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COGNITIVE PROFILE — A COGNITIVE PROFILE at 6;0
The Intimate Study began with a series of quasi-standard experiments. These had two general purposes: first, to provide means for “calibrating” information about Miriam’s knowledge and learning with more general studies in the literature; second, a subset of these experiments were intended to provide a baseline against which I could explore the extent to which her computer experience might alter Miriam’s inclination to think in a more formal fashion. These experiments were audio-taped and videotaped. The protocols have been analyzed in detail, but only summary descriptions are presented here. The standard experiments are presented first, followed by those focused on formal thought, and lastly by others of a more idiographic character.

One to One Correspondence Age: 6;0;10
Once the subject makes a judgment that two sets have the same number of beads, the experimenter determines whether or not the subject changes that judgment when the beads in one set are moved closer together or further apart (References: Jean Piaget, THE CHILD’S CONCEPT OF NUMBER, Chapter 3; J. Flavell, THE DEVELOPMENTAL PSYCHOLOGY OF JEAN PIAGET, p. 313.)
Miriam did not change her judgment as the configuration was changed. She exhibited operational correspondence with lasting equivalence despite rearrangement of members of the sets. In addition to justification through the standard argument “you didn’t take anything away,” she invoked the equivalence of the residuums of the two sets as supporting evidence.

Conservation of Continuous Quantity Age: 6;0;10
The experimenter gets the child to concur that two quantities of liquid are the same. Pouring those same volumes of liquid into containers of different shape and into multiple containers, he explores whether or not the child knows that the quantity of substance remains unchanged. (References: Jean Piaget, THE CHILD’S CONCEPT OF NUMBER, Chapter 1; J. Flavell, The DEVELOPMENTAL PSYCHOLOGY OF JEAN PIAGET.)
Miriam’s judgments show her a conserver of continuous quantity. The justifications she offers exhibit arguments of compensation, history, and reversability.

Conservation of Substance: Clay Age: 6;0;12
After gaining the subject’s concurrence that two balls of clay weigh the same (using a balance), the experimenter changes their shape and inquires whether or not they still weigh the same after the deformations (References: J. Flavell, THE DEVELOPMENTAL PSYCHOLOGY OF JEAN PIAGET, p.299.).
Miriam expects weight to be conserved despite transformations of a material’s shape and its division into pieces. Her conviction that weight will be conserved is not firm (she does not “know” that it will be conserved but will so venture a “guess”).

Conservation of Displacement Volume Age: 6:0:12
The experiment tests whether or not the child knows that the volume of a liquid displaced by a solid does not vary when the shape of that same solid is changed. This conservation is typically a late achievement of the concrete period (References: J. Flavell, THE DEVELOPMENTAL PSYCHOLOGY OF JEAN PIAGET, p. 299.).
Miriam did not expect the displacement volume of an object to be conserved when its shape was changed by deformation or breaking into fragments. She did expect immersion of an object in water to raise the water level in the container, qualitatively at least, in proportion to its size.

Notions of Movement and Velocity Age: 6;0;12
By asking the subject to judge a race between two small dolls, the experimenter determines the extent to which the child distinguishes between velocity and the length of paths covered in equal times (References: J. Flavell, THE DEVELOPMENTAL PSYCHOLOGY OF JEAN PIAGET, p.320.).
At six, Miriam conceives of movement at different velocities in a framework of homogeneous time. She distinguishes between duration and extension in space. It is probable that this distinction recently became operational for her; it is possible the insight occurred during the experiment itself.

Combinations of Bead Families Age: 6;0;14
The experimenter probes the subject’s spontaneous use of systematic procedures in constructing the combinations of small numbers of objects taken two and three at a time. Systematicity is characteristic of children at the threshhold of formal operational thought (eleven or twelve years) (Reference: Piaget and Inhelder, THE ORIGIN OF THE IDEA OF CHANCE IN CHILDREN, Chapter 7.).
Miriam’s combinatorial skill, as seen in this experiment, was clearly pre-operational. She discovered neither all the two-bead nor all the three-bead combinations. Whatever small amount of systematicity may be inferred from the sequence of bead family formation may equally plausibly be explained as an artifact of very simple, local transformations. A close analysis of the protocol detail permits the argument that she failed to distinguish between black and dark brown beads. For this reason, the conclusions of the experiment on combinations of shape families is more dependable.

Combinations of Shape Families Age: 6;0;18
The experimenter probes the subject’s spontaneous use of systematic procedures in constructing the combinations of small numbers of objects taken two and three at a time. Systematicity is characteristic of children at the threshhold of formal operational thought (eleven or twelve years) (Reference: Piaget and Inhelder, THE ORIGIN OF THE IDEA OF CHANCE IN CHILDREN, Chapter 7. The experiment conducted was a superficial modification of Piaget’s task, with a variety of shapes substituted for colored beads.).
Miriam’s assembly of shape combinations shows characteristics of systematicity expected in the Piaget-Inhelder stage II. Restriction of this systematicity to the generation of families and the failure to apply it to the exclusion of duplicate family combinations argue that Miriam’s apparent systematicity may be an artifact of a simple pair generation procedure unrelated to any global understanding of the task (More detail on her performance can be found Chapter 3, “The Equilibration of Cognitive Structures.”).

Multiple Seriation Age: 6;0;21
The experimenter explores first whether or not a child uses seriation in more than a single dimension to organize collections of objects and second, whether or not the child can use an array structure to locate a specific object defined by two characteristics (Reference: Piaget and Inhelder, THE EARLY GROWTH OF LOGIC IN THE CHILD, Chapter 12.).
Miriam did not spontaneously seriate a collection of 32 leaves by both size and color. When asked to put her initial four color-based collections of leaves in better order, she ranged the leaves from small to large within each collection. She was able to make use of the doubly ordered array to locate specifically described leaves directly.

Implicit Multiplication with the Balance Age: 6;0;18
The experimenter probes the subject’s problem solving with a balance to determine the extent to which the child appreciates the implicit multiplication of length times weight along the balance arms (References: Inhelder and Piaget, THE GROWTH OF LOGICAL THINKING FROM CHILDHOOD TO ADOLESCENCE, Chapter 11.).
Miriam’s comprehension of the relation between weight and distance, interpretable as a set of simple procedures, was rudimentary. On this task, her performance is characteristic of stage IIA (concrete operations on weight and distance with intuitive regulations) as described by Inhelder and Piaget.

Abstractness of the Object Concept Age: 6;1;10
The experimenter determines the abstractness of the child’s object concept. The subject uses weights to cause bending of metal rods clamped in a stable apparatus. There are four dimensions of variation in the flexibility of the metal rods used in this experiment (material, length, thickness, and cross sectional shape) (Reference: Inhelder and Piaget, THE GROWTH OF LOGICAL THINKING FROM CHILDHOOD TO ADOLESCENCE, Chapter 3.). The experiment attempts to discover whether the subject analyzes the behavior of individual rods in terms of these four dimensions of variation or not. Only with such a feature analysis can one develop the systematic procedures in this domain characteristic of formal thinking (For an example of how computer experience might affect such mental abilities, see the article “Extending a Powerful Idea” (Lawler, 1982).).
Miriam’s performance on this task placed her at the concrete operation level (substage IIA) as described by Inhelder and Piaget. Her understanding that added weights must be the same when comparing two rods and her predictions based on “skinniness” put her clearly in substage IIA. She showed none of the factor multiplication characteristic of substage IIB.
The most striking characteristic of her predictions was her willingness to subject them entirely to empirical test. For example, though she believed that skinnier rods bent more, she was willing to consider it possible that a fatter rod might bend more than a skinnier one. Her conviction of the dependability of her judgments was weak — with one idiosyncratic exception: she was convinced that color was not implicated in flexibility. If her primary conception of color was as a superficial property, not an intrinsic one of some substances, her adamant refusal to assign it an effective role would be comprehensible. Miriam did not have an abstract object concept. Commitment to an abstract object concept requires a conviction that characteristic features of objects interact in a lawful way. With such a view, existing objects are instances of possibilities resulting from the specification of their interacting features.
For Miriam, those bending rods were each unique objects which exhibited certain properties able to provide guidance for hypotheses about their behavior. But guidance is not the law-like regularity which the abstract object concept leads one to expect.

Non-standard Interpretations:

Class Inclusion Relations Age: 6;0;11
The experimenter explores how the subject deals with problems of class inclusion (References: Piaget and Inhelder, THE EARLY GROWTH OF LOGIC IN THE CHILD, pp.100-110; J. Flavell, THE DEVELOPMENTAL PSYCHOLOGY OF JEAN PIAGET, pp. 303-309.). Younger children may judge, for example, that a collection of five horses and three cows contains more horses than animals. More mature children will not make this non-standard judgment.
Miriam was capable of handling the class inclusion relation. When the general term referring to the including class was modified by a universal quantifier (for example, “all together”), Miriam concluded the intent of the question relates to inclusion. Otherwise, she apparently assumed the intended use of the general term was for disjunctive reference to a secondary class too variegated for specification.
The phenomenon Genevan psychologists uncovered with this experiment is robust, but precisely what its significance may be is not clear (More recently, this task has been dropped from the repertoire of Genevan experiments and other tasks substituted for it. See LEARNING AND THE DEVELOPMENT OF COGNITION by Inhelder, Sinclair, and Bovet.). The experiment was designed to probe a subject’s comprehension of class inclusion relations. But the material of Miriam’s particular experiment may be more richly viewed in terms of another issue, how a child uses specific and generic labels.
Miriam’s ability to grasp inclusion relations does not imply that all her applications of general terms, or even her preferred applications, are for specifying inclusion relations. For example, she showed in this experiment an unexpected and intense disinclination to use a generic name when she knew a specific name which could be applied. Her specificity bias was so extreme that Miriam considered it a mistake to use a term such as flower when one knows that a thing is “really” a tulip. Although admitting that tulips should be included if one planted a flower garden, she denied that tulips are flowers. Although adults may use general terms primarily for specifying hierarchical inclusions, this does not imply that such is their primary use by children. A more important use of general terms, for children, may be as default labels for classes of objects when the specific name is unknown.

The Volume of Solid Objects Age: 6;0;12
The experimenter probes the subject’s ability in logical multiplication by asking the child to construct a building of volume equal to an exemplar but on a different base; thus, height must compensate for differences between the product of the two other dimensions (Reference: J. Flavell, THE DEVELOPMENTAL PSYCHOLOGY OF JEAN PIAGET, pp. 341-342.).
Miriam’s performance on this experiment was atypical. She was instructed not to count the component blocks of which larger shapes were made, but did so anyway. Her heavy dependence on counting and its adequate use prevented engaging the issue of the logical multiplication of spatial dimensions (See question 2 of the set for age 10 years in the Binet test. Miriam’s performance on this Piagetian task sheds light on her unusual performance for the Binet test item.).

Separating Translation and Rotation in a Backspinning Ball Age: 6;0;18
The experimenter explores the subject’s ability to separate conceptually two contrary motions. A backspinning ping pong ball on a smooth table skids forward until the spin countervails and the ball returns to the person who propelled it (Reference: Piaget, THE GRASP OF CONSCIOUSNESS, Chapter 3.).
Although the phenomenon was completely new to her, Miriam easily succeeded in backspinning a ping-pong ball. She found the phenomenon very engaging and showed and described it to other children in the laboratory. Her explanations of the phenomenon are those Piaget classifies as stage IB. Although she described the motions of the ball in detail, Miriam was not able to provide an explanation of why the ball first went away and later returned.
When challenged with a proffered “magical” explanation, Miriam rejected it, then proposed that there was something inside which got “wound up.” She then explained further; this interpretation came from observing an elastic-driven airplane belonging to her brother which would fly in one direction and occasionally circle back.
Miriam was clearly far from conceiving of the phenomenon as an adult would. She distinguished between the ball’s rotational and translational motions and remarked early that the ball skipped on the outbound path and rolled on returning. Convinced that the ball’s action derived from what one did to it, and having observed these specific critical features, how could she possibly fail to understand backspinning ? Miriam did not attempt to explain backspinning by analyzing the action’s features of which she was aware. Instead, she explained the phenomenon through analogy to another situation with which she was familiar. She even speculated that an unseen mechanism, analogous to the elastic band in the airplane, caused a comparable result in this case. Her theory was pre-analytical, in character more like Peirce’s abduction than any combination of inductive and deductive processes. IF MIRIAM WAS A LITTLE SCIENTIST INVESTIGATING THE INTERESTING PHENOMENA OF HER WORLD, SHE WAS LESS LIKE GALILEO — OR ARISTOTLE — THAN LIKE EMPEDOCLES, WHO EXPLAINED THE WORLD AS COMPOUNDED OUT OF DIVERSE, FAMILIAR ELEMENTS.

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