THE EFFECT OF LACK OF FORMAL SCHOOLING ON- NUMBER DEVELOPMENT Thesis §or the Degree of Ph. D. MICHIGAN STATE UNIVERSITY Egon Mermelsfein 1965 LIBRARY 1., Michib a State URlVLfllt‘y mum;«@yujmuwumrwuyulflu an! - “‘5' This is to certify that the thesis entitled THE EFFECT OF LACK OF FORMAL SCHOOLING ON NUMBER DEVELOPMENT presented by Egon Merme 1 stein has been accepted towards fulfillment of the requirements for 7'53: 32 ef/fle Major professor Date February 26‘1 1965 0-169 ‘ ABSTRACT The Effect of Lack of Formal Schooling on Number Development by Egon Nermelstein The primary purpose of this study was to examine whether lack of formal schooling alters and affects the attainment of stages of number deveIOpment. A secondary purpose of this study was to examine the effects of em- ploying particular types of questions and non-verbal techniques in assessing a child's performance. It was hypothesized that lack of schooling does not alter and affect the stages of number develOpment on non- verbal tasks. On verbal tasks, however, it was hypothesized that lack of schooling does alter and affect the stages of number deve10pment. As to the secondary purpose of the study, it was hypothesized that phrasing of the question does Egg affect performance of subjects on Piagetian tasks and further it was hypothesized that the prOportion of subjects passing only the non-verbal task is significantly greater than the prOportion of subjects passing only a verbal discontinuous task. One hundred twenty Negro children, sixty males and sixty females, six and nine years old, were randomly assigned to the eXperimental treatments. Four verbal Egon Nermelstein Piagetian conservation of substance tasks and a non-verbal conservation task were administered to each child. Each child was asked one of a possible three questions on the verbal tasks. Sixty Ss, thirty males and thirty females were selected from Prince Edward County, Virginia, a small rural community of which thirty nine-year-old males and females were deprived of formal schooling. Sixty $3 from Flint, Michigan were matched to Prince Edward County children on the basis of age, sex and socio-economic class. The findings for non-verbal tasks support the hypothesis that lack of schooling does not alter and affect the stages of develOpment. On the other hand, the findings on the verbal tasks do not support the hypothesis that schooling affects and alters the stages of number develOp- ment. As to the secondary purpose of the study, the find- ings support the hypothesis regarding phrasing of the question with continuous tasks but reject the hypothesis for discontinuous tasks. And finally, the results support the hypothesis that the number of subjects only passing the non-verbal task is significantly greater than the ‘ subjettfi filly passing the verbal discontinuous tasks. Egon Nermelstein Consistent with the literature (5), it is concluded that forma schoqling plays a minor role in number develOp- ment. Further, it is concluded that questioning does not generally influence performance; however, further research is needed in this area. It is 1150 concluded that the remarkable difference in performance on verbal and non- verbal tasks suggests that the "presence" or "absence" of language is a relevant variable in studying number develOp- ment. THE EFFECT or LACK or FORMAL SCHOOLING ON NUMBER DEVELOPMENT by Egon Mermelstein A Thesis Submitted To Michigan State University In Partial Fulfillment Of The Requirements For The Degree of DOCTOR OF PHILOSOPHY College of Education 1965 Acknowledgements The writer first wishes to express his appreciation to his committee, Dr. Lee Shulman, Dr. Bernard Corman, Dr. Clessen Martin and Dr. Donald Johnson. Dr. Shulman, the writer's major adviser, provided able guidance, understanding and concern in the study. Dr. German's insights proved to be very beneficial for the study. Dr. Martin's valuable assistance in the design facilitated the study; and Dr. Johnson's comments on the final draft were most helpful. Secondly, the writer wishes to express his apprecia- tion to the graduate students in Educational Psychology and Research Design and DeveloPment who provided constructive criticism of the study. Thirdly, the writer wishes to express his gratitude to Mrs. Joyce Stewart for the typing of all the drafts of the study. Last, but certainly not least, the writer wishes to eXpress his gratitude to his wife, Jan, and daughter, Allison, who have been a consistent source of inspiration and support. ii 7 -~ Tz‘kEJ—aé 7" ‘ “ ‘V‘q\"'fifi‘r~§f~ :‘LC'.\.IC' .luD’J 24.4..“ .. u) o o o O O I— an '71“ "T 54" 1:) C". --..Ja-..a; . . g Q o . r11 '1‘“ A- '3 L S- v'- ‘ 2 .LxJL-..:: . o O o o 7 CUT! A? A “xv"?‘Y-\ AH” L.) VA. V. A;_L—-.J VodL) O O C O .firfi-‘I yam f‘ -, n‘ ..- -fi 1.. aflcvrfi Ii‘L-‘n‘bOJLVLIVA: LX‘I ShifLL-Q'QHA‘IJ- _ fit. “TV‘V ”fl is» 'vJ‘AJ'uiLQs-J . g o o o o o 0 I‘m"- 3": isuyphiu o o o o o o o o o 7 - 93' "a v -1 DISCLCSIOLI £.i_1' COi. vLUS .LOuS n? AH“ 6' 9 813.31.. UULL.\L';fi o o o o o o 0 .‘1‘3‘: Affin‘ A- DI‘dQ-L o o o o o o o 0" "' 5". U O O O O O O O O O O O 0 vs vs a t— L - -N O O I O O O 0 O O O O O O O O Ho Ho Ho Ivmflefiffirfi L LL“ L U '5 L899 -—&— Pl rd. 0&an #1»me 0 CA r3 $1) 0‘ U1 Ox 10 11 x'. 2 x 2 x 2 X 3 x 5 Design Used to Study the Effects of Schooling, Instruction, and anguage on Performance . . . . . . . . . Comparison of Prince Edward County 6- and 9 ’ear Olds' Performance and Flint 6- and 9-Year-Clds' Performance on Task 1, the on-verbal Task . . . . . . . . . . . . . :35 Comparison of Prince Edward County 6-Year- Olds' and Flint 6-Year-Olds' Ierformance on Task 2 and Task 3 . . . . . . . . . . Comparison of Prince Edward County 6-Year- Clds' and Flint 6-Year-Clds' Performance on Ta 81’: 4 . . g Q Q Q Q 0 O O O O . O O 0 Comparison of Prince Edward County 6-Year- Clds' and Flint 6-Year-Olds' Performance ~ :- 011 T3 SLQ J g o o o o o o o o e o o o o o 0 Comparison of Prince Edward County 9-Year- Olds' and Flint 9-Year-Clds' Performance on Task 2 . . . . . . . . . . . . . . . . Comparison of Prince Edward County 9-Year- Olds' and Flint 9-Year-Olds' Performance ‘ fi 01“. T5185 3 o o o o o o o o o o o o o o o 0 Comparison of frince Edward County 9-Year- Olds' and Flint 9-Year-Olds' Performance on Task 4 . . . . . . . . . . . . . . . . Comparison of Irince Edward County 9-Year- Olds' and Flint 9-Year-Clds' Performance m ' V" 011 La 4’s 3 o o o o o o o o o o o o o o o 0 Type A, Type B, Type C Questions and Eerformance of Subjects on Tasa 2 . . . . Type A, Type 3, Type C Questions and Performance of Subjects on Task 3 . . . . iv Fave b.) (h 41 44 46 46 47 47 49 l3 14 15 Type A, Type E, Type C Questions and Performance of Subjects on Task 4 . Type A, Type 8, Type C Questions and Performance of Subjects on Task 5 . Kumber of and Task 4 Only . . . The Number of 6-Year-Olds and 9-Year-Clds Categorized Into Stages of DevelOpment on Tasks l, 2, 3, 4 and 5 Subjects Iassing Task 1 Only 50 50 51 53 "‘1 P0 Pa CO gure 1 LIST 0: FIGURES Photograph of the Non-Verbal Tact JQ5 ’ the Kagic Experiment, Front View . Thotosraph of the Non-Verbal Task, the Magic Experiment, Side View Page 26 27 Appendix II... LIST OF APPENDICES vii Introduction and Statement of Problem In 1959 leading scientists and educators, under the direction of Jerome Bruner, met to discuss how instruction in science and mathematics might be improved in our pri- mary and secondary schools (1). The results of the conference further stimulated the growth of new programs in mathematics and science. The School Mathematics Study Group, the Madison Project, the Illinois Project and the Physical Science Study Committee are but a few of the committees concerned with revising the mathematics and science curriculum (1). All of these committees have stressed teaching for understanding. The emphasis, as Bruner states, was placed on the structure of the subject matter. On this basis, Bruner formulated his bold hypothesis, "that any subject can be taught effectively in some intellectually honest form to any child at any stage of develOpment." Apparently, for Bruner, children are always ready as long as you structure the environment in some honest form. Tyler (16, p. 210) accepts this interpretation when he states that Bruner's hypothesis negates the concept of readiness. Other educators have seized on this hypothesis to justify teaching abstract mathematical concepts to 6 and 7 year olds. Suppes (15) is teaching geometric -2- concepts, sets and logic in the lower primary grades. Seven-year-old English children are taught to manipulate numbers in several bases other than the decimal systems; some 8 year olds are taught to simplify quadratic equa- tions. Tyler points out the apparent inconsistency between the Bruner hypothesis and Bruner's acceptance of riaget's position on intellectual develOpment when he states: "it difficult to understand how he [Eruneg7 is, therefore, can maintain that an subject can be taught effectively H. n some intellectually honest form to any child at any stage of deveIOpment, and at the same time say first, that the 'rreOperational' child cannot grasp the idea of 're- <1 (9 r3 {-7 H. C‘ 'Jo H ity' and second, 'because of this fundamental lack the child cannot understand certain fundamental ideas that lie at the basis of mathematics and physics'." (16, The research findings of Jean Eiaget suggest to the present investigator that you cannot teach most 6-year- olds to understand the concept of number. Piaget argues - 1 that the understanding of number is contingent Upon the ) .— Cf). Ho ld first having passed a particular stage in his cognitive deveIOpment. Chronologically speaking, most children under 8 have not passed the particular stage of develOpment necessary for understanding the concept of number. In addition, Sigel's interpretation of Piaget's results suggest that neither home nor school eXperiences are suf- -3- ficient to alter the "natural processes of adaptation which take place in the child's adjustment to his objective world." (11, p. 9) The school environment has generally been considered the source of the child's number experiences. In school the child is taught to count, add and is provided with many concrete applications of number. The absence of formal schooling would, then, tend to diminish the fre- quency and intensity of these number eXperiences. Accord- ing to Bruner, the structure of the environment plays the major role in concept acquisition. Particularly with reference to formal number eXperienees, the structure of the environment of children who have had formal schooling is vastly different from the structure of the environment of children who have been deprived of formal schooling. Formal number eXperiences, as measured by arithmetic achievement tests, correlate fairly well (r = .59) with success on Piagetian number tasks, according to Dodwell (3). This suggests a positive relationship between success on Piagetian number tasks and formal academic achievement. Consequently, Bruner might argue that formal school ex- periences would contribute more to number develogment, as measured by Piagetian tasks, than little or no formal schooling at all. If this argument is correct, we should expect children who have had formal schooling to be at a -4- "higher" develOpmental level on Piagetian number tasks than children who have been deprived of schooling. On the other hand, if the argument is incorrect, we should expect children who have had formal schooling to be at the same developmental level for number as those children who have been deprived of schooling. The extent to which the absence of school eXperiences influences number develOp- ment affords a test of Piaget's theory and, indirectly, of Bruner's bold hypothesis. This study attempts to re- solve this issue by examining the effects of lack of formal schooling on the attainment of stages of number deveIOpment. Various methods may be employed to ascertain the effects of lack of formal schooling upon the attainment of number concepts: (1) Piaget's clinical method, (2) standardized interview techniques, and (3) non- verbal techniques. Piaget's clinical method which employs non-standardized questions, has been criticized. His critics have maintained that where a child's performance was deficient, either the apprOpriate question was not asked or the child did not understand the question. However, other critics clabm that Piaget often attributes superior performance to a child by interpreting his responses in ways which go far beyond what the child meant by them (12). -5- Critics also argue that the type of question asked may influence the child's performance. In addition, language they claim, may obscure whether a child has a particular Piagetian concept. Therefore, our secondary purpose is to study the effects of employing particular types of questions and non-verbal techniques in assessing the child's performance. The tasks we have selected in- volve determining whether or not a child has attained the concept of conservation of substance. Conservation of Substance The attainment of the concept of conservation of substance in Piaget's system is a critical test of whether the child has acquired the concept of number. By the world "substance" Piaget means "amount of matter," or "amount of material." Piaget maintains that, by two years of age, a child builds a picture of the world as consist- ing of a number of objects that continue to exist even when the objects disappear; the child learns that, as a rule, objects maintain their size and shape. For Piaget, the schema of the permanent object presupposes the most primitive of all principles of conservation. Further, Piaget maintains that conservation or object constancy is a necessary condition for all reasoning. Arithmetical thought is no exception to the rule, though additional -5- conceptions of conservation must also be attained. For example, a discontinuous substance such as a set or col- lection (beads, shells) is conceivable by the child even if it remains unchanged irrespective of the changes in the relationships between the elements. A continuous quantity such as length or volume can be used in reasoning 2212 if it is a permanent whole irrespective of any pos- sible rearrangement of its parts. Piaget has discovered that up to 7-8 years of age, the average child does not appear to understand that the "amount of matter" stays the same regardless of any changes in shape or position (8). According to Lovell (6), this concept of conservation of substance (or in- variance of substance) is an important one, for the mind can deal effectively with a lump of plasticine, a glass of water, or a collection of sea shells, only if it remains constant in amount independent of the rearrangement of its individual parts. From his many experiments involving children's judgments about continuous substances (water, plasticine) and discontinuous substances (beads, shells), Piaget con- cluded that children pass through three stages in attain- ing the concept of conservation of substance; non-con- servation, transition and conservation. -7... In a typical eXperiment, two identical glasses are filled to the same height with water. Children 4-6 years will admit that the amounts of liquid in the two glasses are the same. Next, the water in one glass is left un- disturbed, but the water in the other glass is poured into three glasses. The child is then asked, in approPriate language, if the amount of water in the undisturbed glass is the same as the combined amounts of water in the other glasses. Children of 4-6 years of age deny that the amounts are the same. They notice that the levels in the three glasses are lower, and so for them, there must be less liquid; or they notice that there are three glasses and think there must be more water. By 6 or 7, some children will affirm that the amount of water is the same when it is poured into two glasses, but they will still deny that the amount of water is the same when it is poured into three glasses. However, by 7 or 8 years of age, the child stands firm in his conviction that the amounts are the same no matter in how'many glasses you pour the water. At this point the child is said to have acquired the concept of conservation. -8- Theory and Related Research Formal Schooling and the Acquisition of the Concept pf Conservation of Substance ~ Piaget maintains that the attainment of the concept of conservation of substance is necessary for number work. This concept develops sequentially through a series of discrete stages. The question arises about the role of formal academic training in accelerating or inhibiting this attainment. Although Peel (8) does not deny the role of formal training in concept attainment, he also stresses the importance of play in intellectual growth. A child may acquire the concept of conservation of substance by playing frequently with water pails, milk bottles, grain feed, an abacus, science eXperiment kits or Cuisennaire rods. The determining factors for acquiring the concept of the conservation of substance are the perceptible qualities of the objects and the amount of knowledge the child has about the objects. Sigel (11)supports this view as follows: For example, one of the concepts that has been widely described in stage terms is animism: attributing life to inanimate objects. Laurendeau and Pinard report that the child goes through a variety of steps before he shifts from an animistic point of view to an objective one. When and how he does so depends upon the kinds of objects with which he is dealing. Where rocks and tools are concerned, he loses his sense of animism earlier -9- than would be the case if he were dealing with such objects as automobiles and airplanes. Children tend to lose the concept of animism in relation to the amount of knowledge they gain about particular kinds of things." Lovell and Ogilvie's (7) research also supports the claim that the determining factors in the acquisition of the concept of conservation of substance are the perceptible qualities of the object and the amount of knowledge about the object. For example, they found that about one-third of those children who were non-conservers in a Piagetian plasticine type eXperiment were conservers in a rubber band eXperiment. Similarly, Hyde (5) found that some children who were non-conservers in the test using plasticine balls were conservers when liquid was poured from one vessel into others of different shapes. Such evidence clearly suggests that the kind of content with which the child plays influences his ac- quisition of the concept of conservation of substance. The data further suggest that a wide range of experiences in play, school, etc., might facilitate the acquisition of conservation of substance. The foregoing implies that deprivation of a particular set of eXperiences, such as school, will not necessarily affect the acquisition of the concept of conservation of substance. One might predict that an "academically deprived" child, that is, one from whom formal schooling is withheld, should acquire -10- the concept of conservation of substance at the same age for any given tasks as the "academically eXperienced" child, if the contents of the tasks are not directly and solely academic in nature. Evidence for the assertion that lack of formal schooling does not necessarily impair vauisition of pre-number concepts, such as conservation of substance, is presented by Vohwill (7) who, in an analysis of the attainment of the abstract concept of number, found that Specific related eXperiences (such as counting or numbers) had little relationship to the concept develOpment, but the concept vauisition was related more to a child's cumulative general life eXperience. Similarly, Hyde (5), in her studies of conservation of number, also found no significant association between results on tests of conservation of substance and the number of terms spent by the subjects at school. Hyde suggests that although sampling may be partly responsible for these results, social and environmental factors other than schooling may play a larger part in success on these tests of conservation of substance than Piaget's theories lead one to eXpect. -11.. Smedslund's studies (12) on conservation of substance reinforce Hyde's. They suggest that a child, "regardless of his environment," cannot be taught the concept in question unless he has already attained a particular level of cognitive maturity. For example, children who had acquired conservation of weight in the course of their normal eXperience did not give up that concept in the face of challenging eXperimental conditions. This was in contrast to those who had acquired the concept during the eXperiment. Subjects were presented with two plasticine objects. One was changed in shape and the eXperimenter surreptitiously stole a piece from it. When the child said the quantity was the same despite the change in shape, the eXperimenter proved this answer wrong by weighing the object on a scale. The children who had previously acquired the concept of conservation actually were resistant - insisting for example, that a piece of plasticine must have fallen to the floor. How- ever, the children who had acquired conservation eXperi- mentally quickly reverted to non-conservation. It is therefore hypothesized that, on a non-verbal task which confronts the child with eXperimental condi- tions that challenge his belief in conservation, 9-year- old children who have had the benefit of regular formal -12- 1 will be categorized at the same deveIOpmental schooling level as 9-year-olds who have been deprived of regular formal schooling.2 Six-year-olds from each area will also be examined with the same tasks in order to demon- strate that any differences found are attributable to academic background rather than region. Hence, it is hypothesized that 6-year-olds from both backgrounds will be categorized into the ggmg deveIOpmental level, regard- lggg of the verbal or non-verbal character of the tasks. Success on the Piagetian tasks appears to be in- fluenced by language facility. Increased language facility suggests increased ability to comprehend the exPerimenter's questions.' Children who come from intel- lectually stimulating homes and attend school appear to manifest superior language facility than children who come from intellectually impoverished homes and attend school. Consequently, one might eXpect children who come from intellectually impoverished homes and attend school to manifest superior language facility than 1Negro children who attend an elementary school in Flint, Michigan. 2Negro children from Prince Edward County, Virginia, who received no formal schooling for four years. -13- children who come from intellectually impoverished homes and do not attend school. Accordingly, it is hypothesized that academically eXperienced 9-year-old Flint children will be categorized into a higher deveIOpmental level on Piagetian number tasks than academically deprived 9-year- old Prince Edward County children. Ehrasing of the Questions and the Agguisition of the Concept of Conservation of Substance In his book, Language and Thought of the Child, Piaget considers the concepts of "egocentrism" and "syncretism" central to understanding child communication, in general, and to understanding children's reaponses to questions, in particular. According to Piaget, egocentric thought differs from socialized thought in that: 1. It is non-discursive and goes directly from premises to conclusion in a single act, without any intervening steps of deduction. 2. It makes use of personal schemes of imagery, and, 3. Of schemas of analogy, both of which are extremely active in the conduct of thought and yet extremely illusive because they are uncommunicable and arbitrary. These three features also characterize the phenomenon called "syncretism of thought." According to Piaget, syncretic thought describes a type of thinking which -14- assimilates reality into global, undifferentiated schemes; the individual contents of the assimilated reality interpenetrate and fuse with one another, any- thing being joined to or combined with anything else. Syncretic thought is a pervasive characteristic of child thought which emerges from his egocentric thought. (4. p. 273) The construct, egocentric thought, describes the child viewing all reality from only his frame of reference. Only his own point of view can really figure in other activities, since he is unaware that others see things differently. The child asshmilates reality to his own perspective, which includes his own motives and inner promptings. Thus, much of the child's talk is talk-for- self, even when in the company of others. Further, the child finds it difficult or unnecessary to communiate with others, since this frequently demands focusing on the others' perspectives. Moreover, the child assumes that since he knows the information to be communicated, everyone else does also. Therefore, there is no need to communicate with others. Consequently, egocentric thought serves to satisfy the child's basic needs in the same way that communication satisfies certain adult needs. -15- According to Piaget, in egocentric thought, argu- ments seem convincing because the premises and conclusions are connected by schema; primitive structures which tie things together in terms of the needs and motives of the child. It is through schemes that the hunch leaps from a premise to a conclusion. Little value is attached to proving or checking conclusions. The vision of the whole brings about a state of belief and a feeling of security far more rapidly than if each step in the argument were made eXplicit. In arriving at conclusions, egocentric thought mobilizes personal schemes of analogy and memories of earlier reasoning. Visual schemes also play an important role since they frequently take the place of proof in supporting the deduction that is made. Because egocentric thought is essentially unanaLyti- cal, the result is that the child ignores isolated words and deals with whole sentences, understanding them or altering them as they stand, without analyzing them in detail. Furthermore, the child emphasizes events them- selves rather than the relations of thme (order) or cause which unite them. The child's egocentrism induces him to believe that he understands everything and prevents him from understand- ing word for word the terms and prOpositions he hears. Therefore, instead of analyzing what he hears in detail, he reasons about it as whole. -16- Piaget maintains that up until 7 or 8 years, all child thought is characterized by egocentrism in general and syncretism in particular. After 7 or 8, the conse- quences of egocentrism do not disappear immediately, but occur in purely verbal thought (those thoughts not con- nected with immediate observation). Piaget chooses to call this verbal syncretism - a phenomenon which manifests itself until 11 or 12 years of age. The syncretic nature of child thought suggests that questions which are non-identical in the specific words employed, but equivalent in their general content regard- ing specific tasks will be perceived as identical. Con- sider the following task: An eXperimenter presents a child with two containers of water, one long and narrow, the other short and stout. Three possible questions, of varying complexity, all emphasizing amount are: 1. "Is the amount of water the same, more, or less?" 2. "Does one glass have more water?" 3. ”If you were thirsty, which glass would you drink?" An examination of the literature reveals that most experimenters have utilized these question types. (7, 9, 13) These three questions may be ordered as to their complexity. The first question involves a disjunctive -17.. relation; the second a comparison and the third a comparison related to a need. To the present investigator, the first question ap- pears the most difficult for the child because of the disjunctive relation. Further, children are infrequently asked such abstract questions. The third question appears the simplest to the child because it is part of his everyday eXperience. Children frequently choose between two glasses of water or soda. For example, a child may be unhappy because his daddy has the larger glass with more soda. The second question appears next in difficulty. It is neither as abstract as the first nor as concrete as the third. Because of its less abstract nature, the second question represents a midpoint in difficulty. However, all three questions emphasize amount or quantity. We may consider amount or quantity an 2223;. The questions differ in the way they ask the child to relate to the event. If syncretic thought dominates the child's mental processes, he will attend to the event,? but not to the relationships to the event. On the basis of this, one can hypothesize that children, regardless of which of the questions is asked, so long as the events 7 are the same, reapond as if the questions are identical. For our purposes, we will define a question whose events -18- are identical to another question, but which calls for attention to different relationships, a "rephrased question." The underlined sentences in the following two examples of Piaget's clinical approach to data-gathering are "rephrased questions." Blas (4; 0): 'Look, your mummy has poured out a glass of lemonade for herself (L) and she gives you this glass (L1). We want you to pour into your glass as much lemonade as your mummy has in hers. - (She poured rather quickly and exceeded the level equal to that in L that she was trying to achieve.) - Will you both have the same like that? - No - Who will have more? - Me - Show me where you.must pour so that you both have the same. - (She poured up to the same level.) - Will you and mummy have the same amount to drink like that? - Yes - Are you sure? - Yes - Now watch what 1' m doing (putting L1 next to L). I am goim to pour that one (L) into this one (L1). Will that make the same here (L1) as there (L)? - Yes - (When I did so, the child laughed); Mummy has more. - Why?‘ Mus (5; 0): 'Look (same story as for Blas). Show me with your finger how'far I mustLpour. - There (indicating the same level in L as in A). - (I filled it slightly higher). Will there be the same amount to drink? - You've put too much. There's a little more there (in L). I've a little more to drink - What could you do to see if its the same? (Putting L1 next to L) - Where will it come up1 to if we pour that one (A) into this one (L1)? - To there (pointing to the same level as in A). - (I did so.) - Mummy has more (with great surprise) - How did that happen? - Be- cause the glass L 1) is smaller - And if I pour this one (L ) back into that (A) which will have the most? - Both a little, both the same. - (I poured it back). Whose has more to drink? - Both less.' -19.. Both questions stress the event, i.e., amount, but the questions differ in their relationships to the event. The question in the second example appears less complex than the first since it focuses more on action than the first. Also, the question in the second example is a more common experience to the child that the question in the first example. The two above examples are typical illustrations of Piaget's clinical method. This method Flavell (4, p. 28), states "has more in common with diagnostic and therapeutic interviews, with projective testing, and with the kind of informal eXploration often used in pilot research throughout the behavioral sciences. The crux of it is to eXplore a diversity of child behaviors in a stimulus- response-stimulus-response sequence; in the course of this rapid sequence, the experimenter uses all the insight and ability at his command to understand what the child says or does and to adapt his own behavior in terms of this understanding." Furthermore, according to Flavell, Piaget feels that only through such a method can one get to the heart of the child's cognitive structure and describe it as it really is." . . . Once a task is presented to the child, one is committed to try and to follow the child's thought wherever it -20- seems to be going, and this precludes a standard, unvary- ing interview. Piaget freely admits the usefulness of more standardized, 'test-like' procedures for a number of psychometric purposes. However, if one's primary concern is simply to describe and explain the variety of intellectual structures which children at different levels possess rather than to construct rigorous develoP- mental scales for diagnostic purposes, Piaget believes the clinical method to‘be the method of choice." Flavell agrees with Piaget in his estimate of the advantages of the clinical method, but stresses that Piaget could have retained these advantages and secured obvious additional ones by a semistandardization pro- cedure. For example, children could be asked a set of identical stimulus questions; over and above that, how- ever, there would be relative freedom given to the experimenter in working with the child. Lovell's (7) questioning technique does combine the clinical approach with some degree of standardization. For example, a test of conservation of weight: Technique - (1) "Say, 'Here are two balls of plasticine. I want you to tell me which one is heavier. Use the scales if you like.‘ Record the child's actions and his reply. Whatever the child decides is ac- cepted provided that he has held the two balls in his hand. If he is content to judge merely by -21- looking, he is told to pick up the balls and satisfy himself as to which is the heavier. (2) How do you know that (indicates the ball chosen) is heavier? (3) One ball (R2) is rolled into a 'sausage.' Say - Now which is heavier, the sausage or the ball? Don't pick them up, try to think it out. (4) Why do you think that? (5) The 'sausage' is further rolled so that it becomes even longer and thinner. Say - Which is heavier now? (6) Why are you so sure? To this point we have followed the Piagetian pro- cedure closely so that conservers, in his sense of the word, are those who answer questions 3 and 5 correctly, and in addition, gave such answers to questions 4 and 6 as 'nothing has been added or taken away;' 'They were the same before;' 'The sausage is longer but its thinner;' 'You've only rolled one ball.‘ Further questions were then put to both conservers and non-conservers. For example, the latter gave their reasons for failing to conserve weight (7, p. 139)." On the other hand, Smedslund (l) stresses the standardized questions and minimizes the use of the clinical technique. For example: Test of Conservation of Substance: 'Two equal balls of plasticine were presented and the child was told that they contained the same amount of clay. This was emphasized and repeated so to ensure prOper attention. Then the eXperimenter changed one of the balls into another form, commenting on it by saying: 'Now I change this one into a . . . (ring, cross, etc.); after each deformation the following standard question was asked: 'Do you think the . . . contains more or the same amount as or less clay than the ball?‘ After each answer, the eXperimenter asked in a neutral but interested voice: 'Why do you think so?‘ -22- At this point, the research appears equivocal as to the superiority of either the clinical or the standard technique, or some combination of them. Peel (8) indi- cates that Piaget's findings concerning stages of develoP- ment have repeatedly been confirmed. This suggests that the questioning technique plays a minor role in ascertain- ing whether a child has attained a particular concept. The questioning technique, however, dictates the approach whether clinical or standardized. The clinical technique utilizes "rephrased" questions, whereas the standardized approach does not. Clearly, then, the question of which technique is most apprOpriate depends largely upon whether "rephrasing" of the question affects performance. A secondary purpose, then, of this investigation is to study the extent to which "rephrasing" of the question affects performance. The ACquisition_of Conservation of Substance; Verbal and Non-Verbal Tasks According to Piaget, language is molded on habits of thought. The present investigator interprets this to mean that language is formulated Eggm perceptions, i.e., perception precedes language in deveLOpment. Perceptions initially are characterized by egocentrism and hence are syncretic - that is, inaccurate observations of things, heaped upon each other. Since language comes later in -23- develOpment than perception, it would be reasonable to assume that, at a given moment during language develOp- ment, the perceptions associated with a given task might be less egocentric and, consequently, less syncretic than the language. For example, two tasks are given a child, one which involves language and one which does not. It seems plausible, assuming the tasks are measuring the same phenomenon, that the perceptions of the non-verbal task would be less syncretic, since the child's perceptions on the verbal task are further corrupted by syncretic verbal understanding. Therefore, one would eXpect 6- and 9-year-olds' reSponses to be categorized at a higher develOpmental level on non-verbal tasks than on verbal tasks. Although the literature is scanty with reapect to non-verbal tests of conservation of substance, Zimiles (l9) attests to the superiority of Wohlwill's non-verbal test procedure over the verbal testgprocedures when he states: At no time in the verbal test is a Specific request made for a numerical rather than a spatial reSponse. This is in sharp contrast with the non-verbal test procedure where S's response to the altered Spatial arrangement must be made in terms of numerical symbols rather than ambiguous language. According to the interpretation presented here, the necessity to respond in terms of number serves as a set to use numerical rather than Spatial criteria; hence, the superiority of non-verbal as Opposed to verbal test performance in both the pre- and post-sessions. -24- Smedslund (14) implies the use of the non-verbal cues, shock and surprise, as indices of conservation of mass when he states that children (non-conservers in the Piagetian Sense) were not shocked or surprised when the law of conservation was violated. Dixon (2) takes surprise, confusion and the Spontaneous verbalization of nursery-school children as indicators of familiarity with an apparently contradicted Size relationship. Dixon reports good agreement between two observers and between two presentations on the task. In view of this, Dixon (2) suggests that contradiction of eXpectations provides another approach to studying children's un- verbalized generalizations. Theoretical Considerations in Selecting Tasks As mentioned earlier, language may be a source of difference between academically deprived Prince Edward County children and academically eXperienced Flint, Michigan children. Accordingly, eXperiments involving both verbal and non-verbal communication must be utilized if we wish to investigate the develOpmental changes in children's thinking as a function of their school back- grounds. Standard Piaget eXperiments and a non-verbal technique, the Magic Experiment, will be employed to ascertain whether a child has attained the concept of conservation -25- of substance. The standard Piagetian conservation of substance eXperiments involve considerably more linguistic communication than the Magic EXperiment. Task 1: Magic EXperiment The Magic EXperiment involves first getting the child to agree that two 150 m.l. beakers are filled with an equal amount of water. Then pouring one of the beakers into a 1000 m.l. jar and "noting" the comments of the child as the water from the 150 m.l. beaker apparently fills the 1000 m.l. jar (Figures 1 and 2, p. 26, 27) the child has the concept of conservation of substance, then this apparent distortion of reality will elicit comments such as "that's funny," "crazy," a gesture of surprise or a smile of incredulity. On the other hand, if the child does not have this concept, he will not make any noticeable gestures indicative of surprise or astonish- ment. Tasks 2, 3, 4 and 5 are the standard Piagetian con- servation of substance eXperiments. Piaget (9), Lovell (6, 7), Smedslund (12) and others have employed these tasks regularly to ascertain whether a child has the concept of conservation of substance. They will be described in detail in the next section. A .m PROCEDURES Statement of Hypotheses: A. No significant difference exists between Prince Edward County, Virginia and Flint, Michigan subjects in the frequency of reSponses scored at any particular developmental stage. No significant difference exists in the frequency of responses at any particular develOpmental level between Prince Edward County, Virginia 6-year-olds and Flint, Michigan 6-year-olds on the verbal Piagetian tasks (Tasks 2, 3, 4 and 5). Flint, Michigan 9-year-olds make significantly more stage 3 responses than Prince Edward County 9-year- olds on the verbal Piagetian tasks. Phrasing of the question does Egg affect the frequency of reSponses at any particular deve10pmental level. Thus, for any task, there will be no significant dif- ferences in scoring attributable to type of question asked. The proportion of subjects passing only Task 1, the non-verbal task for conservation of continuous sub- stances, is significantly greater than the prOportion of subjects passing only Task 4 and 5, the verbal tasks for discontinuous substances. This prediction is in 28 -29- variance with Piaget's findings that the conservation of discontinuous substances always precedes continuous substances develOpmentally. POpulation and Sample In 1959 the Prince Edward County, Virginia, Board of Supervisors confronted by a court order to integrate their schools, failed to allocate funds for the operation of a public school system. The school closing presented a condition somewhat unique to modern education and pre- sented an opportunity to investigate the role that schools play in develOpment. The schools in Prince Edward County, Virginia, were reopened in the fall of 1963 under the Sponsorship of the Free Schools Association, a private school system. A period of four years had intervened in which the schools were closed.3 During the years 1959-1963, few Prince Edward County Negro children received four years of schooling. Various organizations provided money to send some Negro children to school in different states. Among the 9-year-old Prince Edward County Negro children who participated in this study, at least 50% received no formal education 3In June, 1964, a Supreme Court Decision ordered Prince Edward County to reOpen its public schools. Since Fall, 1964, Prince Edward County Negro children have re- ceived public education. -30- during this period; 25% of them received from 1 to 3 years and no data are available for the remaining 25%. In addition to their lack of formal schooling, most of these children came from low income families. A sample of 60 academically eXperienced Flint, Michigan Negro children was selected for comparison with a sample of Prince Edward County, Virginia Negro children in order to study the effects of lack of formal schooling on number develOpment. Males and females were equally represented in each sample, as were 6- and 9-year-olds. Six-year-olds and nine-year-olds were selected be- cause Piaget's writings indicate that, in general, most 6-year-olds do not yet possess the concept of conservation of substance while most 9-year-olds do possess this con- cept. Six and nine-year-olds were Operationally defined as between 6 1/2 years to.7 years and 9 l/2 years to 10 years respectively. Description of Tasks: Task 1: The Magic Experiment This exPeriment consists of allowing the child to satisfy himself that two 150 m.l. beakers contain the same quantity of liquid; then pouring the contents of one into a 1000 m.l. jar which apparently fills and noting the child's comments. -31- Scoring of Responses: Gestures Of "surprise," "puzzlement," "smile," "chee," "wow," etc., will be scored at stage 3. The absence of observable change in behavior will be scored at stage 1. The transition stage, stage 2 reSponses, are difficult to assess on a non-verbal task. Further, Piaget (9) questions the universality of a transitional stage. Consequently, all responses will be scored at stage 1, absence of the concept of conservation or stage 3, presence of the concept of conservation. Task 2: The Conservation of Continuous Quantities The child is Shown two large containers of similar dimensions filled with an equal amount of liquid. He is allowed to satisfy himself that the amounts of the liquid are the same. The liquid is poured from one container into three smaller ones, and the child is then questioned about the equality of the two quantities as a result Of this Operation. Task 3: The Conservatign of Contiguous Quantities The child is asked to tell the examiner when a graduated cylinder is filled with water to a 50 m.l. line. Then the water is poured into a 600 m.l. beaker. He is again asked to declare when the graduated cylinder is filled to 50 m.l. The water is now poured into a .100 m.l. beaker. The child is then questioned about the equality of the two quantities as a result of the Operation. -32.. Task 4: The Conservation of Discontinuous_guantities and fits Relation to One—E3*One Corre5pondence A child is told to put gum balls into a container one by one; at the same time the eXperimenter is putting gum balls one by one into another container. The contents of one container are then poured into a long, narrow tube. The child then is asked whether the total quantities are the same. Task 5: The Conservation of Discontinuousguantities and its Relation to One to One Correspondence A child is told to put gum balls into a container one by one; at the same time the eXperimenter is putting gum balls one by one into another container. The contents of one container are then poured into three small con- tainers. The child then is asked whether the total quantities are the same. According to Flavell (4), Piaget has maintained that conservation on a continuous quantity task is more dif- ficult (i.e., exhibits higher mean age of acquisition) than on a discontinuous quantity task. If, however, Task 4 and Task 5, verbal discontinuous tasks, have a higher mean age of acquisition than Task 1, a continuous non-verbal task, then Task 1 has a lower mean age of acquisition than all continuous verbal tasks. -33.. §gg£ing of the Responses: Tg§k§_g.3. 4 and 5 The responses such as "the amounts are the same," "no difference," etc., will be scored at Stage 3. Re- Sponses such as "no, the amounts are not the same,but if you pour the liquid back, they are the same," or "the amounts are the same when the liquid is poured into two glasses, but not the same when the liquid is poured into three glasses," will be scored at Stage 2. Other re- aponses such as "no, one glass has more," or "there is more in this glass," etc., will be scored at Stage 1. Any irrelevant responses such as, "Daddy says so," etc., will be scored at Stage 1. Procedure: Each child was presented with Tasks l-5. The sequence in which the eXperiments were administered was counter- balanced to control for any order effects. Five sequences, labelled a-e in Table l, were utilized. In order to study the effects of different types of questions on the responses of subjects, three types of questions (A, B and C) within each of the two major samples, were systematically employed: Type A question on Tasks 2 and 3: "Is the amount of water the same, more or less? Why do you think that?" - 34.. Type A question on Tasks 4 and 5: "Is the amount or number of gum balls the same, more or less? Why do you think that?" Type 8 question on Tasks 2 and 3: "Does one glass have more water? Why do you think that?" Type B question on Tasks 4 and 5: "Does one glass have more gum balls? Why do you think that?" Type C question on Tasks 2 and 3: "If you were thirsty, which glass would you drink? Why do you think that?" Type C question on Tasks 4 and 5: "If you could have the gum balls to keep, which glass would you want?" On Task 1, however, the type of question was irrelevant since it is a non-verbal task. For any particular subject, a given type of question (A, B or C) was consistently employed across all tasks. Hence, a subject asked a Type B question on Task 2 and 3 was also asked Type B question on Tasks 4 and 5. An equal number of subjects, within each of the major samples, balanced for age and sex, was assigned to each question tYpe. -35- Design: Table l is the 2 x 2 x 2 x 3 x 5 design used in the study. Within the design, the variables of age, sex, type of question, and sequence of tasks presented were balanced. he order of task presentation is represented by the letters a-e. -36.. mH ooHenomH oOHommmHoOHmn Mwm_.He0H mm «H u m o s v «H u m u q u «H c o o s U «H o a o q mH o w o m o mH o m o m 0 MH 0 m u m o mH o w o m NH 9 N n N 9 NH 9 n n N 9 NH n w a N o NH n m n N HH m o m H s HH w o m H a HH m m m H m HH m o m H m < o m < 0 m < o m < r Mk 3 oOHomomH oOHom mmHmoHom omHooH em qH no use: Hum Hus vdH Hum we HuqH cm as MH 0 m u m u mH o m u m nva o m o m o mH o w o m NH 3 N n N n NH 9 N n N nHNH n m n N 9 NH n n n N HH m o m H m HH m o m H stH m o m H m HH m o m H m < o m < o m < o m 4 mHmEom onz onfiom mHmz HGHHm hasnoo cumSum mocme oocweuomuom co omwswcmH was GOHuoawumcH .wcHHoosum no mucoumm one AUSum on teen stwmQ m x m x N x N x N H MHm