carroll views aptitude as the amnount of time required by the learner to attain mastery , . V- "rm-'1’— I’li' K" ofa H A- A—J n: in PE QQ\&1. What SEES “5 43 of a learning task. Benjamin Bloom observes that Implicit in this formulation is the assumption that, given enough time, all students can conceivably attain mastery of a learning task. If Carroll is right, then learning mastery is theoretically gliglgglzazg Studeéi.fifi can find the means for In order to facilitate the transition of material from one level of thinking to the next requires the development of special instructional programs and techniques to be used by the disadvantaged pupil. According to Beilin and Gotkin, these pupils will benefit from the translation of motor activity to reasoning with perceptual and audio types of presentations. They believe that the most difficult task are those in "which reasoning in relation to one form of representation is made equivalent to reasoning in another.")45 4 Transfer of knowledge according to Ausubel 6 occurs xnost effectively if what was learned was rendered meaningful to the learner. Gagneu7 and Piaget“8 have demonstrated that a unit in mathematics should link new material and *what preceded it. Once this link has been established, subsequent mastery is within the realm of accomplishment, #6 because meaningfulness of the subject matter has been introduced. If, as Ausubel suggested, meaningful learning results in positive transfer, it follows that the most stable objects of instruction are concepts, principles and general strategies, rather than isolated facts. However, when one teaches Euclidean geometry they should be embedded in a matrix of concepts and principles. When facts are related to conceptual schema, there is less chance of the student forgetting. Although many of the Specific associations may be forgotten, the presence of that organizing framework or matrix will, according to the Gestalt theory of learning, increase the likelihood of their reconstruction or rediscovery at a point in time when their application is needed. This matrix of concepts and principles were contained in the test instrument employed in this study. 1:7 Chapter 2 REFERENCES CITED The Disadvantaged Child 1. Anne Anastasi, Differential Psychology, New York. MacMillan and Company, 1958] p. 112. 2. A. Kerber and W. R. Smith, Educational Issues in A Changing Society, Detroit: Wayne"State University Press, 1962, p. 28. 3. Martin Deutsch and Others, "Guidelines for Testing Minority Group Children," Journal of Social Issues, 20: 130, April, 196“. u. Harry A. Passow, editor, Education In Depressed Areas, New York: Teachers College Press, 1963, p. 333. 5. Ibid., pp. 333-348. 6. Martin Deutsch, "Some Psychological Aspects of Learning in the Disadvantaged, " in The Disadvantaged Child, Martin Deutsch and Associates, New York: Basic Books, Inc., 1967, p. U4. 7. David Ausubel, "How Reversible Are The Cognitive and Motivational Effects of Cultural Deprivation? Implications for Teaching the Culturally Deprived Child," Urban Education, 1: 25, Summer, 196N. 8. Martin Deutsch, Op. Cit., p. 30. 9. Kenneth L. Bean, "Negro Responses to Verbal and Non- ‘Verbal Test Material," Journal of Psychology, 13: 348, April , 191:2 . ”353 Key ('1 .4 O /.L . '4 n) (f' /. " ' (v!- _/o L H (7 A8 10. Joseph Clarence Spain, Definition of Familar Nouns by_Cultura11nyeprived and Non—Deprived Children of Varying Ages, Unpublished Doctoral"Thesis, Nashville, Tennessee: George Peabody College for Teachers, 1962. 11. Edmund W. Gordon, "Counseling Socially Disadvantaged Children," Mental Health of the Poor, Edited by Frank Riess- man, Jerome, and Arthur Pearl, New York: Free Press of Glen- coe, 196“, p. 277. 12. Martin Deutsch and Bert Brown, "Social Influences of Negro-White Intelligence Differences," Journal of Social Issues, 20: 24-35, April, 1965. 13. Joseph Hunt, Intelligence and Experience, New York: Ronald Press Co., 1961, hl6 pp. 1“. Catherine S. Chilman, "Child-Rearing and Family Relationship Patterns of the Very Poor," Welfare in Review, 3: 15, January, 1965. 15. Frank Reissman, "The Culturally Deprived Child: A New View," Programs for Educationally Disadvantaged, U.S. Department of Health, Education, and Welfare, Office of Education, Bulletin Number 17, Government Printing Office, ‘Washington, D.C., 1963, pp. 3-10. 16. Frank Reissman, The Culturally Deprived Child, New York: Harper and Row, 1962, p. 25. IEvolution of Euclidean Geometry 1. B. Russell, Introduction to the Philosophy of Maths, Cambridge, Mass., 1923. 2. Aristotle, Posterior Analytics in Introduction to Aristotle , ed. R. McKeon, New York: The Modern Library , 19117 , pp . 9-109 . ions bv .r Educ 1960 “9 Birkhoff and Beatley's Geometry 1. George Birkhoff and Ralph Beatley, "A New Approach to Elementary Geometry," The Teaching of Geometry, Fifth Yearbook of the National Council of Teachers of Mathematics, Teachers College, Columbia University, Bureau of Publications, New York, 1930. 2. George Birkhoff and Ralph Beatley Basic Geometry, Chicago: Scott, Foresman and Company, 1945. Theories of Cognitive Psychology 1. John B. Carroll, "Analysis of Reading Instruct- ions," in Theories of Learning and Instruction, edited by E. Hilgard, National Society for the Study of Education, University of Chicago Press, Chicago, Illinois, 1960, p. 3“90 2. Harry Beilin and Lassar Gotkin, "Psychological Issues in the Development of Mathematics Curricula for Socially Disadvantaged Children," Paper read at the Conference on Mathematics Education for Below Average Achievers, School Mathematics Group, Stanford, Calif., 196A, pp. 21—22. 3. Ibid., p. 23. h. J.H. Flavell, The Developmental Psychology of Jean.Piaget, Princeton: Vbn Nostrand, 1963. 5. Hanes G. Furth, Piaget and Knowledge, New York: Prentice Hall, 1969. 6. I.E. Sigel and Frank H. Hooper (eds.), Logicial CNminking in Children, New York: Holt, Rinehart and Winston, lQETL. 7. Flavell, Op. Cit., p. 261. t” u; AU 7 Au m Inn 0 «.y. .Illlll III 50 8. J. Piaget, The Psychology of Intelligence, translated by Malcolm Piercy and Daniel C. Berlyne, Littlefield, Adams and Co., Patterson, 1960. 9. B. Inhelder and J. Piaget, The Growth of Logical Thinking from Childhood to Adolescence, trans- lated by Anne Parsons and Stanley Milgram, Basic Books, Inc., New York, 1961, 350 pp. 10. S.A. Hill, "A Study of the LOgical Thinking Abilities of Children," Unpublished Doctoral Thesis, Stanford University, 1960. 11. L.W. Yudin and S. Kates, "Concept Attainment and Adolescent Development," Journal of Educational Psychol- ogy, 5“: 177-182, August, 1963. 12. Jerome S. Bruner, The Process of Education, Harvard University Press, Cambridge, 1960. 13. Alfred North Whitehead, The Aims of Education, Mentor Books, New York, l9“9. 1“. John H. Flavell, The Developmental Psychology of Jean Piaget, van Nostrand Co., Princeton, New Jersey, 1953. 15. John Dewey, The Quest for Certainty, Minton Balch and Co., New Yorkj_1929. 16. Lloyd Scott, Trends in Elementary School Mathe- Inatics, Rand-McNally Co., Chicago, Illinois, 1966. 17. Frank Reissman, "The Culturally Deprived Child: ‘A New View," School Life, “5:6, April, 1963. 18. Edmund W. Gordon, "Counseling Socially Dis- zuivantaged Children," Mental Health of the Poor, Edited by IEransziessman, Jerome Cohen, and Arthur Pearl, New York: Free Press of Glencoe, 196“, p. 277. AJL Viv Ill of V 9 5‘ NH 4 .‘l' v.3. QM r\ r . . Cu O 0 AU 31 T & fi\U ”I V I1!“ ‘11. o &v r; r; i.» O h... P9 51 19. Jerome Bruner, The Process of Education, Op. Cit. 20. Jerome Bruner, "Some Theorems on Instruction Illustrated With Reference to Mathematics," in Theories of Learning and Instruction, Ernest R. Hilgard Ied.§, National Society for the Study of Education, University of Chicago Press, Chicago, Illinois, 196“, p. 331. 21. E.A. Peel, The Pupil's Thinking, Oldbourne Book Co., Ltd., London, 1960, pp. 132-137. 22. David Ausubel, "In Defense of Verbal Learning," Educational Theory, 11: 18, January, 1961. 23. David P. Ausubel, The Psychology of Meaningful Verbal Learning, Grunne and Stratton, New York, 1963. 2“. E.B. Hunt, Concept Learning: An Information Processing Approach, New York: Wiley and Sons, 1962. 25. David P. Ausubel, Introduction to Part I," in Readings in the Psychology of Cognition, pp. 9, 10. Teaching Mathematics to Disadvantaged Children 1. Harry Beilin and Lassar Gotkin, "Psychological Issues in the Development of Mathematics Curricula for Socially Disadvantaged Children," Paper read at the Conference on Mathematics Education for Below Average .Achievers, School Mathematics Group, Stanford, Calif., 196“, p. 2“. 2. Martin Deutsch, Minority Class Status As Related tn) Social and Personality Factors in Scholastic Achieve— nuant, Society for Applied Anthropology, Monographs No. 2, Cornell University, Ithaca, N.Y., 1960, 32 pp. 52 3. Cynthia Deutsch, "The Effects of Environmental Deprivation on Basic Psychological Processes," Art Edugafi tion, 22: 20, January, 1969. “. A.L. Baldwin, Behavior and Development in Child- hood, The Dryden Press, New York, 1955. 5. V.L. Nelson, "An Analytical Study of Child Learn- ing," Child Development 7: 95-11“, June, 1936. 6. J.S. Bruner, "The Course of Cognitive Growth," American Psychologist, 20: 1007-1017, 1965. 7. I. Sigel and B. McBane, The Relationship Between Cognigive Competence and Level of Symbolization Amongy Five-Year Old Children, Merrill-Palmer Institute, Chicago, 1966: 8. Basil Bernstein, "Elaborated and Restricted Codes: Their Social Origins and Some Consequences," American Anthropology, II, 66: 55-69, Special PublicatIBn, J. Gomperz and D. Hymes (eds.), December, 196“. 9. M.C. Templin, Certain Skills in Children, Univer— sity of NHnneapolis Press, Minneapolis, 1957, p. 50. 10. David O. Montague, "Arithmetic Concepts of Kind- ergarten Children in Contrasting Socioeconomic Area," Elementary School Journal, 6“: 388, April, 196“. 11. Martin Deutsch, Minority Group and Class Status as Related to Social and Personality Factors in Scholas- ‘tic Achievement, Society for Applied Anthropology, Mono- graphs No. 2, Ithaca, N.Y.: Cornell University, 1960, 32pp- 12. Jerome Siller, "Socioeconomic Status and Conceptual flnxinking," Journal of Abnormal Social Psychologxg 55: 365-71, November, 1957. 13. Allison Davis, "Society, The School, and The (hilturally Deprived Student," Improving English Skills of? Culturally Different Youths, Bulletin No. 5, U.S. ’fiepartment 0TH. E. W., Washington, 196“, pp. 10- 21. Ave' ‘u -7\ It») 5“: pe Lea‘ 196 53 1“. Arthur R. Jensen, "Learning Ability in Retarded, Average and Gifted Children," Merrill-Palmer Quarterly, 9: 123-“0, April, 1963. 15. D. C. Findlay and C. McGuire, "Social Status and Abstract Behavior," Journal of Abnormal Social Psychology, 5“: 135-137, 1957. 16. Martin Deutsch, "Social and Psychological Per— spectives on the Development of the Disadvantaged Legfiner," Journal of Negro Education, 33: 232-““, Summer, 19 . 17. Eunice S. Newton, "Verbal Destitution: The Pivotal Barrier to Learning," Journal of Negro Educa— tion, 29: “97-99, Fall, 1960. 18. David O. Montague, "Arithmetic Concepts of Kindergarten Children in Contrasting Socioeconomic Areas," Reading Teacher, 13: “O-““, October, 1959. 19. M.E. Dunkley, "Some Number Concepts of Disadvan- taged Children," Arithmetic Teacher, 12: 359-361, May, 1965. 20. Wilbur H. Dutton, "Attitudes of Junior High School Pupils Toward Arithmetic," School Review, 6“: 18-22 , January , 1956 . 21. Marvin E. Binkley, First Grade Entrance ‘Variables Related to Achievement and PersonalityJ A Eitudy of Culturally Deprived Fourth Graders, Unpublished Doctoral Dissertation, University of Tennessee, 1967. 22. Robert E. Searle, Mathematical Abilities Possessed by Kindergarten Children from Disadvantaged Communities, Unpublished Doctoral Dissertation, University of California, 1968. 23. Dora Helen Skypak, T§e_Re1ationship of Socio- Economic Status to the DevelOpment of Conservation of thnbers, Unpublished Doctoral Dissertation,‘Univer8ity of Wisconsin , 196 7 . 5“ 2“. Ebba Wahlstrom, "The Computational Arithmetic of Social Experiences of Third Grade Children," Journal of Educational Research, 30: 12“—29, October, 1936. 25. LeLand H. Erickson, "Certain Ability Factors and Their Effect on Arithmetic Achievement," Arithmetic Teacher, 5: 287-293, December, 1958. 26. A. Davis, Social Class Influences Upon Learn— ing, Harvard University Press, Cambridge, l9“8. 27. I. Lorge and R.L. Thorndike, The Lorge-Thorn- dike Intelligence Tests, Houghton-Miffiin, Boston, 195“. 28. T.A. Dodes, "The Science of Teaching Mathe- matics," Mathematics Teacher, “6: 157-66, 1953. 29. Ralph T. Heimer, "Conditions of Learning in Mathematics Sequence Theory Development," Review of Educational Research, 39: 506, October, 1967. 30. P. Suppes, L. Hyman, and M. Jerman, "Linear Structural Models for Responses and Latency Perform— ance in Arithmetic on Computer Controlled Terminals," Psychology Series, Institute for Mathematical Studies in the Social Science Report 90, Stanford University, Stanford Calif., 1966, p. 160. 31. V.A. Kruteskie, "Some Characteristics of the Thinking of Pupils With Little Capacity for Mathematics," in B. and J. Simon (eds.), Educational Psychology in the U.S.S.R., Stanford University Press, Stanford, Calif., 1963 o 32. Robert J. Havighurst,"Who Are the Socially Dis- advantaged?" Journal of Negro Education, 33: 217, 196“. 33. Beilin and Gotkin, gp4w9i23, p. 1“. m c ui‘ lri v u hfl ‘\ fr: - .n Amq.’ t l 55 3“. Frank Reissman,"The Overlooked Positives of Disadvantaged Groups," Journal of Nggro Education, 3“: 166, Spring, 1965. 35. Eunice S. Newton, "Planning for the Language Development of Disadvantaged Children and Youth," Journal of Negro Education, 3“: 175, Spring, 1965. 36. Jermone S. Bruner, Toward a Theopy_of Instruction, Belknap Press, Cambridge, 1966, p. 72. 37. Jerome Bruner, The Process of Education, Harvard University Press, Cambridge. 38. Robert Gagne, Conditions of Learning, 2nd edition, Holt, Rinehart and Winston, 1968, p. 38. 39. David P. Ausubel, "A Cognitive Structure View of Word and Concept Meaning," in Readingyin the Psychology of Cognition, edited by Richard Anderson and David Ausubel, Holt, Rinehart and Winston, Inc., New York, 1961, p. 23. “0. David P. Ausubel, Op. Cit., p. 2“. “1. Lloyd Scott, Trends in E1ementary_School Mathematics, Rand-McNally and Co., Chicago, 1966, pp. 15-16. “2. R. Kelson, New Curriculums and the Teachingyof the Disadvantaged, McGraw Hill, New York, p. 29. “3. John Carroll, "A Model for School Learning," {Teachers College Record,_6“: 723-733, 1963. ““. Benjamin Bloom, "Learning for Mastery," in livaluation Comment, Bulletin of the U.C.L.A. Center for tine Study of Evaluation of Instructional Programs, May, 1968, p. 3. “5. Beilin and Gotkin, Op. Cit., p. 16. 56 “6. David P. Ausubel, Educational Psychology: 5 Cogpitive View, Holt, Rinehart and Winston, 1965. “7. Robert Gagne, The Conditions of Learning, Holt, Rinehart and Winston, 1965. “8. Jean Piaget, The Child's Conpeption of Number, Humanities Press, New York, 1952. “9. David Ausubel, Op. Cit., pp. 58-75. RD 1N u 57 Chapter 3 RESEARCH DESIGN AND SAMPLING PROCEDURES Sample Selection In this study 1000 culturally disadvantaged seventh and eighth grade Junior High School pupils in Philadelphia were used as subjects for the present study. Thirty class sections, equally divided between the two grades, were chosen from the Gillespie Junior High School which is located in a racially encapsulated area and has a 95 percent Negro enrollment. Guilfordl has maintained that there is no absolute distinction between large and small sample statistics. Many of the small-sample statistical tests are based upon the statistic known as the student's t. Actually t is defined as the ratio of a deviation from the mean or other parameter, in a distribution of sample statistics, to the standard error of that distribution.2 The distinction between large and small sample statistics 3 becomes critical below sample size of 30. Otherwise, the 58 distribution of t approaches the standardized normal distribution as sample size increases. Furthermore, If really good accuracy is desired in determining interval probabilities the t distribution should be used when the sample size is around 100 cases. Beyond this number, the normal probabilities are extremely close to the exact t probabilities.“ It is for the reasons discussed in the preceding paragraph, that 100 subjects were randomly selected from a total 5 pOpulation of 1000 students. The Index of Socioeconomic Status 6 The Index of Socioeconomic Status (SES) as developed by Suzanne Keller and Estelle Cherry at the Institute for Developmental Studies was used by this researcher to assign social class ratings to the sub- jects involved, (See Appendix A) Each category for the Index was derived from an apprOpriately weighted composite measure of the occupational status of the main [wage earner] and education of the main [wage earner]. The weights assigned to the indicators were derived from a regression equation based on the degree of inter- correlation among these three variables.7 59 The occupational status of the Index was derived 8 from the Empey Scale of Occupational Prestige. The correlation was over .90 between the scale used in the Index of Socioeconomic Status and the Hollingshead Two 9 Factor Index of Social Position. The educational variable of the Index was divided into eight categories ranging from one (0-“ years of school) to eight (graduate training). Each occupa- tion was given a rating from one (lowest prestige) to ten (highest prestige), based upon the scale constructed 10 11 12 by Empey, Smith, and by Hatt and North. This scale 13 had a rank order correlation of .97. This treatment concurs with that used by Deutsch. The distribution of educational and occu- pational ratings were treated as if they rep— resented parametric data, and the ratings were converted into standard scores. A social class score was obtained by adding the two derived scores.1“ The scores were then divided into the following three levels: Level I. A typical family in this group has as a main wage earner a person who is unemployed, or who has an unskilled or semiskilled job. The educa- tional level ranged from elementary schooling to completion of the Ninth grade. Level II. The typical family at this level is headed by a wage earner with a semiskilled, clerical, or sales job whose education ranged from about nine grades to high school graduation. Level III. The typical household is headed by a professional or managerial wage earner whose education would be high school graduation, college, or graduate work.l5 Again according to Deutsch ”the index shows a . . .degree of internal cohesiveness [and] has con— siderable construct validity.”16 Additional validity for this social class index was determined in a study by Bloom, Whiteman, and Deutsch.l7 Based on Deutsch's SES Index, it was deter- :mined.that those students participating in this study (nui'be categorized as follows: Level I - low, 88% J I. A.“ AC. 61 Level II - middle, 9%; Level III - high, 3%. These findings compare favorably with the find- 18 ings of Bloom, Whiteman, and Deutsch for inner-city children in “deprived” areas. Data Gathering Procedures A questionnaire containing personal information items, total number of individuals living in the home and schooling of father and mother was administered to the entire pOpulation of this study. (See Appendix B) The questionnaire was developed by this research- er with the assistance of the school counselors and social workers who were desirous of ascertaining current information about the student pOpulation being tested.* * Without their participation and cooperation, this study would have been very difficult to administer. They introduced the investigator to the teachers, the administrators and assisted him in the distribution and collection of the test material given to the participating classroom teachers. Also, all pertinent student infor- mation was made available to the investigator and social workers. 62 The principal of the school, sincere in his desire to aid the research study, did not inform any of the other teachers in the school of this project. The participating teachers received information directly from the researcher as to the nature of the study, how to administer the student questionnaire, the pre-and post- tests and the geometry lessons. Each teacher involved in this study was instruct- ed not to inform their students that they were partici- pating in a research project. They were told to empha- size that the questionnaire was not a test and that the students should respond freely to the questions. All of these teachers were instructed to assist the students, ‘where necessary, in completing the questionnaire or an- swering any of the items. Attached to each questionnaire was a “" x 5" card also to be filled out by the students. (This card would identify the questionnaire for possible follow-up by ruiving a number identical to that of the questionnaire.) 63 The students completed their questionnaires in their assigned classrooms during one time period. The advantage of having all students answering the question- naire at the same time was to standardize the experience. The time allocated for the questionnaire was “5 minutes, or one classroom period. They were collected by the investigator from each of the partici- pating teachers during the next classroom period. Evaluative Instrument The evaluative instrument consisted of a workbook containing 10 separate lessons pertaining to specific types of geometric constructions, 10 fifteen minute instruct— ional audiotapes, recorded at 3 3/“ ips, which were necessary for completing each of the 10 geometry lessons. Each lesson, along with it's corresponding audio tape, was administered to the population under investigation for the successive days. These materials were develOped by Klinelg in accordance with the following design principles: 1. The concepts to be communicated in each presentation were limited in number. 2. Practical experiences were designed to lead to intellectual discovery. 3. Correct responses were reinforced immediately to produce motive satisfaction. “. The principle of concept generalization (knowledge transfer). 5. Each concept sequence was carefully pro- grammed so that each geometrical principle served as a base for higher order learning, et. seq. The workbook contained the following geometry lessons: Lesson 1 This was an introductory lesson and includes back- ground presentation, explanation of the need and use of Geometry by todays student. Discussion of points, lines, planes, solids, etc. Lesson 2 This lesson included a discussion of angles, an explanation of rays, the vertex of an angle, right, acute, obtuse, straight and reflex angles. Methods of labelling and referring to angles were also explained. Lesson 3 Brief review of lessons 1 and 2. Discussion and explanation of adjacent angles, methods of adding and subtracting angles based on axioms. A simple geometric proof was included and explained. Lesson “ Explanations concerning pairs of angles are given. Complementary, supplementary and vertical angles are discussed and their relationship to other angles dis- cussed in previous lesson is explained. The lesson includes work related to acute, obtuse, right and other angles. A simple formal proof is explained in an informal manner. Lesson 5 Introduction to the compass and straight edge. Simple constructions include; constructing a line segment equal to a given line segment, bi—secting a given line and constructing an angle equal to a given angle. The last part of the lesson deals with the construction of perpendiculars. Lesson 6 Students were instructed how to construct angles to a given size with a compass and straight edge. Practice is given in the construction of 90°, “5°, 60°, and other angles. These constructions are taught by the relationship to a circle method. Lesson 7 This lesson included the construction of para— llels to a given straight line with a complete ex— planation of alternate-exterior angles and correspond— ing angles (sometimes called exterior-interior angles). The lesson also includes the relationships and equalities of these angles formed by parallel lines cut by a trans— versal. Lesson 8 This lesson included the construction of circles, triangles and quadrilaterals from given data. The latter part of the lesson includes constructing a square equal in area to a given polygon. Simple formulae are reviewed to clarify the lesson. Lesson 9 This lesson included (1) the construction of per- pendiculars to a given point; (tangent) (2) the con- struction of inscribed and circumscribed triangles, hexagons, squares and octagons. 66 Lesson 10 This lesson was concerned with the construction of triangles equal in area to given polygons.21 The materials, in the geometry workbook, contain- ed the accepted geometric constructions of Euclid as presented by Birkhoff and Beatley. This approach was discussed in Chapter 3. (See Appendix C for a copy of the workbook) Both the workbook, containing the above listed geometry lessons, along with its corresponding audio tapes were designed in such a manner that the student could compare his responses with correct constructions as the lesson progressed. By so doing, the correct responses by the student are progressively strenghtened by being followed immediately by motive satisfaction. . .The method used to allow the student to make this comparison was accomplished by including correct responses in the student material immediately Opposite the drawing area.22 The workbook contained printed material to assist the student in interpreting the audio lesson, enabling 1mim.to make the basic geometric constructions as direct— ed by the audio lesson, and answers to the supplementary 67 material was included in the teachers' notes. The audio- tapes stressed the use of the relative pause, voice inflections and connotational emphasis. Grammatical structure normally used for written composition was considered of lesser value than the importance of "conversational" speech acceptable to the disadvantaged child. Reliability of the Instrument An analysis of variance technique, which was developed by Hoyt, was used to compute the estimated test reliability of the instrument used in this research. According to Hoyt, the formulas were developed for estimating the reliability of a test by means of analysis of variance. . .It is essentially the method suggested by Johnson and Neyman and later used by Jackson. This particular approach does not use a new or different result for the problems of tests of significance but does possess consider- able advantage in attacking problems of estimation.2 The residual sums of squares were used by Hoyt .as a.basis for estimating the discrepancy between 68 observed variance and true variance; i.e., variance due to error in the test instrument. The residual sum of squares is obtained by subtracting the among students sum of squares and the among items sum of squares from the total sum of squares. The formula for computing the reliability coefficient rtt is as 2“ follows: P = V _ tt 3 Vr V s where rtt = The reliability coefficient of the test, VS = Variance among students, and Vr = Remainder variance. When using Hoyt's technique, for estimating test reliability by analysis of variance, the residual sum of squares serves as the means for estimating the discrepancy between the obtained variance and true variance of the student's score on a test. 59 This estimate of the discrepancy is a better one than obtained by dividing the test into odd and even halves because in the latter case the partic- ular split of the test, which is only one of many possible ways of splitting a test, may be an un- lucky division and may result in either an over- estimate or an underestimate of the coefficient of reliability. Furthermore, it has been shown. . . that the particular estimate of the discrepancy between the obtained and the 'true' scores is the best linear estimate where 'best' is considered in the light of the least 'squares' criterion. Hence, it is clear that this method of estimating the reliability of a test gives a better estimate than any method based upon an arbitrary division of the test into halves or into any other fractional parts. The fact that Hoyt's technique for estimating test reliability yields precisely the same result as Kuder and Richardson's split-half procedure lends strong verification to the utilization of this technique. But, the Kuder and Richardson procedure has "some 6 of the limitations of the split~ha1f method."2 Thus, Hoyt's method is an improvement over the split-half method, as well as the Kuder and Richardson procedure. This technique provides a better estimate ‘between the obtained variance and true variance by 7O eliminating the possibility of an unlucky odd-even split of the students' scores on a test. The computation for the estimated reliability of the test, using Hoyt's technique, is shown in Table 1. Table 1 ANALYSIS OF VARIANCE OF 10 ITEMS IN GEOMETRY, ADMINISTERED TO 100 STUDENTS Source of d.f. Sum of Squares Variance * Variation Among Stu- 99 20.699 20.9 dents Among Items 9 29.789 3.30988 Residual 891 159.911 .179“7 Total 999 210.399 0.2106 The coefficient of reliability of the test instrument is rtt = 20.9 - 0.17947 20.9 rtt = 0.9913 * Variance in this application is the same as mean squares in standard application. 71 An estimated test reliability of 0.9913 indicates a non-ambiguous test reliability across individual students. This test instrument, therefore, has a high degree of internal consistency and it is reliable across individual students. Standard Error of Measurement of the Test Though it may seem obvious to the reader that a test with such a high reliability coefficient (.9913) should have a low amount of measurement error, Hoyt's Standard Error of Measurement27 was nonetheless computed as a further check. The Standard Error of Measurement, according to Hoyt, is obtained by taking the square root of the residual sum of squares and dividing it by the degrees of freedom for among students found in Table l. The computation for the Standard Error of Measurement is as follows: / l .11 __§2___. = 1.27 99 The Standard Error of Measurement is equal to 1.27. This measurement is a ”standard deviation of an 72 [individual'g] hypothetical distribution over measured occasions."2 It can be interpreted in the following manner: 1. The chances are two out of three that the individual's obtained score was not more than 1.27 units from his true score. 2. The chances are 95 out of 100 that the individual's obtained score was not more than 2.5“ units from his true score. 3. The chances are 99 out of 100 that the individual's obtained score is not more than 3.81 units from his true score. The small standard error of measurement indicates that the test has a low degree of measurement error and thus that a considerable of confidence can be placed in scores obtained from the test instrument. Test Validipy Since this study did not include a previously standardized criterion measure of geometric skills it is not possible to compute a validity coefficient. How- 73 ever, it would seem logical to assume that a test which requires the student to demonstrate specific geometric skills is a reasure of the attainment of those skills and thus has reasonable validity for purposes of this study. Acceptance of the above logic implies, however, that the test include a representative sampling of the broad spectrum of skills which contribute to competence in geometry. In other words, the test would be biased if it overly emphasized a few geometric skills at the expense of others. In its develOpment, Kline incorporated the skills generally included in elementary geometry textbooks. Statistical Procedures The statistical methods that were used to analyze the data from this study are as follows: Product moment coefficient of linear correlation, and the "t" test for correlated means. A product moment coefficient of linear correla- tion was used to estimate the degree of relationship be- tween the variables used in this study: mathematics and 7“ verbal achievement scores, grades earned in math and English, socioeconomic factors, home crowding factor, whether or not there is a father in the home and the de- pendent variable which is the pre-and posttest scores. The 10 pre—and posttest items contained the same materials that inferred a knowledge of geometric constructions and did not contain specific questions that could be directly related to the test instrument. The scores on the pre-and posttest were based upon a ten point scale. An item analysis of these scores are shown in table 2. (See Appendix D for a copy of the pre-and posttest) The student's achievement scores in mathematics and reading were obtained from the Iowa Tests of Basic Skills that each student had taken from fourth grade through eighth grade, inclusively. The math and English course grades from fourth through eighth grade were ascertained from the cumulative records of each of the students. A two tailed test was used to determine the signi- ficance of all differences when TABLE 2 75 ANALYSIS OF TEST INSTRUMENT BY ITEM Item Percent Passing Percent Failing 1 77 23 2 78 22 3 72 28 A 83 17 5 “3 57 6 66 3“ 7 55 “5 8 36 6“ 9 37 63 10 95 5 76 No prior hypotheses about the direction of the difference between p1 and p2 is made. The test of significance should take into account both the probability of a positive difference and the prob— ability of a negative difference.29 A significance level of .01 was the criterion for accepting or rejecting the research hypotheses involved. The "t" Test In this research study, course effectiveness was evaluated by a repeated measurements design. This design was chosen because this research study did not employ a control group. The term repeated measurements describes a type of research design in which . . .two measurements are made on each element. If the order in which the treatments are administered has no effect upon the final outcome, then the difference between the two measures on the same element on a common criterion provides a measure of the relative effective- ness of the treatments. This measure is but systematic effects associated with the elements themselves. In this respect each element serves as its own control group.30 77 Moreover, "one of the primary advantages of repeated measures is the potential reduction due to experimental error.”31 When using a repeated measurements design, the standard ”t” test is not utilized because a fundamental assumption of that test is that the means being evaluated are independently derived or orthogonal. In a repeated measurements design, the fundamental assumption underlying a ”t" test is violated because the same individuals appear in both sets of measurements. Therefore, in this research study it was necessary to use the "t" test for correlated means. 32 The "t” test for correlated means is a technique which computes the correlation between the means and then uses it to correct the standard error of the difference between the means. This technique has the effect of reducing the denominator of the "t" test, which is the error term. In other words, any variation reflected in the correlation coefficient can be described to a known cause rather than being placed under unexplained experimental error. 78 The computation of ”t", for this research design, is provided in Table 3 is further discussed in the next chapter on findings of the study. Research Hypptheses This study was designed to test the assumption that a teaching methodology can be develOped to overcome certain sociological and environmental factors that tend to hamper the educational achievement of the disadvantaged child. To do so, the following null hypotheses, were tested: Hypothesis 1: It is postulated that the difference between the means of the pre-and posttests will be signi— cant. Hypothesis 2: It is postulated that the correlation between student performance on the test instrument and SES will not be significant. Hypothesis 3: It is postulated that the correlation between student performance on the test instrument and "father"* will not be significant. Hypothesis “: It is postulated that the correlation between student performance on the test instrument and crowding* will not be significant. Hypothesis 5: It is postulated that the correlation between student performance on the test instrument and verbal achievement scores will not be significant. Hypothesis 6: It is postulated that the correlation between student performance on the test instrument and mathematics achievement scores will not be significant. Hypothesis 7: It is postulated that the correlation between student performance on the test instrument and grades will not be significant. * "Father" refers to a home in which the father is present as Opposed to one in which he is not. * "Crowding" is the number of peOple in a home divided by the number of rooms in the home. Chapter 3 REFERENCES CITED 1. J. P. Guilford, Fundamental Statistics in Psychology and Education, McGraw-Hill, “th Edition, New York, 1965. 2. Ibid., p. 182. 3. Ibid., p. 181. “. William L. Hays, Statistics for Psychologists, Holt, Rinehart and Winston, New York, 1966, p. 307. 5. The random table Of numbers were generated by an IBM/360 Scientific Subroutine package. 6. Martin Deutsch, Alma Maliver, B. R. Brown and Estelle Cherry, Communication Of Information in the Elementary_School Classroom, Cooperative Research Pro- ject NO. 908 of the Office of Education, U.S. Depart- ment of Health, Education and Welfare, April, 196“. 7. Ibid., p. 135. 8. LaMar T. Empey, "Social Class and Occupational Aspirations: A Comparison Of Absolute and Relative Measurement," American Sociological Review, December, 1956. pp. 703-709. 9. A.B. Hollingshead and F.C. Redlich, Social Class and Mental Illness, New York: John Wiley and Sons, 1958. 10. Empey, Loc. Cit. 11. M. Smith, "An Empirical Scale of Prestige of Occupations," American Sociological Review, 8: 185-192, April, 19“3. 81 12. P.K. Hatt and C.C. North, “Jobs and Occupations; A Popular Evaluation,” in Class Status and Power, edited by R. Bendix and S.M. Lipset, The Free Press of Glencoe, l9“9, pp. “ll—“26. 13. Ibid. l“. Deutsch, Maliver, Brown and Cherry, Op. Cit., p. 13“. 15. Ibid. 16. Ibid. w 17. R. Bloom, M. Whiteman and M. Deutsch, "Race and Social Class as Separate Factors Related to Social Environ- ment," The American Journal Of Sociology, 60: “71-“76, January, 1965. 18. R. Bloom, M. Whiteman and M. Deutsch, LOO. Cit. 19. Robert D. Kline, "A Study to Determine If Educa- tional Materials Designed Specifically for a Developing Nation are Equally Effective in Producing Student Achievement in a Developing Nation," Unpublished Doctoral Dissertation, Syracuse University, 1967. 20. Ibid., p. 110. 21. R.D. Kline, Workbook for Geometry, Syracuse University, Syracuse, 1967, “3 pp. 22. Kline, Op. Cit., p. 35. 23. Cyril Hoyt, "Testing Reliability Estimated By .Analysis of Variance," Psychometrika, 6: p. 156. 2“. Ibid., p. 155. 25. Hoyt, 9p. Cit., p. 155. 26. N.M. Downie and R.W. Heath, Basic Statistical Ifiathods, Harper and Row Publishers, New York, 1965, p. 220. 82 27. Hoyt, Op. Cit., p. 156. 28. William L. Hays, Op. Cit., p. 29“. 29. Allan Edwards, Experimental Design in Psycholo- gical Research, Holt, Rinehart and Winston, N.Y., 196“, p. 5“. 30. B.J. Winer, Statistical Principles in Experimental Design, McGraw-Hill Book Company, 1962, p. 39. 31. Ibid., p. “2. 32. J.P. Guilford, Op. Cit., p. 177. 83 Chapter “ RESEARCH FINDINGS The data gathered in this study includes achieve- ment test scores, course grades assigned by teachers, certain familial characteristics, and scores on the test instrument Of the teaching method being evaluated by this research study. Findings are presented in terms of the several hypotheses stated in Chapter 3. The Research Hypotheses And The Findings Hyppthesis 1: It is hypothesized that the difference between the means of the pre—and posttests will be significant. In order to evaluate this hypothesis it must be stated in the "null" form. The null hypothesis (HO) to be evaluated is that: There is no significant difference between the means of the pre—and posttests. (Hon2-Ml=0) The .01 level of significance was selected as the criterion for rejection of the null hypothesis. A "t" test for correlated means, which was discussed in the previous 8“ chapter, was used to evaluate the significance of the differ- ence between the means of the pre-and posttest scores. The data is presented in Table 3 with the probability of "t" being based upon a two—tailed comparison. Table 3 Analysis of Mean Scores of Test Data Means Difference SD Computed df Probability Pre Post (Post-Pre) Pre Post "t" of "t" “.72 7.“8 2.76 1.9 1.3 1.75 98 less than .01 Since the "t” score necessary for the rejection of the null hypothesis at the .01 level is 2.5“, a computed "t" Of 17.50 is clearly significant and the probability Of obtaining such differences by chance is very small. Therefore, we are able to reject the null hypothesis and the alternative hypothesis (H1) seems tenable. The range for this study was based upon one standard deviation in both directions from the mean. As such, the range for 68 percent of the cases is equal to 7.“8 : 1.3; i.e., the range is 6.18 to 8.78. The fact that the study did not incorporate a control group poses some questions as to the validity of the above con- clusion. For example, under some circumstances, the improvement reflected in the students' performance on the posttest could be due to some maturational factor which occurred during the time between the administration of the two tests. In this case, however, the two tests were administered within the Span of one-half month so matura- tional factors as such can be discounted. Another counter explanation for the improvement Of these students' test scores is that the pretest may have influenced their posttest scores by sensitizing them to what was expected of them or through the effect of practice.1 The investigator recognizes this as a legitimate criticism of the repeated measures design utilized in this study. It is quite possible that some Of the improvement in the scores is due to the effect of the pretest. However, the magnitude of improvement Observed was sufficient to warrante serious question that more than a minor portion could be accounted for by practice. Statistical regression may also be a reason for the improvement in the posttest scores. However, without a control group there is no way to evaluate the extent to which statistical regression is involved in a repeated measures design. While it is true that these students were not selected because of low scores on achievement tests, their scores were still low because students of minority background tend to score low on such tests. This is an artifact of doing research involving minority subjects. It will be noted later that the relationship between performance on the test instrument and performance on standardized achievement tests was not significant. Therefore, it seems illogical that statistical regression accounts for that extent Of improvement observed in this sample. Hypothesis 2: It is postulated that the correlation between student performance on the test instrument and SES will not be statistically significant. In order to evaluate this hypothesis it is necessary to test the assumption that the null hypothesis that the population correlation is zero is true such that 87 r(n—2)l/2 fl ll (l-r2)1/2 which has a t distribution with n—2 degrees of freedom and can be evaluated by means of the table of t with alpha set at .01.2 A two-tailed t test is necessary since the above hypothesis does not designate the direction of a significant departure from zero correlation. By substitution into the above formula it can be shown that a correlation coefficient of .264 is required for significance at the .01 level. In a repeated measurements design it is possible to generate three test performance scores: a pretest score, a posttest score and the difference between these two scores. The results of this test are presented in Table H. 88 Table & Corrleations Between SBS And Test Instrument Variables gorrelation Coefficient d: Significance Pre vs 838 .095 98 No Post vs SES -.010 98 No Gain*vs SES -.124 98 No Since none of the correlations in Table 4 are significant, Hypothesis 2 was confirmed in this sample. Therefore, it would seem that a student's socioeconomic status has little effect upon his capacity to respond to the method of teaching geometry under investigation. hypothesis 3: It is postulated that the correlation between student performance on the test instrument and “father”** will not be significant. The null hypothesis to be tested is that the population correlation is zero. A two-tailed t test with alpha equal to .01 are the criteria for rejection of the null hypothesis. * Gain represents an improvement score drived by subtracting a student's score on the pretest from his score on the posttest. ** "Father" refers to a home in which a father is present (scored as +1) as opposed to a home in which no father is present (scored as O). In this study 78 percent of the population did not have a father present in the home; whereas 22 percent did have a father present in the home. 89 However, it is necessary to use the point-biserial correlation coefficient rather than the Pearson r's since 5 3 "father” is a dichotomous variable. The formula used in the computations reads M - M r= p q 7r: (pq)l/2 where p= "father” present, q= ”father” absent and t= total group. The data is summarized in Table 5. Table 5 Correlations Between Father And The Test Instrument Variables Point-Biserial r g: Significance Pre vs Father .134 98 No Post vs Father .080 98 No Gain vs Father -.O97 98 No Since all three point—biserial r's are much less than .26“ Hypothesis 3 remains tenable. According to the data on this sample, the presence or absence of a father in the 90 home produces no systematic effect upon the performance of students on the teaching method in question. Hypothesis M: It is postulated that the correlation between student performance on the test instrument and crowding* will not be statistically significant. The hypothesis to be tested is that the pOpulation correlation equals zero by utilizing a two—tailed t test with alpha equal to .01 in the manner discussed previously in the analysis of Hypothesis 2. In order to reject the null hypothesis a correlation coefficient equal to or greater than .264 is required. The data is summarized in Table 6. Table 6 Correlations Between Crowding And The Test Instrument Variables Correlation Coefficient d: Significance Pre vs Crowding -.157 98 No Post vs Crowding -.l34 98 No Gain vs Crowding .080 98 No * Crowding is a ratio with the number of peOple in the Ihome as the numerator and with the number of rooms in the :home as the denominator. 91 Since none of the correlation coefficients listed in Table 5 are significant, Hypothesis 4 remains tenable. Therefore, the data indicates that crowding in the home does not appreciably affect a student's capacity to profit from the teaching technique being investigated. Hypothesis 5: It is postulated that the correlation between student performance on the test instrument and verbal achievement scores* will not be significant. In order to test this hypothesis, we will again use the null hypothesis that the pOpulation correlation equals zero as well as a two—tailed t test with alpha equal to .01. The degrees of freedom is N-2 = 100—2 = 98. In order to reject the null hypothesis in regard to any one of the computed correlations, the coefficient must equal or exceed .264. The data is summarized in Table 7 on the following page . M 5‘ Scores on the verbal component of the Iowa Test of Basic Skills. 92 Table 7 Correlations Between Verbal Achievement By Grade Level And The Test Instrument Test Instrument Pre Post Gain Ll “.023 COMB 0066 5 -.082 .014 .111 Achievement 7 -.099 .040 .153 8 -9098 .038 0150 None of the correlations are sufficient to reject the null hypothesis and Hypothesis 5 remains tenable. It should be noted, however, that the correlation between gain and sixth grade verbal achievement (.227) would have been significant had alpha been equal to .05. (The critical r for an alpha of .05 is .205.) The data offers no explanation for this one coefficient being so much greater than the others. In addition, it is interesting that all of the co- efficients associated with the pretest are negative in sign whilxe all the others are positive in sign. This same trend 93 will be observed in the next section in regard to mathematics achievement. Since this trend was not anticipated, the author is unable to evaluate its meaning with the present research design. One possible explanation is that the change in sign is due to the rather large movement (improvement) between the pre—and posttest scores on the test instrument. In summary, the performance on the test instrument of this sample of 100 students was not significantly related to their performance on tests of verbal achievement. (Refer to Appendix B for scatterplots of Mathematics Achievement Scores for grades four through eight) Hypothesis 6: It is postulated that the correlation between student performance on the test instrument and mathematics achievement scores* will not be significant. The null hypothesis to be tested is that the population correlation is zero. For a two-tailed t test with 98 degrees of freedom the critical value of r for the .01 level of significance remains at .264. The data is summarized in Table 8 on the following page. ; 8 Scores on the verbal component of the Iowa Test of Basic Skills. Table 8 Correlations Between The Test Instrument And Mathematics Achievement By Grade Level Test Instrument Pre Post Gain 4 -.121 -.044 .110 5 -.108 .011 .140 Mathematics 6 -.115 .050 .188 Achievement 7 -0126 .018 0168 8 —.084 .0145 .139 None of the above coefficients are significant. Triearefore, Hypothesis 6 remains tenable. It should be noted that all of the coefficients associated with the pretest are negative in sign while all bunt: cone of the others are positive in sign. This trend was observed and discussed in the preceding discussion of Hypothesis 5 and the situation is comparably difficult t 0 eXp lain. 95 On the basis of this data it would seem that the ability of this sample of 100 students to respond to the teaching method being evaluated was not significantly re— lated to their performance on standardized tests of mathematics achievement. (Refer to Appendix E for scatterplots of Verbal Achievement Scores for grades four through eight) Hypothesis 7: It is postulated that the correlation between student performance on the test instrument and grades will not be significant. The null hypothesis that the pOpulation correlation equals zero will be tested by means of a two-tailed t test with 98 degrees of freedom. The critical r for rejection at the .01 level of significance is again .264. The correlations between the test instrument and grades received in mathematics courses are summarized in Table 9 on the following age. The correlations between the test instrument and grades received in English courses are summarized in Tab 1e 10 . Since the same trends are observed in both tables they will be discussed together. Correlations Mathematics Grades Table 9 And Mathematics Grade S Between The Test Instrument Test Instrument Pre Post Gain 4 -.155 -.127 .083 5 —.018 .024 .041 6 -.062 -.039 .043 7 .089 .068 -.052 8 .010 - 003 -.015 'Table 10 Correlations Between The Test Instrument English Grades And English Grades Test Instrument Pre Post Gain 4 -.094 -.073 .053 5 -.l74 -.027 .183 6 .014 -.044 .053 7 -.007 -.098 .037 8 .008 .109 .080 97 None of the coefficients in either table are sig- nificant. Therefore, Hypothesis 7 remains tenable. Since there is no discernible pattern to the positive and negative signs of the coefficients, no explanation can be offered. In effect, there is little relationship between the perfor- mance of this sample of 100 students on the test instrument and the grades they received in various mathematics and English courses. 98 Chapter 4 REFERENCES CITED 1. Anne Anastasi, Differential Psychology, 3rd edition, New York, Macmillan, 1958, pp. 190-191. 2. Allen L. Edwards, Experimental Design In Psychological Research, Holt, Rinehart and Winston, New York, 1964, p. 782 3. J. P. Guilford, Fundamental Statistics in Psychology and Education, McGraw-Hill, New York, 1965, p. 322. Chapter 5 CONCLUSIONS AND RECOMMENDATIONS Conclusions In this study the predicted non-correlation toetween social and familial variables and student Eichievement were found. The non-significance of these ccxrrelations were determined by a two—tailed t test for ccarrelated means and the t ratio for testing the scignificance of a correlation coefficient. The results of this study indicated that familial (zliaracteristics or sociocultural variables did not Zirifluence student achievement with this teaching method. {Pliis teaching method did not require reading competence 2111 the students. This particular skill is one that the 3.i:terature reviewed in this paper has shown impedes the ESLiccess of disadvantaged children in learning mathematics. According to the data of this sample, the presence C>I‘ absence of a ”father” in the home produces no systematic Eiffifect upon the performance of students on the teaching Inerthod in question. 100 In a similar manner, the null hypothesis concerned with the correlation between student performance on the test instrument and crowding in the home was rejected. Based upon the results of this study, it can be stated ‘that it is what, rather than who, is in the learning ennvironment of the disadvantaged child, that has the greater eaffect upon the student's success with the teaching nuethodology utilized in this study. Although the conclusions previously stated are Inelated to a methodology for teaching disadvantaged child- IWBH, other conclusions may also be drawn from the results 0 12‘ this study . These conclusions are: l. Sociocultural variables are not significantly czcxrrelated with student performance on the test instrument. 101 2. Vocabulary deficiencies are not a barrier to successful learning when the disadvantaged child is presented with a teaching methodology that does not emphasize reading skills. Recommendations The sociocultural environment has been studied as a means of understanding the factors which influence the intellectual development of disadvantaged children. Research studies cited in this paper have shown repeatedly that this environment greatly influences the intellectual development of disadvantaged children. The foregoing statement implies that there should be an exploration of Piaget's theory of interaction between the organism and his environment. A stimulating educa- tional environment in the home may influence the academic growth of the child. In a similar manner, the capacity of the child to profit from such an environ- ment may influence the parental efforts in providing a stimulating environment. A similar phenomenon may occur in the school environment. This chain—like cause and effect relationship, if studied, should provide further 102 understanding about the interaction between the disadvan- taged child and his environment. Such investigations may involve longitudinal studies as well as intensive case studies in order to obtain empirical data about the possible interaction between the disadvantaged child and his educa- tional environment. If a high correlation between the environ- mental factors and achievement scores is sustained by future research, then a wide variety of topics for studying the intellectual growth of the disadvantaged child may become evident. One of the areas for further research would be to determine whether the relation between parallel measurements over a given amount of time is directly related to the intellectual development represented at the different stages of development. These measures could include data on physical characteristics, personality development, achievement data, home environment, and any changes in the socioeconomic status between infancy and adulthood. A longitudinal study would also appear to be useful, especially at the elementary stage. It seems 103 necessary to study the relationship between the measure- ment of the educational environment in the home at the time the disadvantaged child is first admitted to school and his educational achievement throughout school. If these relationships are found to be comparable to those found in the present study, the environment and socioeconomic measurements are likely to be very useful in making academic predictions. Another area for further research is to study the role of social class as it affects language develop- ment and cognition. Such studies will provide further understanding about the influences of the intellectual environment in the home at different stages of development. It would appear that the deficiencies of the sociocultural environment make it more difficult for disadvantaged children to understand a teaching methodology which presupposes a variety of experiences which they have not been afforded. The results of this study, however, indicate that a teaching methodology can be developed for this impoverished intellectual background. 1014 If replications of this study confirm the present findings, then further research should be focused on environmental variables and their relationship with other pertinent variables. One area of research may be directed toward the develOpment and evaluation of a curriculum that would overcome the multilateral influences of social deprivations on learning. 105 Chapter 5 REFERENCES CITED 1. Jerome Bruner, Toward a Theory of Instruction, Cambridge: Harvard University Press, 1966. 2. David Ausubel, Educational Psychology: A Cognitive View, New York: dolt, Rinehart and Winston, Co., 1965. 3. Jean Piaget, B. Inhelder and A. Szeminaka, The Child's Conception of Geometry, translated by E. A. Lunzer, Sew York: Basic Book, Inc., 1960. 4. Basil Bernstein, ”Social Structure, Language, and Learning,“ in Harry Passow, Miriam Goldberg, Abraham J. 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UNPUBLISHED ARTICLES Battle, H.J. “Application of Inverted Analysis in a Study of the Relation Between Values and Achievement of High School Pupils," Unpublished Doctoral Dissertation, University of Chicago, 195H. Bechtold, C. ”The Use of Extraneous Material in Developing Problem—Solving Ability of Pupils in Algebra 1.," Un— published Doctoral Dissertation, Teachers College, Columbia University, 1965. Binkley, M.E. "First Grade Entrance Variables Related to Achievement and Personality, A Study of Culturally Deprived Fourth Graders," Unpublished Doctoral Disserta- tion, University of Tennessee, 1967. Hill, S.A. "A Study of the Logical Thinking Abilities of Children,” Unpublished Doctoral Thesis, Stanford University, 1960. Kline, R.D. "A Study to Determine if Educational Materials Designed Specifically for a Developing Nation are Equally Effective in Producing Student Achievement in a Developing Nation," Unpublished Doctoral Disserta- tion, Syracuse, University, 1967. Meconi, L.J. ”An Experimental Study of Concept Learning and Retention in Mathematics," Unpublished Doctoral Dissertation, The Ohio State University, 1966. Post, R. "A Study of Certain Factors Affecting the Understanding of Verbal Problems in Arithmetic,” Un- published Doctoral Dissertation, Teachers College, Columbia University, 1958. Rosner, B. "Community Socioeconomic Status in Mental Organization," Unpublished Doctoral Dissertation, Teachers College, Columbia University, 1955. Searle, R.E. "Mathematical Abilities Passed by Kindergarten Children from Disadvantaged Communities," Unpublished Doctoral Dissertation, University of California, 1968. Siller, J. "The Effect of Differential Socioeconomic Status Upon the DeveIOpment of Conceputal Ability," Un- published Doctoral Dissertation, New York University, 1956. Skypak, D.H. ”The Relationship of Socioeconomic Status to the Deve10pment of Conservation of Numbers,” Un- published Doctoral Dissertation, University of Wisconsin, 1967. Spain, J.C. ”Definition of Familar Nouns by Culturally Deprived and Non-Deprived Children of Varying Ages,” Unpublished Doctoral Dissertation, George Peabody College for Teachers, 1962. APPENDI XES INDEX OF SOCIOECONOMIC STATUS 134 APPENDIX A INSTITUTE FOR DEVELOPMENTAL STUDIES Department of Psychiatry New York Medical College Instructions in Use of the Index of Socioeconomic Status* The index of socioeconomic status (SES) developed at the Institute for Deve10pmental Studies in New York City utilizes two factors to estimate the relative social posi— tioning of individuals in a given community. These factors are identified as: 1. occupation of main support of the family 2. education of main support of the family Implicit assumptions in the use of the scale are that: 1. within any family unit, the social status of an individual can be derived from certain characteristics of the head of that family, and 2. within a community certain individuals are accorded more prestige than others on the basis of their occupation, education and/or income. The following instructions outline the steps in obtaining an SES rating for children who are to be tested. The procedure involved is simple and the rating can be & Original, 1961; revised, 1965. 135 obtained in a few short steps. INSTRUCTIONS 1. Find the occupation of the specified head of the family in the occupational classification given in the following pages: OCCUPATIONAL RATING SCALE OCCUPATION HAT N U.S. Supreme Court Justice U.S. Diplomat or Foreign Service State Governor, Mayor of large city U.S. Cabinet Member U.S. Senator, Congressman lO Physician College President or Chancellor College Professor Scientist (Government or other) State Attorney Bank Executive Investment Broker Captain of ocean—going vessel County Judge Department Head, State Government Motion Picture Actor, (not “extra") Minister Lawyer Architect Postmaster, City Chemist Dentist Electronic Engineer Nuclear Physicist Civil Engineer 9 Mathematician Radio entertainer (except announcer) Director, Large Corporation Business Executive, Advertising Executive Airplane Pilot Inventor OCCUPATION RATING Editor-Owner newspaper Psychologist Veterinarian Historian, Economist Sociologist Medical Researcher, Biologist Author 8 Accountant, C.P.A. Registered Nurse Justice of the Peace Government Investigator (FBI, Justice Dept., etc.) Artist, performing artist Professional Athlete Interior Decorator, Industrial Designer, Fashion Designer Factory, Department Store Owner High School Teacher Building Contractor Radio Operator Mine owner-Operator Owner of logging camp Musician in symphony orchestra Small Retail Owner Sheriff-County Army-Captain or above Elementary School Teacher 7 Railroad-Supervisor Real Estate Agent Agricultural Agent-County Laboratory Technician Detective of Police Fire Lt. or above 136 137 OCCUPATION RATI§§_ Private Secretary Undertaker Social, Welfare Worker Foreman or Supervisor, Factory Labor Union official-National only Radio Announcer Farm owner-Operator Hotel Manager 6 Newspaper Columnist Owner-Operator print Shop Railroad-Engineer Electrician Matchmaker, factory Trained Machinist Mason Dental Technician Auto Salesman Office Manager Owner-operator dry cleaning Linotype Operator, printer Newspaper reporter, proofreader Oil well driller (not engineer) Manager small store Policeman, private investigator 5 Mail clerk, carrier Bookkeeper Insurance Agent Traveling Salesman Receptionist, typist secretary Bank Clerk Railroad Conductor, ticket agent Practical Nurse I.E.M. Keypunch operator OCCUPATION RATING Playground worker Teachers Aid Structural Iron worker Carpenter Pawnbroker Tenant farmer Auto mechanic Dressmaker Beautician A Plumber ‘elephone Operator, lineman Labor union official-Local only Lunch stand operator Painter, house and/or non factory Salesclerk, grocery clerk Musician—pOpular, dance, singer Furniture finisher T.V. repairman Fireman Welder, offset prcssman Machinist-Factory Barber Shoe repair man Railroad baggage handler Other semi—skilled Cook-restaurant or hotel, short order Chauffer-private Fisherman Motorman, bus driver, conductor Milk route man Shipping clerk Cashier Merchant seaman Truck driver UJ Gas station attendant Quarry worker Night club singer Porter—railroad Taxi driver Waiter—Bartender Farm worker All unskilled laborers Coal miner Night watchman Janitorial-Building super— intendent Elevator operator Freight handler Nurse's Aide Laundry worker Newsboy Soda clerk Peddler Grinder-tool, etc. Odd Job worker Share crOpper-migratory worker Scrub woman Garbage collector Street sweeper Shoe Shiner 2. Occupational categories have been grouped into clusters; each has a prestige ratin 139 Assign a rating to each child based on the occupation of main support of his family. For example, U.S. Supreme Court Justice is rated ”10”, Milk Route Man is rated "3". will be the occupation rating of each child. This number 3. Similarly, the education level of the head of the child's family is to be rated. A. The following table specifies the ratings to be assigned for level of education of the main support in IMO the child's family. EDUCATION RATING 0-4 years 1 5—6 years 2 7—8 years 3 Some high school High School graduate 5 Some college 6 College graduate 7 Post graduate or professional training 8 5. You now have two (2) ratings for each child. One the basis of these two ratings (occupations and educa- tion) you can now derive an estimated SES rating for each child as follows: 6. Referring to the table on the following page: oo 10 838 CONVERSION TABLE Education of Main Support 1A1 l 2 3 A 5 6 7 8 I I I I I II II II I I I I II II II III Occupa- I I I I II II III III tion I I I II II III III III of Main I I I II II III III III Support I I II II III III III III I II II III III III III III II II II III III III III III II II III III III III III III II II III III III III III III l. locate the occupation rating of main support for a given child on the left hand side of the figure; 2. locate the education of main support for a given child across the top of the figure; 142 3. find the coordinate of these two by bring- ing your finger down to the point where they both meet. You will find that they meet in a box numbered I, II or III. This numerical value is the overall SES rating for the child. 7. Enter this number in the space marked "SES-A" in the lower right hand corner of the child's Background Information Sheet. 8. In the space marked “SES-B" enter your own judgmental estimate of the child's relative social status based on any familiarity that you may have with the child or his family. Use the numerals I, II or III where I will represent "Low” and III will represent ”High". QUESTIONN AIRE 1A3 APPENDIX B Dear Teacher, It is possible that some of your students may have a reading difficulty. Please feel free to assist them in reading and/or interpreting the questions as this information is of extreme importance to this study. Thank you for your cooperation in this regard and on the other phase of the program. Sincerely, Steven Newstat (This letter was sent with the packet of questionnaires to each c00perating teacher involved in this study.) mat-311123311331: 11111 1" 1’. 11.313! (2111181101: (11.33.6111: 11111.1 11117111131 111.111 1.8 111.131 TO YOUR NISL‘ 1'1‘ "m'1{t1.:s,\'(1':12.332315. 13(1). 'ACli (‘EIU "M“: 3011 I-IAY OZIIT ANY O. 1.311.“. 13113011 1;)... 10:31.0 mart”. 1'03: '10 1.15.124, 171:3;- 1123:: .‘1‘1~:3:-71-:;< Jim-3'1 1.1.1. 11" YOU 1".)355113111' C111. . 1- Are ye Inale or female? 6. Where have you spent (a) Male most of your life? (b) Female (3) In thS 'ty, or ‘ county '2, How old were you on your last (b) In this state but birthday? _ outsirk: this citgg (a) 1.0 (0) 1’1 town, or county (h) l] (f) 15 (c) In another state (C) 12 (g) 16 older in the U.S. (d) 13 (d) Irllhlcrto fhtwo or 3. Where were you born? another 0.8. poss- . ess5.on (a) Alabama (08) NOW Jersey (0) In Mexico b) Alas:ka (ff) New Mexico ‘ (f) In Canada (C) Aid-zeta). (5'31) 110“ Y0 "3‘11x (g) In a Country other (d) Arkansas (hh) onth Ca .rolina 1 than the U.S., Canada ((2) California (173) I: nth D3 kota or 11e>3flco (f) Colorado (jj) Oh3o (3,) Connecticut (111x) Oklahoma '(1!) Delavz‘nfe (11) (”1‘83“ 7. In what type of corm‘mnity (1) District of (mm) Pennsylvania have you spent most ot_ Columbia (nn) Rhode Island your life? (CIVC your (J) 111015-05: (00) 50““) (331011?“ best estimate if: you are. (1;) Georgia (pp) south Dakota not sure.) (3-) Ismaii (HQ) UCBBCSSQC (a) In the open country (m) Idaho (rr) TGKUS or in a farming (n) IlliJwais (ss) Utatm confinhqlty (0) Indiana (tt) Vermont (b) In a small town (p) Iowa (uu) Vir2inia (less than 10,000 (q) Kansas (VV) WafihLUECOD people) that was not (r) Kentucky (WV) WGSt Virginia a suburb (9) LOUiSiCHC (XX) Wisconsin (c) Inside a medium size (I) Maine (23) Wyoming city (10,000 to 100,00: (u) Maryland (22) U.S. possess- on people) (v) Massachusetts (American San mo (d) In a suburb of a medium (w) Michigan Canal Zone, Guam, size city . (X) Minnesota & V). 1"? in 11816711618) (9) Inside a large city (y) Mississi.ppi (383) Puerto Rico (100,000 to 500N000 (2) Missouri (bbb) NCXiCO peeplc) (aa) Montana (CCC) Cflnéfla (f) In a suburb of a (bb) Nebraska (ddd) Country other large City (cc) Nevada than the U.S. or (g) in a very large Clty (dd) N Hampshire ltS POSSESSiOUS, . (over 500,000 peeple) Pucrto Rico, Canada (b) In a suburb of a very or Mex1co large Clty (eee) I don't know 4. ‘Wbertrwas your mother born? 8. When was the last time you Chang c-d schools (not .___ counting pluz‘..utlox‘; :3 fr (T1 one school to anor1.er)? (a) I have not changed 5. Ifiwzre was your father born? schools (b) Less than a year ago (c) About one year ago ((1) About two year ago. __,_ ‘o 9. v 10. How far do you want to go in 15- school? ' (a) ]' dC)1lot.\mant Ix) illiish higfiv scln3ol' (b) I want. to finish high SChOCd-(NIlf (C) I VHNit to go to tcwlr3ical, 16- nursin,, or busin*ss school after hLLh school (d) Ekxwe colqun3 trainiinj, but less t1k11¢3 years (c) I want to graduate from a 4 year college (i) I want to do pro he sional or graduate work after I finis h college 17. Cijxrle ttm: itenu; that )mnir flniily now has. (a)'l elev15110n Sct (b) lelephone (c) Record player, hi-fi, or 18. Stcnkfio (d) Electric or gas refrigerator (e) I)ict3(nwar)' (f) Set ot encyclopedias (g) Automobile (h) Vacuum c]: .an at (1) Daily newspaper 11. How many books are in your home? 12. 13. 14. (a) lkxie or \er3 ikna (o~9) (b) A it»: (1.0- 24) (c) One bookcase full (23*99) (d) Two bookcases full(lOO-2&9) (e) Three or more bookcases full (230 or more) Do you usually find writing papers ‘a difficult task, or do you have relatively little difficulty getting your ideas down on paper? (a) I find writing papers a very difficult t; sk (b) I frequently have some deficulty writi-ng (e) Usually I do not have much difficulty writing (d) I have little if any difficulty eXprcss sing myself in writing [M3 you make notes while reading a book? (a) No or almost never 19. (b) Once in a while, depending upon the subject (c) I generally do, but I have no particular notemaking system (d) I almost always make notes while reading, and I have a systematic method ior deing so. Dill you go to kindergarte 1:? 1’15 Did you go to nursery school before you went to kinder .xtcn? (a) Yes (b) No (C) 1 (lorl't rcuuenlic1‘. When you were in grade school, about how often did you use a public library for reading not required by your school? (a) (b) (C) (0) Once a we*k or more. 'lX-zo or three times a month. Once a month or less. 11'803.’ r. How many maeazincs do you and. you: family get legularly at heme? (8) (b) (C) 3:11 1. c. 1‘. IQone (d) 33 or (3 l or 2 (e) 7 or more. 3 or 4 of the iollowing magazines do you and yoUr family get regularly? (a) (b) (C) (d) (e) (f) (s) (h) (i) (j) (k) (1) (m) (n) (0) ' (P) (q) (r) (S) (r) (U) Jet Good Housekeeping Igulies lkrne Jcnirnal. family Circle McCall's Reader's Digest Saturday ICVICW Time 1.301: Life Newsweek Astro Science Raama *7 ts Nation Ebony Better Homes and Gardens Scientific American Jack and Jill The Instructor None. ............ ooooooooo Did anyone at home read to you before you started going to school? (a) (b) (C) (d) (0') No. Once in a while. Many times, but not regularly Many times and regularly. I don't remember GO ON 10 THE NEXT PACE............. 20. 22. (a) (b) (C) (d) (C) Who ls now a lather to you? lfiy real JIJLher, \dK) LS llxurng at home. bk; real linther, \dwo 18 livrng at home. My stepfather. My tester talher. My grandfather. Another relatxve (uncle, etc.) Another grownup (not a relatlvc). No one. not now actlng as your mother? "rtz1l nkotln2r" ll: ycnl 81H? achoptLCCl. (a) (b) (C) (d) (e) (f) (s) (h) (a) (b) (C) (d) (O) (f) (s) (h) (1') My real mother, who is 11VJng at home. Iy real mother, l3v1ng, at home. thy stepmother. My foster mother. [3 glénldfifi‘thtflf. Other rclat1ve(aunt, etc.) Other adult. No one. who is not: How far in school did your father g)? None, or some grade school. Completed grade school. Some hlgh school, but did not graduate. Graduated from hlgh school. Technical or buslncss school after hlgh school. Some college but less than 4 years. Graduated fr m a 4-year college. Attended graduate or professlonal school. I (knu't know. 23. Bow I2n:.rn school did your mother go? 24. 25. (a) (b) (C) (d) (C) (f) (g) (h) (1) Does home ? (a) (b) (C) Where that (a) try father's work. (b) (C) lax Lngltare Department bkmue, or some grade school. Coaq)leted grade school. Some hlgh school, but did not graduate. Graduated frOm hlgh school. Technlcal, nur51ng, or busirmms school after high school. Sonmécxfllcgc but less than 4 years. (Sraduated from a regular 4-year college. 26. lhxat vagrk chaos )wntr'ltujwur_lh:?_l9£ You tnwflud)ly wrll.zu3t flnd hls exact JOb listed, hut check the one that comes closest. If he is now out of work or if he is retired, nark the one that he ustunlly' dltl. lhlrk CMxly tlls nwiin Jed) ll lwe yxwrks (n1 ma;))', l)zn31;01 , government orrlcial or inspecttnf, etc. (c) Sales manager, store manager, office manager, factory supervisor, etc. (d) Otnnor of axsnnall tunalncss, wholesaler, retaller, contractor, rcstxununut owner etc. (0) Factory machlne operator, bus or cab drlver, meat cutter, etc. Bank teller, bookkeeper, sale— clerk, offlce clerk, mail carricn:,xnessengxu , etc. (g) Barber, walter, etc. (h) Policeman,'detect1ve, sherxi: flrccnnu, etc. (1) Real estate or 1nsurancc salesman, factory represent- ative, etc. (f) (3) Farm or ranch manageror ownc1_ (k) Farm worker on one or more than one farm. (1) Factory or mlne worker, fisherman, ftlllng station .attendant, longshorcman, etc. (m) Accountant, artlst, clergyman dentist, doctor, engineer, lawyer, librarian, sclentlst, college professor, socral worker, school teacher. Baker, carpenter, electrlcjafi enlisted man 1n the armed forces, mechanic, plumber, plasterer, tatlor, foreman in a factory or mine. (0) I don't know. (D) Ikttendcd graduate or profe551onal school. I don't know. your nmfiimr have a Job out51de your YCS, fell-tlme. Yes, part-tlme. tic. ' (hugs most or the money come from pa)q; for your famlly expenses? (f) Frlcnds 1), mo t’ her ' 5 work . (3) Other Youxrcmn1xmndm (e) Relatives ”3“ low good a student does your mother want you to be 1n school? (a) One of the best tn my class. (b) Above the middle of the class (c) In the middle of my class. (d) Just good enough to get by. (c) I don't know. GO ON TO THE err PACE.......... . ~r—vn—o—p—M-—.-4 '-~-"‘l-->‘- .~‘-.- 28. 29. .30. 31. 32. 33. How good a student does your father 34- want you to he in school? ' (a) One of the best in my class. (b) Above the middle of the class. (c) In the middle of my class. (d) Just good enough to get by. (e) I don't know. HOW often do you and your parents talk about your school work? (a) Just about every day. 3). (h) Once or twice a week. (c) Once or twice a month. (d) Never or hardly ever. How much education does your father want you to have? (a) Doesn't care if I finish high school or not. (b) Finish high school only. . (c) Technical, nursing, or bUSiness school after high . a school. 36. (d) Some college but less than 4 years. (c) Graduate from a 4-year college. (f) Professional or graduate school. (g) Father is not at home. (h) I don't know. ' How much education does your mother 37. want you to have? (a) Doesn't care if I finish high school or not. (b) Finish high school only. (c) Technical, nurSing, or bUSiness school after high school. . (d) Some college but less than 4 years. (c) Giaduate fromexé-year college. (f) Professional or graduate school. 38. (g) Mother is not at home. (h) I don't know. How many of your brothers and sisters left high school before finishing? (3) Have no older brothers or Sisters. (b) None. (c) 1 (h) 6 (d) 2 (1) 7 - (e) 3 (j) 8 or more 39. (f) 4 (k) I don't know. (8) 5 How many of your brothers and Sisters attended a year or more of college? (3) Have no older brothers or sisters. (b) None. (h) 6 (c) 1 (i) 7 40. (d) 2 (J) 8 or more. (C) 3 (k) I don't know. (f) 4 (s) 5 - How many of your lnfothcrs or Sisters.graduated from college? (r) Have no older brothers or sisters. (b) l (s) 6 (c) 2 (h) / (d) 3 (i) 8 or more. (C) 4 (J) I don't know. (I) 5 . (k) None. How much education do you want 1 have? (a) I don't care. (b) Some college training,but less than 4 years. -. I...‘“~+vl\—- .4 (c) Graduate from a 4-yearCO11033 (d) A graduate degree such as' M. A. or Ph.D. (e) A profesSional degree such law (LLB) or mediCine (lib. (f) Undecided. Do you ever find yourself bored in class? (a) Almost all of the time. (b) Fairly often. (c) Occasionally. (d) Almost never. -m-~q—.~. a“ .. . .- During the last school year, did; you ever stay away from school just because you didn't want to come? (a) No. ' ' ' (b) Yes, for l or 2 days. (c) Yes, for 3 to 6 days. (d) Yes, for 7 to 15 days. (0) Yes, for 16 or more days. On an average weekday, how much time do you spend studying? (a) None or almost none. (b) About 1/2 hour a day. (c) About 1 hour a day. (d) About 1 & 1/2 hours a day. (e) About 2 hours a day. (f) About 3 hours a day. (3) 4 or more hours a day. Compared with your classmates here in school, do you study more or less than they do? (a) More than others. (b) About the same as others. (c) Less than others. (d) I don't know. How do you and your friends rate socially in school? (a) At the top. (b) Near the toP. (c) About the middle. ((1) Near t‘ 3 bottom. .’ I —_ifi— - 41Jhmrbright do you think you are in comparison with the other students in your classes this year? (a) Among the brightest. (b) Above average. .(c) Average. (d) Below average. (c) Among the lowest. 42.1 would make any sacrifice to get ahead (d) 5 in the world. (a) Ital-CC (b) Not sure. (c) Disagree. 43:1f I could change,1 would be someone different from myself. (a) Agretu (b) Not sure. (c) Disagree. 44.1 sometimes feel that I just can't learn. (a) Agree. (b) Not sure. (c) Disagree. 45.1 would do better in school work if teachers didn't go so fast. (a) Agree. (b) Not sure. (c) Disagree. . 46.?00ple like me don't have much of a chance to be successful in life. (a) lugree. (b) Not sure. (c) Disagree. 47.The (a) (0) “(C) 46.1 am able to do many things well. (a) Agree. (b) Not sure. (c) Disagree. Agree. Not sure. Disagree. 49.About how long does it take you to get ill thClIO. "" ' ‘x ? '- 1 rning to SCthl (d) Deiinitely not. from your home (a) 10 minutes (b) 2U minutes. (c) 30 minutes. (d) 45 minutes. (e) One hour or more. or less. 50.now do you u5ually come to school in the morning? (8) Automobile. (b) Walk. (c) School Bus. (d) Train, trolley, subway, or bus other thaneaschooltnm_ (e) BLCleC. (f) Other. tougher the Job,the harder I work. 51.How many people are iivin§"Ifi"” your home at the present time including yourself,brothcrs, sisters,parents,relatives, and others who lived with you? (a) 2 (c) 6 (i) 10 (b) 3 (f) 7 (J) 11 or (c) 4 (g) d more. (h) 9 52.Huw many rooms are there in your family's house? Count only the rooms your family lives in. Count the kitchen (if separate) but 325 the bathrooms. (a) l (e) 5 (1) 9 (b) 2 (f) 6 ‘(J) 10 or (c) 3 (g) 7 more. (d) 4 (h) d 53.Does anyone in your home speak a language other than English most of the time? Spanish,1talian, Polish, German, etc.)‘ (a) Yes. (b) No. 54.Do you speak a foreign language other than English outside of school? (a) Yes, frequently. (b) Yes, occasionally. (c) Yes, rarely. (d) No. - 55.Are you planning to go to high school? . (a) Definitely yes. (b) Probably yes. (c) Probably not. (d) Definitely not. 56.Aic you planning to finish high school? (a) Definitely yes. (b) Prohably_yes. (c) Probably not. 57.When you finish school,what sort of Job do you think you will have? Pick the one that is closest. BOYS Assure PROM SELECTIONS Iggggg_ (a) Draftsman or medical techniCian. (b) Banker,company officer,or govern- ment OILLCLBlv (c) Store owner or manager,officc manager. (d) Sales c]erk,office clerk,truck driver,waiter,puliceman,bookkeepcr, mailman, barber. Salesman. Farm or ranch manager or owner. on one or more than (0) (f) (g) Farm worker one farm. GO ON TO CHILI IQISXT l’ACI-I. . . . . . . . . . . . . . . . . [9'97“ '9‘- I‘d-4-... (- _ '-‘0"¢-”—4-w.~.l<-—.-.--—-o-m-. ‘_ . A." 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